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## 120 Math Word Problems To Challenge Students Grades 1 to 8

Written by Marcus Guido

## Hey teachers! 👋

Use Prodigy to spark a love for math in your students – including when solving word problems!

- Teaching Tools
- Subtraction
- Multiplication
- Mixed operations
- Ordering and number sense
- Comparing and sequencing
- Physical measurement
- Ratios and percentages
- Probability and data relationships

You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.

A jolt of creativity would help. But it doesn’t come.

Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.

This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.

There are 120 examples in total.

The list of examples is supplemented by tips to create engaging and challenging math word problems.

## 120 Math word problems, categorized by skill

Addition word problems.

Best for: 1st grade, 2nd grade

1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?

2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?

3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?

5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?

6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?

8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?

## Subtraction word problems

Best for: 1st grade, second grade

9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?

10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?

11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

## Practice math word problems with Prodigy Math

Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade!

12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?

13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?

14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?

15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?

16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?

## Multiplication word problems

Best for: 2nd grade, 3rd grade

17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?

18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?

19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?

20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?

21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?

## Division word problems

Best for: 3rd grade, 4th grade, 5th grade

22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?

23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?

24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?

25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?

26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?

## Mixed operations word problems

27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?

28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?

29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?

30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?

## Ordering and number sense word problems

31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?

32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?

33. Composing Numbers: What number is 6 tens and 10 ones?

34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?

35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?

## Fractions word problems

Best for: 3rd grade, 4th grade, 5th grade, 6th grade

36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?

37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?

38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?

39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?

40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?

41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?

42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?

43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?

44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.

45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?

46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.

## Decimals word problems

Best for: 4th grade, 5th grade

47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?

48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?

49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?

50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?

51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?

52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?

## Comparing and sequencing word problems

Best for: Kindergarten, 1st grade, 2nd grade

53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?

54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?

55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?

56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?

57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?

58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?

59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?

## Time word problems

66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?

69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?

70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?

71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?

## Money word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade

60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?

61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?

62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?

63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?

64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?

65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?

67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.

68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?

## Physical measurement word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade

72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?

73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?

74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?

75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?

76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?

77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?

78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?

79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?

80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?

81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?

## Ratios and percentages word problems

Best for: 4th grade, 5th grade, 6th grade

82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?

83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?

84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?

85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?

86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?

87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?

88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?

## Probability and data relationships word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade

89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?

90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?

91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.

92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?

93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?

94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?

95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .

## Geometry word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade

96. Introducing Perimeter: The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?

97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?

98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?

99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?

100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?

101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?

102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?

103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?

104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?

105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?

106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?

107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?

108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?

109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?

110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?

111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?

112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?

113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?

114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?

## Variables word problems

Best for: 6th grade, 7th grade, 8th grade

115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?

116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.

117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.

118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.

119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?

## How to easily make your own math word problems & word problems worksheets

Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:

- Link to Student Interests: By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
- Make Questions Topical: Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
- Include Student Names: Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
- Be Explicit: Repeating keywords distills the question, helping students focus on the core problem.
- Test Reading Comprehension: Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
- Focus on Similar Interests: Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
- Feature Red Herrings: Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.

A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.

## Final thoughts about math word problems

You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.

Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.

The result?

A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.

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- Derivatives: chain rule and other advanced topics
- Applications of derivatives
- Analyzing functions
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- Applications of integrals
- Differentiation: definition and basic derivative rules
- Differentiation: composite, implicit, and inverse functions
- Contextual applications of differentiation
- Applying derivatives to analyze functions
- Integration and accumulation of change
- Applications of integration
- AP Calculus AB solved free response questions from past exams
- AP®︎ Calculus AB Standards mappings
- Infinite sequences and series
- AP Calculus BC solved exams
- AP®︎ Calculus BC Standards mappings
- Integrals review
- Integration techniques
- Thinking about multivariable functions
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- Applications of multivariable derivatives
- Integrating multivariable functions
- Green’s, Stokes’, and the divergence theorems
- First order differential equations
- Second order linear equations
- Laplace transform
- Vectors and spaces
- Matrix transformations
- Alternate coordinate systems (bases)

## Frequently Asked Questions about Khan Academy and Math Worksheets

Why is khan academy even better than traditional math worksheets.

Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

## What do Khan Academy’s interactive math worksheets look like?

Here’s an example:

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Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.

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## Want to get even more out of Khan Academy?

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## Simple Algebra Problems – Easy Exercises with Solutions for Beginners

JUMP TO TOPIC

## Understanding Algebraic Expressions

Breaking down algebra problems, solving algebraic equations, tackling algebra word problems, types of algebraic equations, algebra for different grades.

For instance, solving the equation (3x = 7) for (x) helps us understand how to isolate the variable to find its value.

I always find it fascinating how algebra serves as the foundation for more advanced topics in mathematics and science. Starting with basic problems such as ( $(x-1)^2 = [4\sqrt{(x-4)}]^2$ ) allows us to grasp key concepts and build the skills necessary for tackling more complex challenges.

So whether you’re refreshing your algebra skills or just beginning to explore this mathematical language, let’s dive into some examples and solutions to demystify the subject. Trust me, with a bit of practice, you’ll see algebra not just as a series of problems, but as a powerful tool that helps us solve everyday puzzles.

## Simple Algebra Problems and Strategies

When I approach simple algebra problems, one of the first things I do is identify the variable.

The variable is like a placeholder for a number that I’m trying to find—a mystery I’m keen to solve. Typically represented by letters like ( x ) or ( y ), variables allow me to translate real-world situations into algebraic expressions and equations.

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like ( x ) or ( y )), and operators (like add, subtract, multiply, and divide). For example, ( 4x + 7 ) is an algebraic expression where ( x ) is the variable and the numbers ( 4 ) and ( 7 ) are terms. It’s important to manipulate these properly to maintain the equation’s balance.

Solving algebra problems often starts with simplifying expressions. Here’s a simple method to follow:

- Combine like terms : Terms that have the same variable can be combined. For instance, ( 3x + 4x = 7x ).
- Isolate the variable : Move the variable to one side of the equation. If the equation is ( 2x + 5 = 13 ), my job is to get ( x ) by itself by subtracting ( 5 ) from both sides, giving me ( 2x = 8 ).

With algebraic equations, the goal is to solve for the variable by performing the same operation on both sides. Here’s a table with an example:

Algebra word problems require translating sentences into equations. If a word problem says “I have six less than twice the number of apples than Bob,” and Bob has ( b ) apples, then I’d write the expression as ( 2b – 6 ).

Understanding these strategies helps me tackle basic algebra problems efficiently. Remember, practice makes perfect, and each problem is an opportunity to improve.

In algebra, we encounter a variety of equation types and each serves a unique role in problem-solving. Here, I’ll brief you about some typical forms.

Linear Equations : These are the simplest form, where the highest power of the variable is one. They take the general form ( ax + b = 0 ), where ( a ) and ( b ) are constants, and ( x ) is the variable. For example, ( 2x + 3 = 0 ) is a linear equation.

Polynomial Equations : Unlike for linear equations, polynomial equations can have variables raised to higher powers. The general form of a polynomial equation is ( $a_nx^n + a_{n-1}x^{n-1} + … + a_2x^2 + a_1x + a_0 = 0$ ). In this equation, ( n ) is the highest power, and ( $a_n$ ), ( $a_{n-1} $), …, ( $a_0$ ) represent the coefficients which can be any real number.

- Binomial Equations : They are a specific type of polynomial where there are exactly two terms. Like ($ x^2 – 4 $), which is also the difference of squares, a common format encountered in factoring.

To understand how equations can be solved by factoring, consider the quadratic equation ( $x^2$ – 5x + 6 = 0 ). I can factor this into ( (x-2)(x-3) = 0 ), which allows me to find the roots of the equation.

Here’s how some equations look when classified by degree:

Remember, identification and proper handling of these equations are essential in algebra as they form the basis for complex problem-solving.

In my experience with algebra, I’ve found that the journey begins as early as the 6th grade, where students get their first taste of this fascinating subject with the introduction of variables representing an unknown quantity.

I’ve created worksheets and activities aimed specifically at making this early transition engaging and educational.

6th Grade :

Moving forward, the complexity of algebraic problems increases:

7th and 8th Grades :

- Mastery of negative numbers: students practice operations like ( -3 – 4 ) or ( -5 $\times$ 2 ).
- Exploring the rules of basic arithmetic operations with negative numbers.
- Worksheets often contain numeric and literal expressions that help solidify their concepts.

Advanced topics like linear algebra are typically reserved for higher education. However, the solid foundation set in these early grades is crucial. I’ve developed materials to encourage students to understand and enjoy algebra’s logic and structure.

Remember, algebra is a tool that helps us quantify and solve problems, both numerical and abstract. My goal is to make learning these concepts, from numbers to numeric operations, as accessible as possible, while always maintaining a friendly approach to education.

I’ve walked through various simple algebra problems to help establish a foundational understanding of algebraic concepts. Through practice, you’ll find that these problems become more intuitive, allowing you to tackle more complex equations with confidence.

Remember, the key steps in solving any algebra problem include:

- Identifying variables and what they represent.
- Setting up the equation that reflects the problem statement.
- Applying algebraic rules such as the distributive property ($a(b + c) = ab + ac$), combining like terms, and inverse operations.
- Checking your solutions by substituting them back into the original equations to ensure they work.

As you continue to engage with algebra, consistently revisiting these steps will deepen your understanding and increase your proficiency. Don’t get discouraged by mistakes; they’re an important part of the learning process.

I hope that the straightforward problems I’ve presented have made algebra feel more manageable and a little less daunting. Happy solving!

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## What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

- The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
- The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
- The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
- The calculus section will carry out differentiation as well as definite and indefinite integration.
- The matrices section contains commands for the arithmetic manipulation of matrices.
- The graphs section contains commands for plotting equations and inequalities.
- The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

## Math Topics

More solvers.

- Add Fractions
- Simplify Fractions

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## Basic Algebra Worksheets

Welcome to the Math Salamanders' Basic Algebra Worksheets. Here you will find a range of algebra worksheets to help you learn about basic algebra, including generating and calculating algebraic expressions and solving simple problems.

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## Basic Algebra Support

Generate the Expression Worksheets

## Calculate the Expression Worksheets

- Solve the Equations Worksheets
- More recommended resources
- Basic Algebra Online Quiz

Want to gain a basic understanding of algebra?

Looking for some simple algebra worksheets?

Do you need a bank of useful algebra resources?

Look no further! The pages you need are below!

Here is our selection of basic algebra sheets to try.

We have split the worksheets up into 3 different sections:

- Generate the algebra - and write your own algebraic expressions;
- Calculate the algebra - work out the value of different expressions;
- Solve the algebra - find the value of the term in the equation.

By splitting the algebra up into sections, you only need to concentrate on one aspect at a time!

Each question sheet comes with its own separate answer sheet.

Want to test yourself to see how well you have understood this skill?.

- Try our NEW quick quiz at the bottom of this page.

What is an algebraic expression?

An expression is a mathematical statement where variables and operations are combined.

- 2a + 5 is an expression involving the variable a
- 5(y 2 - 6) is another expression

What is an algebraic equation?

An equation is where an algebraic expression is equal to something, which might be a number, or another algebraic expression.

- 2a + 5 = 7 is an equation
- 5(y 2 - 6) = 3y + 8 is another equation

How to Generate an Expression

When we are generating an expression, we are taking a rule and turning it into algebra.

- Subtract 6 from n could be written as n - 6.
- Multiply d by 4 could be written as d x 4 or 4d.
- Add 5 to p and then double the result is written as (p + 5) x 2 or 2(p + 5)

How to Calculate an Expression

When we are calculating the value of an expression, we work out the value of the expression when we give a value to the variable.

- p + 5 has a value of 11 when p = 6 because 6 + 5 = 11
- 4(n - 2) has a value of 32 when n = 10 because 4 x (10 - 2) = 4 x 8 = 32
- 4(n - 2) has a value of -8 when n = 0 because 4 x (0 - 2) = 4 x (-2) = -8

How to Solve a Simple Equation

When we are solving an equation, we are finding out the value(s) of the variable in the equation.

- If p + 5 = 9 then p = 4 because 4 + 5 = 9
- then (n - 2) = 28 ÷ 4 = 7
- if (n - 2) = 7 then n = 7 + 2 = 9
- Answer: n = 9
- means that 3f = 12
- so f = 12 ÷ 3 = 4
- Answer: f = 4

## Basic Algebra Worksheets for kids

- Generate the Expression 1
- PDF version
- Generate the Expression 2
- Generate the Expression 3

## Generate the Expression Word Problems

- Algebra Word Problems 1
- Algebra Word Problems 2
- Algebra Word Problems 3
- Algebra Word Problems 3 UK Version

## Algebra Word Problems Walkthrough Video

This short video walkthrough shows the problems from our Algebra Word Problems Worksheet 2 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

- Calculate the Expression 1
- Calculate the Expression 2
- Calculate the Expression 3

## Solve the Equation Worksheets

- Solve the Equation 1
- Solve the Equation 2
- Solve the Equation 3

## More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

## Free Algebra Problem Solver

The Mathway Calculator is a great way to solve algebra problems that you can type into a calculator.

Try using this online calculator tool to solve one of your problems and watch it work!

There are a range of calculators to choose from to meet your needs.

The Mathway problem solver will answer your problem instantly and also give you a link to view each of the steps needed.

If you choose to 'View the steps' you will be directed to the Mathway website where you will be able to see in more detail each of the steps needed to solve the problem. Please note that Mathway may charge you a small fee for this!

- 6th Grade Distributive Property Worksheets

The sheets on this page have been designed to factorize and expand a range of simple expressions using the distributive property..

- Expressions and Equations 6th Grade

The sheets on this page have been specially designed for 6th graders and are a great introduction to expressions and equations.

## Factorising Quadratic Equations

Are you stuck on a quadratic equation and don't know what to do?

Are you looking for some worksheets on factorising quadratic equations to print out?

Take a look at our support pages on quadratic equations where you will hopefully find what you are looking for.

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If you are looking for a fun printable algebra game to play then try out our algebra game page.

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The only equipment you need is a scientific calculator, some dice, and a few counters!

## PEMDAS Worksheets

The sheets in this section involve using parentheses and exponents in simple calculations.

There are also lots of worksheets designed to practice and learn about PEMDAS.

Using these worksheets will help your child to:

- know and understand how parentheses works;
- understand how exponents work in simple calculations.
- understand and use PEMDAS to solve a range of problems.
- PEMDAS Problems Worksheets 5th Grade
- 6th Grade Order of Operations

## Interactive Equality Explorer

This interactive equality explorer has been produced by PhET Interactive Simulations at the University of Colorado.

It is a useful tool for exploring different ideas including negative numbers and algebra equations and equality.

Probably the most useful part of the app is to use the 'Solve It' section once you are confident how it works.

You can then select your level of difficulty and start solving some algebraic equations by getting your variables onto one side of the equation and the numerical values on the other, and then multiplying or dividing the equation until you find the value of the required variable.

- Interactive Equality Explorer by PhET

## Basic Algebra Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge and skill at generating and calculating expressions, as well as solving equations.

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## Solving Word Questions

With LOTS of examples!

In Algebra we often have word questions like:

## Example: Sam and Alex play tennis.

On the weekend Sam played 4 more games than Alex did, and together they played 12 games.

How many games did Alex play?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

## Turning English into Algebra

To turn the English into Algebra it helps to:

- Read the whole thing first
- Do a sketch if possible
- Assign letters for the values
- Find or work out formulas

You should also write down what is actually being asked for , so you know where you are going and when you have arrived!

Also look for key words:

## Thinking Clearly

Some wording can be tricky, making it hard to think "the right way around", such as:

## Example: Sam has 2 dollars less than Alex. How do we write this as an equation?

- Let S = dollars Sam has
- Let A = dollars Alex has

Now ... is that: S − 2 = A

or should it be: S = A − 2

or should it be: S = 2 − A

The correct answer is S = A − 2

( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")

## Example: on our street there are twice as many dogs as cats. How do we write this as an equation?

- Let D = number of dogs
- Let C = number of cats

Now ... is that: 2D = C

or should it be: D = 2C

Think carefully now!

The correct answer is D = 2C

( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")

Let's start with a really simple example so we see how it's done:

## Example: A rectangular garden is 12m by 5m, what is its area ?

Turn the English into Algebra:

- Use w for width of rectangle: w = 12m
- Use h for height of rectangle: h = 5m

Formula for Area of a Rectangle : A = w × h

We are being asked for the Area.

A = w × h = 12 × 5 = 60 m 2

The area is 60 square meters .

Now let's try the example from the top of the page:

## Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?

- Use S for how many games Sam played
- Use A for how many games Alex played

We know that Sam played 4 more games than Alex, so: S = A + 4

And we know that together they played 12 games: S + A = 12

We are being asked for how many games Alex played: A

Which means that Alex played 4 games of tennis.

Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!

A slightly harder example:

## Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?

- Use a for Alex's work rate
- Use s for Sam's work rate

12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

## Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?

- The number of "5 hour" days: d
- The number of "3 hour" days: e

We know there are seven days in the week, so: d + e = 7

And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27

We are being asked for how many days she trains for 5 hours: d

The number of "5 hour" days is 3

Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.

3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours

Some examples from Geometry:

## Example: A circle has an area of 12 mm 2 , what is its radius?

- Use A for Area: A = 12 mm 2
- Use r for radius

And the formula for Area is: A = π r 2

We are being asked for the radius.

We need to rearrange the formula to find the area

## Example: A cube has a volume of 125 mm 3 , what is its surface area?

Make a quick sketch:

- Use V for Volume
- Use A for Area
- Use s for side length of cube
- Volume of a cube: V = s 3
- Surface area of a cube: A = 6s 2

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

An example about Money:

## Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?

- Joel's normal rate of pay: $N per hour
- Joel works for 40 hours at $N per hour = $40N
- When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
- Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
- And together he earned $660, so:

$40N + $(12 × 1¼N) = $660

We are being asked for Joel's normal rate of pay $N.

So Joel’s normal rate of pay is $12 per hour

Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660

More about Money, with these two examples involving Compound Interest

## Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?

This is the compound interest formula:

So we will use these letters:

- Present Value PV = $2,000
- Interest Rate (as a decimal): r = 0.11
- Number of Periods: n = 3
- Future Value (the value we want): FV

We are being asked for the Future Value: FV

## Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?

The compound interest formula:

- Present Value PV = $1,000
- Interest Rate (the value we want): r
- Number of Periods: n = 9
- Future Value: FV = $1,551.33

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33

And an example of a Ratio question:

## Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?

- Number of boys now: b
- Number of girls now: g

The current ratio is 4 : 3

Which can be rearranged to 3b = 4g

At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1

b + 4 g − 2 = 2 1

Which can be rearranged to b + 4 = 2(g − 2)

We are being asked for how many students there are altogether now: b + g

There are 12 girls !

And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys

So there are now 12 girls and 16 boys in the class, making 28 students altogether .

There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1

And now for some Quadratic Equations :

## Example: The product of two consecutive even integers is 168. What are the integers?

Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.

We will call the smaller integer n , and so the larger integer must be n+2

And we are told the product (what we get after multiplying) is 168, so we know:

n(n + 2) = 168

We are being asked for the integers

That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.

Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES

Check 12: 12(12 + 2) = 12×14 = 168 YES

So there are two solutions: −14 and −12 is one, 12 and 14 is the other.

Note: we could have also tried "guess and check":

- We could try, say, n=10: 10(12) = 120 NO (too small)
- Next we could try n=12: 12(14) = 168 YES

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).

## Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?

Let's first make a sketch so we get things right!:

- the length of the room: L
- the width of the room: W
- the total Area including veranda: A
- the width of the room is half its length: W = ½L
- the total area is the (room width + 3) times the length: A = (W+3) × L = 56

We are being asked for the length of the room: L

This is a quadratic equation , there are many ways to solve it, this time let's use factoring :

And so L = 8 or −14

There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

So the length of the room is 8 m

L = 8, so W = ½L = 4

So the area of the rectangle = (W+3) × L = 7 × 8 = 56

There we are ...

... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?

## 30 Fun Maths Questions with Answers

Table of Contents

## Introduction

Mathematics can be fun if you treat it the right way. Maths is nothing less than a game, a game that polishes your intelligence and boosts your concentration. Compared to older times, people have a better and friendly approach to mathematics which makes it more appealing. The golden rule is to know that maths is a mindful activity rather than a task.

There is nothing like hard math problems or tricky maths questions, it’s just that you haven’t explored mathematics well enough to comprehend its easiness and relatability. Maths tricky questions and answers can be transformed into fun math problems if you look at it as if it is a brainstorming session. With the right attitude and friends and teachers, doing math can be most entertaining and delightful.

Math is interesting because a few equations and diagrams can communicate volumes of information. Treat math as a language, while moving to rigorous proof and using logical reason for performing a particular step in a proof or derivation.

Treating maths as a language totally eradicates the concept of hard math problems or tricky maths questions from your mind. Introducing children to fun maths questions can create a strong love and appreciation for maths at an early age. This way you are setting up the child’s successful future. Fun math problems will urge your child to choose to solve it over playing bingo or baking.

Apparently, there are innumerable methods to make easy maths tricky questions and answers. This includes the inception of the ideology that maths is simpler than their fear. This can be done by connecting maths with everyday life. Practising maths with the aid of dice, cards, puzzles and tables reassures that your child effectively approaches Maths.

If you wish to add some fun and excitement into educational activities, also check out

- Check out some mind-blowing Math Magic Tricks!
- Mental Maths: How to Improve it?

Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12 . Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.

## Fun Maths Questions with answers - PDF

Here is the Downloadable PDF that consists of Fun Math questions. Click the Download button to view them.

Here are some fun, tricky and hard to solve maths problems that will challenge your thinking ability.

Answer: is 3, because ‘six’ has three letters

What is the number of parking space covered by the car?

This tricky math problem went viral a few years back after it appeared on an entrance exam in Hong Kong… for six-year-olds. Supposedly the students had just 20 seconds to solve the problem!

Believe it or not, this “math” question actually requires no math whatsoever. If you flip the image upside down, you’ll see that what you’re dealing with is a simple number sequence.

Replace the question mark in the above problem with the appropriate number.

Which number is equivalent to 3^(4)÷3^(2)

This problem comes straight from a standardized test given in New York in 2014.

There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?

This question comes directly from a second grader's math homework.

To figure out how many small dogs are competing, you have to subtract 36 from 49 and then divide that answer, 13 by 2, to get 6.5 dogs, or the number of big dogs competing. But you’re not done yet! You then have to add 6.5 to 36 to get the number of small dogs competing, which is 42.5. Of course, it’s not actually possible for half a dog to compete in a dog show, but for the sake of this math problem let’s assume that it is.

Add 8.563 and 4.8292.

Adding two decimals together is easier than it looks. Don’t let the fact that 8.563 has fewer numbers than 4.8292 trip you up. All you have to do is add a 0 to the end of 8.563 and then add like you normally would.

I am an odd number. Take away one letter and I become even. What number am I?

Answer: Seven (take away the ‘s’ and it becomes ‘even’).

Using only an addition, how do you add eight 8’s and get the number 1000?

Answer:

888 + 88 + 8 + 8 + 8 = 1000

Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother times her age?

41 years ago, when Sally was 13 and her mother was 39.

Which 3 numbers have the same answer whether they’re added or multiplied together?

There is a basket containing 5 apples, how do you divide the apples among 5 children so that each child has 1 apple while 1 apple remains in the basket?

4 children get 1 apple each while the fifth child gets the basket with the remaining apple still in it.

There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?

Fill in the question mark

Two girls were born to the same mother, at the same time, on the same day, in the same month and the same year and yet somehow they’re not twins. Why not?

Because there was a third girl, which makes them triplets!

A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each rung in 20cm and the bottom rung touches the water. The tide rises at a rate of 10cm an hour. When will the water reach the fifth rung?

The tide raises both the water and the boat so the water will never reach the fifth rung.

The day before yesterday I was 25. The next year I will be 28. This is true only one day in a year. What day is my Birthday?

You have a 3-litre bottle and a 5-litre bottle. How can you measure 4 litres of water by using 3L and 5L bottles?

Solution 1 :

First, fill 3Lt bottle and pour 3 litres into 5Lt bottle.

Again fill the 3Lt bottle. Now pour 2 litres into the 5Lt bottle until it becomes full.

Now empty 5Lt bottle.

Pour remaining 1 litre in 3Lt bottle into 5Lt bottle.

Now again fill 3Lt bottle and pour 3 litres into 5Lt bottle.

Now you have 4 litres in the 5Lt bottle. That’s it.

Solution 2 :

First, fill the 5Lt bottle and pour 3 litres into 3Lt bottle.

Empty 3Lt bottle.

Pour remaining 2 litres in 5Lt bottle into 3Lt bottle.

Again fill the 5Lt bottle and pour 1 litre into 3 Lt bottle until it becomes full.

3 Friends went to a shop and purchased 3 toys. Each person paid Rs.10 which is the cost of one toy. So, they paid Rs.30 i.e. total amount. The shop owner gave a discount of Rs.5 on the total purchase of 3 toys for Rs.30. Then, among Rs.5, Each person has taken Rs.1 and remaining Rs.2 given to the beggar beside the shop. Now, the effective amount paid by each person is Rs.9 and the amount given to the beggar is Rs.2. So, the total effective amount paid is 9*3 = 27 and the amount given to beggar is Rs.2, thus the total is Rs.29. Where has the other Rs.1 gone from the original Rs.30?

The logic is payments should be equal to receipts. We cannot add the amount paid by persons and the amount given to the beggar and compare it to Rs.30.The total amount paid is ₹27. So, from ₹27, the shop owner received 25 rupees and beggar received ₹ 2. Thus, payments are equal to receipts.

How to get a number 100 by using four sevens (7’s) and a one (1)?

Answer 1: 177 – 77 = 100 ;

Answer 2: (7+7) * (7 + (1/7)) = 100

Move any four matches to get 3 equilateral triangles only (don’t remove matches)

Find the area of the red triangle.

To solve this fun maths question, you need to understand how the area of a parallelogram works. If you already know how the area of a parallelogram and the area of a triangle are related, then adding 79 and 10 and subsequently subtracting 72 and 8 to get 9 should make sense.

How many feet are in a mile?

Solve - 15+ (-5x) =0

What is 1.92÷3

A man is climbing up a mountain which is inclined. He has to travel 100 km to reach the top of the mountain. Every day He climbs up 2 km forward in the day time. Exhausted, he then takes rest there at night time. At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined. Then how many days does it take him to reach the mountain top?

If 72 x 96 = 6927, 58 x 87 = 7885, then 79 x 86 = ?

Answer:

Look at this series: 36, 34, 30, 28, 24, … What number should come next?

Look at this series: 22, 21, 23, 22, 24, 23, … What number should come next?

If 13 x 12 = 651 & 41 x 23 = 448, then, 24 x 22 =?

Look at this series: 53, 53, 40, 40, 27, 27, … What number should come next?

The ultimate goals of mathematics instruction are students understanding the material presented, applying the skills, and recalling the concepts in the future. There's little benefit in students recalling a formula or procedure to prepare for an assessment tomorrow only to forget the core concept by next week.

Teachers must focus on making sure that the students understand the material and not just memorize the procedures. After you learn the answers to a fun maths question, you begin to ask yourself how you could have missed something so easy. The truth is, most trick questions are designed to trick your mind, which is why the answers to fun maths questions are logical and easy.

## About Cuemath

Cuemath, a student-friendly mathematics and coding platform, conducts regular Online Classes for academics and skill-development, and their Mental Math App, on both iOS and Android , is a one-stop solution for kids to develop multiple skills. Understand the Cuemath Fee structure and sign up for a free trial.

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- Units Conversion and Calculators
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## 15 Common Problem-Solving Interview Questions

In an interview for a big tech company, I was asked if I’d ever resolved a fight — and the exact way I went about handling it. I felt blindsided, and I stammered my way through an excuse of an answer.

It’s a familiar scenario to fellow technical job seekers — and one that risks leaving a sour taste in our mouths. As candidate experience becomes an increasingly critical component of the hiring process, recruiters need to ensure the problem-solving interview questions they prepare don’t dissuade talent in the first place.

Interview questions designed to gauge a candidate’s problem-solving skills are more often than not challenging and vague. Assessing a multifaceted skill like problem solving is tricky — a good problem solver owns the full solution and result, researches well, solves creatively and takes action proactively.

It’s hard to establish an effective way to measure such a skill. But it’s not impossible.

We recommend taking an informed and prepared approach to testing candidates’ problem-solving skills . With that in mind, here’s a list of a few common problem-solving interview questions, the science behind them — and how you can go about administering your own problem-solving questions with the unique challenges of your organization in mind.

## Key Takeaways for Effective Problem-Solving Interview Questions

- Problem solving lies at the heart of programming.
- Testing a candidate’s problem-solving skills goes beyond the IDE. Problem-solving interview questions should test both technical skills and soft skills.
- STAR, SOAR and PREP are methods a candidate can use to answer some non-technical problem-solving interview questions.
- Generic problem-solving interview questions go a long way in gauging a candidate’s fit. But you can go one step further by customizing them according to your company’s service, product, vision, and culture.

## Technical Problem-Solving Interview Question Examples

Evaluating a candidates’ problem-solving skills while using coding challenges might seem intimidating. The secret is that coding challenges test many things at the same time — like the candidate’s knowledge of data structures and algorithms, clean code practices, and proficiency in specific programming languages, to name a few examples.

Problem solving itself might at first seem like it’s taking a back seat. But technical problem solving lies at the heart of programming, and most coding questions are designed to test a candidate’s problem-solving abilities.

Here are a few examples of technical problem-solving questions:

## 1. Mini-Max Sum

This well-known challenge, which asks the interviewee to find the maximum and minimum sum among an array of given numbers, is based on a basic but important programming concept called sorting, as well as integer overflow. It tests the candidate’s observational skills, and the answer should elicit a logical, ad-hoc solution.

## 2. Organizing Containers of Balls

This problem tests the candidate’s knowledge of a variety of programming concepts, like 2D arrays, sorting and iteration. Organizing colored balls in containers based on various conditions is a common question asked in competitive examinations and job interviews, because it’s an effective way to test multiple facets of a candidate’s problem-solving skills.

## 3. Build a Palindrome

This is a tough problem to crack, and the candidate’s knowledge of concepts like strings and dynamic programming plays a significant role in solving this challenge. This problem-solving example tests the candidate’s ability to think on their feet as well as their ability to write clean, optimized code.

## 4. Subarray Division

Based on a technique used for searching pairs in a sorted array ( called the “two pointers” technique ), this problem can be solved in just a few lines and judges the candidate’s ability to optimize (as well as basic mathematical skills).

## 5. The Grid Search

This is a problem of moderate difficulty and tests the candidate’s knowledge of strings and searching algorithms, the latter of which is regularly tested in developer interviews across all levels.

## Common Non-Technical Problem-Solving Interview Questions

Testing a candidate’s problem-solving skills goes beyond the IDE . Everyday situations can help illustrate competency, so here are a few questions that focus on past experiences and hypothetical situations to help interviewers gauge problem-solving skills.

## 1. Given the problem of selecting a new tool to invest in, where and how would you begin this task?

Key Insight : This question offers insight into the candidate’s research skills. Ideally, they would begin by identifying the problem, interviewing stakeholders, gathering insights from the team, and researching what tools exist to best solve for the team’s challenges and goals.

## 2. Have you ever recognized a potential problem and addressed it before it occurred?

Key Insight: Prevention is often better than cure. The ability to recognize a problem before it occurs takes intuition and an understanding of business needs.

## 3. A teammate on a time-sensitive project confesses that he’s made a mistake, and it’s putting your team at risk of missing key deadlines. How would you respond?

Key Insight: Sometimes, all the preparation in the world still won’t stop a mishap. Thinking on your feet and managing stress are skills that this question attempts to unearth. Like any other skill, they can be cultivated through practice.

## 4. Tell me about a time you used a unique problem-solving approach.

Key Insight: Creativity can manifest in many ways, including original or novel ways to tackle a problem. Methods like the 10X approach and reverse brainstorming are a couple of unique approaches to problem solving.

## 5. Have you ever broken rules for the “greater good?” If yes, can you walk me through the situation?

Key Insight: “Ask for forgiveness, not for permission.” It’s unconventional, but in some situations, it may be the mindset needed to drive a solution to a problem.

## 6. Tell me about a weakness you overcame at work, and the approach you took.

Key Insight: According to Compass Partnership , “self-awareness allows us to understand how and why we respond in certain situations, giving us the opportunity to take charge of these responses.” It’s easy to get overwhelmed when faced with a problem. Candidates showing high levels of self-awareness are positioned to handle it well.

## 7. Have you ever owned up to a mistake at work? Can you tell me about it?

Key Insight: Everybody makes mistakes. But owning up to them can be tough, especially at a workplace. Not only does it take courage, but it also requires honesty and a willingness to improve, all signs of 1) a reliable employee and 2) an effective problem solver.

## 8. How would you approach working with an upset customer?

Key Insight: With the rise of empathy-driven development and more companies choosing to bridge the gap between users and engineers, today’s tech teams speak directly with customers more frequently than ever before. This question brings to light the candidate’s interpersonal skills in a client-facing environment.

## 9. Have you ever had to solve a problem on your own, but needed to ask for additional help? How did you go about it?

Key Insight: Knowing when you need assistance to complete a task or address a situation is an important quality to have while problem solving. This questions helps the interviewer get a sense of the candidate’s ability to navigate those waters.

## 10. Let’s say you disagree with your colleague on how to move forward with a project. How would you go about resolving the disagreement?

Key Insight: Conflict resolution is an extremely handy skill for any employee to have; an ideal answer to this question might contain a brief explanation of the conflict or situation, the role played by the candidate and the steps taken by them to arrive at a positive resolution or outcome.

## Strategies for Answering Problem-Solving Questions

If you’re a job seeker, chances are you’ll encounter this style of question in your various interview experiences. While problem-solving interview questions may appear simple, they can be easy to fumble — leaving the interviewer without a clear solution or outcome.

It’s important to approach such questions in a structured manner. Here are a few tried-and-true methods to employ in your next problem-solving interview.

## 1. Shine in Interviews With the STAR Method

S ituation, T ask, A ction, and R esult is a great method that can be employed to answer a problem-solving or behavioral interview question. Here’s a breakdown of these steps:

- Situation : A good way to address almost any interview question is to lay out and define the situation and circumstances.
- Task : Define the problem or goal that needs to be addressed. Coding questions are often multifaceted, so this step is particularly important when answering technical problem-solving questions.
- Action : How did you go about solving the problem? Try to be as specific as possible, and state your plan in steps if you can.
- Result : Wrap it up by stating the outcome achieved.

## 2. Rise above difficult questions using the SOAR method

A very similar approach to the STAR method, SOAR stands for S ituation, O bstacle, A ction, and R esults .

- Situation: Explain the state of affairs. It’s important to steer clear of stating any personal opinions in this step; focus on the facts.
- Obstacle: State the challenge or problem you faced.
- Action: Detail carefully how you went about overcoming this obstacle.
- Result: What was the end result? Apart from overcoming the obstacle, did you achieve anything else? What did you learn in the process?

## 3. Do It the PREP Way

Traditionally used as a method to make effective presentations, the P oint, R eason, E xample, P oint method can also be used to answer problem-solving interview questions.

- Point : State the solution in plain terms.
- Reasons: Follow up the solution by detailing your case — and include any data or insights that support your solution.
- Example: In addition to objective data and insights, drive your answer home by contextualizing the solution in a real-world example.
- Point : Reiterate the solution to make it come full circle.

## How to Customize Problem-Solving Interview Questions

Generic problem-solving interview questions go a long way in gauging a candidate’s skill level, but recruiters can go one step further by customizing these problem-solving questions according to their company’s service, product, vision, or culture.

Here are some tips to do so:

- Break down the job’s responsibilities into smaller tasks. Job descriptions may contain ambiguous responsibilities like “manage team projects effectively.” To formulate an effective problem-solving question, envision what this task might look like in a real-world context and develop a question around it.
- Tailor questions to the role at hand. Apart from making for an effective problem-solving question, it gives the candidate the impression you’re an informed technical recruiter. For example, an engineer will likely have attended many scrums. So, a good question to ask is: “Suppose you notice your scrums are turning unproductive. How would you go about addressing this?”
- Consider the tools and technologies the candidate will use on the job. For example, if Jira is the primary project management tool, a good problem-solving interview question might be: “Can you tell me about a time you simplified a complex workflow — and the tools you used to do so?”
- If you don’t know where to start, your company’s core values can often provide direction. If one of the core values is “ownership,” for example, consider asking a question like: “Can you walk us through a project you owned from start to finish?”
- Sometimes, developing custom content can be difficult even with all these tips considered. Our platform has a vast selection of problem-solving examples that are designed to help recruiters ask the right questions to help nail their next technical interview.

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## 6 REST API Interview Questions Every Developer Should Know

## Top 20 Problem Solving Interview Questions (Example Answers Included)

Mike Simpson 0 Comments

## By Mike Simpson

When candidates prepare for interviews, they usually focus on highlighting their leadership, communication, teamwork, and similar crucial soft skills . However, not everyone gets ready for problem-solving interview questions. And that can be a big mistake.

Problem-solving is relevant to nearly any job on the planet. Yes, it’s more prevalent in certain industries, but it’s helpful almost everywhere.

Regardless of the role you want to land, you may be asked to provide problem-solving examples or describe how you would deal with specific situations. That’s why being ready to showcase your problem-solving skills is so vital.

If you aren’t sure who to tackle problem-solving questions, don’t worry, we have your back. Come with us as we explore this exciting part of the interview process, as well as some problem-solving interview questions and example answers.

## What Is Problem-Solving?

When you’re trying to land a position, there’s a good chance you’ll face some problem-solving interview questions. But what exactly is problem-solving? And why is it so important to hiring managers?

Well, the good folks at Merriam-Webster define problem-solving as “the process or act of finding a solution to a problem.” While that may seem like common sense, there’s a critical part to that definition that should catch your eye.

What part is that? The word “process.”

In the end, problem-solving is an activity. It’s your ability to take appropriate steps to find answers, determine how to proceed, or otherwise overcome the challenge.

Being great at it usually means having a range of helpful problem-solving skills and traits. Research, diligence, patience, attention-to-detail , collaboration… they can all play a role. So can analytical thinking , creativity, and open-mindedness.

But why do hiring managers worry about your problem-solving skills? Well, mainly, because every job comes with its fair share of problems.

While problem-solving is relevant to scientific, technical, legal, medical, and a whole slew of other careers. It helps you overcome challenges and deal with the unexpected. It plays a role in troubleshooting and innovation. That’s why it matters to hiring managers.

## How to Answer Problem-Solving Interview Questions

Okay, before we get to our examples, let’s take a quick second to talk about strategy. Knowing how to answer problem-solving interview questions is crucial. Why? Because the hiring manager might ask you something that you don’t anticipate.

Problem-solving interview questions are all about seeing how you think. As a result, they can be a bit… unconventional.

These aren’t your run-of-the-mill job interview questions . Instead, they are tricky behavioral interview questions . After all, the goal is to find out how you approach problem-solving, so most are going to feature scenarios, brainteasers, or something similar.

So, having a great strategy means knowing how to deal with behavioral questions. Luckily, there are a couple of tools that can help.

First, when it comes to the classic approach to behavioral interview questions, look no further than the STAR Method . With the STAR method, you learn how to turn your answers into captivating stories. This makes your responses tons more engaging, ensuring you keep the hiring manager’s attention from beginning to end.

Now, should you stop with the STAR Method? Of course not. If you want to take your answers to the next level, spend some time with the Tailoring Method , too.

With the Tailoring Method, it’s all about relevance. So, if you get a chance to choose an example that demonstrates your problem-solving skills, this is really the way to go.

We also wanted to let you know that we created an amazing free cheat sheet that will give you word-for-word answers for some of the toughest interview questions you are going to face in your upcoming interview. After all, hiring managers will often ask you more generalized interview questions!

Click below to get your free PDF now:

## Get Our Job Interview Questions & Answers Cheat Sheet!

FREE BONUS PDF CHEAT SHEET: Get our " Job Interview Questions & Answers PDF Cheat Sheet " that gives you " word-word sample answers to the most common job interview questions you'll face at your next interview .

CLICK HERE TO GET THE JOB INTERVIEW QUESTIONS CHEAT SHEET

## Top 3 Problem-Solving-Based Interview Questions

Alright, here is what you’ve been waiting for: the problem-solving questions and sample answers.

While many questions in this category are job-specific, these tend to apply to nearly any job. That means there’s a good chance you’ll come across them at some point in your career, making them a great starting point when you’re practicing for an interview.

So, let’s dive in, shall we? Here’s a look at the top three problem-solving interview questions and example responses.

## 1. Can you tell me about a time when you had to solve a challenging problem?

In the land of problem-solving questions, this one might be your best-case scenario. It lets you choose your own problem-solving examples to highlight, putting you in complete control.

When you choose an example, go with one that is relevant to what you’ll face in the role. The closer the match, the better the answer is in the eyes of the hiring manager.

EXAMPLE ANSWER:

“While working as a mobile telecom support specialist for a large organization, we had to transition our MDM service from one vendor to another within 45 days. This personally physically handling 500 devices within the agency. Devices had to be gathered from the headquarters and satellite offices, which were located all across the state, something that was challenging even without the tight deadline. I approached the situation by identifying the location assignment of all personnel within the organization, enabling me to estimate transit times for receiving the devices. Next, I timed out how many devices I could personally update in a day. Together, this allowed me to create a general timeline. After that, I coordinated with each location, both expressing the urgency of adhering to deadlines and scheduling bulk shipping options. While there were occasional bouts of resistance, I worked with location leaders to calm concerns and facilitate action. While performing all of the updates was daunting, my approach to organizing the event made it a success. Ultimately, the entire transition was finished five days before the deadline, exceeding the expectations of many.”

## 2. Describe a time where you made a mistake. What did you do to fix it?

While this might not look like it’s based on problem-solving on the surface, it actually is. When you make a mistake, it creates a challenge, one you have to work your way through. At a minimum, it’s an opportunity to highlight problem-solving skills, even if you don’t address the topic directly.

When you choose an example, you want to go with a situation where the end was positive. However, the issue still has to be significant, causing something negative to happen in the moment that you, ideally, overcame.

“When I first began in a supervisory role, I had trouble setting down my individual contributor hat. I tried to keep up with my past duties while also taking on the responsibilities of my new role. As a result, I began rushing and introduced an error into the code of the software my team was updating. The error led to a memory leak. We became aware of the issue when the performance was hindered, though we didn’t immediately know the cause. I dove back into the code, reviewing recent changes, and, ultimately, determined the issue was a mistake on my end. When I made that discovery, I took several steps. First, I let my team know that the error was mine and let them know its nature. Second, I worked with my team to correct the issue, resolving the memory leak. Finally, I took this as a lesson about delegation. I began assigning work to my team more effectively, a move that allowed me to excel as a manager and help them thrive as contributors. It was a crucial learning moment, one that I have valued every day since.”

## 3. If you identify a potential risk in a project, what steps do you take to prevent it?

Yes, this is also a problem-solving question. The difference is, with this one, it’s not about fixing an issue; it’s about stopping it from happening. Still, you use problem-solving skills along the way, so it falls in this question category.

If you can, use an example of a moment when you mitigated risk in the past. If you haven’t had that opportunity, approach it theoretically, discussing the steps you would take to prevent an issue from developing.

“If I identify a potential risk in a project, my first step is to assess the various factors that could lead to a poor outcome. Prevention requires analysis. Ensuring I fully understand what can trigger the undesired event creates the right foundation, allowing me to figure out how to reduce the likelihood of those events occurring. Once I have the right level of understanding, I come up with a mitigation plan. Exactly what this includes varies depending on the nature of the issue, though it usually involves various steps and checks designed to monitor the project as it progresses to spot paths that may make the problem more likely to happen. I find this approach effective as it combines knowledge and ongoing vigilance. That way, if the project begins to head into risky territory, I can correct its trajectory.”

## 17 More Problem-Solving-Based Interview Questions

In the world of problem-solving questions, some apply to a wide range of jobs, while others are more niche. For example, customer service reps and IT helpdesk professionals both encounter challenges, but not usually the same kind.

As a result, some of the questions in this list may be more relevant to certain careers than others. However, they all give you insights into what this kind of question looks like, making them worth reviewing.

Here are 17 more problem-solving interview questions you might face off against during your job search:

- How would you describe your problem-solving skills?
- Can you tell me about a time when you had to use creativity to deal with an obstacle?
- Describe a time when you discovered an unmet customer need while assisting a customer and found a way to meet it.
- If you were faced with an upset customer, how would you diffuse the situation?
- Tell me about a time when you had to troubleshoot a complex issue.
- Imagine you were overseeing a project and needed a particular item. You have two choices of vendors: one that can deliver on time but would be over budget, and one that’s under budget but would deliver one week later than you need it. How do you figure out which approach to use?
- Your manager wants to upgrade a tool you regularly use for your job and wants your recommendation. How do you formulate one?
- A supplier has said that an item you need for a project isn’t going to be delivered as scheduled, something that would cause your project to fall behind schedule. What do you do to try and keep the timeline on target?
- Can you share an example of a moment where you encountered a unique problem you and your colleagues had never seen before? How did you figure out what to do?
- Imagine you were scheduled to give a presentation with a colleague, and your colleague called in sick right before it was set to begin. What would you do?
- If you are given two urgent tasks from different members of the leadership team, both with the same tight deadline, how do you choose which to tackle first?
- Tell me about a time you and a colleague didn’t see eye-to-eye. How did you decide what to do?
- Describe your troubleshooting process.
- Tell me about a time where there was a problem that you weren’t able to solve. What happened?
- In your opening, what skills or traits make a person an exceptional problem-solver?
- When you face a problem that requires action, do you usually jump in or take a moment to carefully assess the situation?
- When you encounter a new problem you’ve never seen before, what is the first step that you take?

## Putting It All Together

At this point, you should have a solid idea of how to approach problem-solving interview questions. Use the tips above to your advantage. That way, you can thrive during your next interview.

## FREE : Job Interview Questions & Answers PDF Cheat Sheet!

Download our " Job Interview Questions & Answers PDF Cheat Sheet " that gives you word-for-word sample answers to some of the most common interview questions including:

- What Is Your Greatest Weakness?
- What Is Your Greatest Strength?
- Tell Me About Yourself
- Why Should We Hire You?

## Click Here To Get The Job Interview Questions & Answers Cheat Sheet

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Home » Job Tips » Interview Guide » Problem Solving Interview Questions

## Top 17 Problem-Solving Interview Questions for Freshers & Experienced Professionals

Problem-solving skills are essential for success in almost any job position. Employers are in search of individuals who possess the ability to think critically, tackle obstacles and situations systematically, and develop efficient resolutions. In this guide, you will get different problem-solving interview questions and answers and valuable tips to equip you to prepare for your upcoming interview.

Table of Contents

## What are Problem-Solving Interview Questions?

Problem-solving interview questions are questions that focus on a candidate’s aptitude for collecting information, evaluating an issue, considering its advantages and disadvantages, and arriving at a sound conclusion. Employers use these questions to understand and analyze one’s critical thinking abilities and ability to make informed decisions.

These questions are designed to assess a candidate’s critical thinking and decision-making skills. You can develop the right attitude and approach to solving a problem by checking out this complete guide on what are problem-solving skills .

## Problem-Solving Interview Questions and Answers for Freshers

Below are the common problem-solving interview questions you might likely come across as a fresher. You can also check out this interview preparation course to equip yourself with common interview etiquette .

## Q1. When faced with a problem, what is your action plan?

Answer: When I encounter a problem, my first step is to explore how others have successfully addressed similar challenges. This research provides me with diverse solutions, enabling me to choose the most fitting approach for both myself and the organization. Subsequently, I collaborate with my managers and colleagues, ensuring clear communication as we implement the selected solution.

## Q2. What factors do you implement to weigh the pros and cons of a decision?

Answer: When evaluating decisions, I consider various factors, such as the potential impact the decision has on both short-term and long-term goals, assess the risks involved, seek input from relevant team members, and how relevant the decision aligns with the organization’s goals and values. With this comprehensive approach, anyone can make a well-informed decision.

## Q3. How do you know when to seek assistance or tackle an issue on your own?

Answer: I evaluate the complexity and urgency of the issue. If it’s something I can handle within a stipulated time frame, I will address it on my own. However, for more complex or time-sensitive issues, I promptly seek help from colleagues or supervisors to ensure a quick and effective resolution.

## Q4. Describe a situation when you identified an issue early on and resolved it before it got out of hand?

Answer: In my previous position as an intern, I discovered inaccuracies in the data during a project. Without hesitation, I took it upon myself to thoroughly examine and resolve these discrepancies to ensure precise outcomes. This valuable experience taught me the importance of attention to detail and enhanced my commitment to quality work.

## Q5. Describe a situation when you had a task but lacked the abilities needed to finish it?

Answer: In my entry-level role, I successfully managed a sudden increase in customer inquiries caused by a website glitch. I worked with the team to address the issue, prioritized urgent cases, communicated transparently with customers, and provided temporary solutions until a permanent fix was implemented. This situation demonstrated my proficiency in managing high-pressure situations and delivering exceptional service to customers.

## Q6. Describe a situation where you handled a crisis well?

Answer: During my internship as a client relations specialist, we encountered an unforeseen rise in customer discontentment due to concerns about the quality of our products. Working closely with relevant departments, I identified the root cause and devised a plan of action. By prioritizing urgent cases and maintaining open communication with affected customers while providing prompt updates, we effectively restored their satisfaction and prevented any further damage to our brand reputation.

## Q7. Give an example of a challenging circumstance you experienced at work that called for quick thought and decisive action?

Answer: In a previous internship role, I faced a challenging project with strict deadlines and limited resources. To overcome this obstacle, I employed strategic resource allocation techniques, prioritized tasks effectively, and worked closely with my team members. Through careful planning and delegating responsibilities efficiently, not only did we meet clients’ expectations, but we surpassed the client’s expectations by delivering the completed project within the given deadline.

## Q8. How would you respond to a disappointed and angry client?

Answer: When faced with an unhappy client, my focus is to remain calm and positively interact with them to prevent the situation from getting worse. I start by engaging in dialogue to comprehend the reasons for their discontentment, gathering all the essential information needed for effective problem-solving. Once I have a clear understanding of the issue at hand, I reassure the customer that we are dedicated to resolving it quickly. By providing frequent updates throughout the resolution process, we strive to keep our clients informed and build trust in our efforts toward finding a satisfactory solution.

## Q9. What metrics do you usually use to monitor your strategies?

Answer: I use key performance indicators (KPIs) particular to the objectives of the project or work at hand to keep monitoring my methods. Conversion rates, customer satisfaction ratings, and project schedules are a few examples of these KPIs. By monitoring these metrics regularly, I can evaluate the performance of my strategies and alter them based on data as necessary.

## Q10. How would you assess the impact of potential issues?

Answer: To evaluate the effects of potential problems, I utilize a methodical strategy. Initially, I determine the type and extent of the issue by assessing its potential to cause disruptions or hinder project objectives. Then, I consider how it may impact related tasks and timelines. After prioritizing these issues based on severity and their overall impact on goals, I create contingency plans proactively and allocate resources efficiently. This approach allows me to effectively manage challenges before they escalate, ultimately minimizing any negative consequences for the success of the project.

Also Read: Common Interview Questions for Freshers .

## Problem-Solving Questions with Answers for Experienced Candidates

Here are some problem-solving questions and answers for experienced individuals.

## Q11. How would you approach a new idea that has enormous profit potential but could have legal ramifications for the business?

Answer: When faced with a project that involves both financial opportunities and possible legal consequences, I would prioritize caution and thorough evaluation. I would conduct in-depth research and seek guidance from legal specialists to fully understand the implications and compliance requirements involved. Then, I would collaborate with lawyers, cross-functional teams, and stakeholders to develop a comprehensive plan that minimizes potential legal risks while maximizing revenue possibilities.

## Q12. Give an example of a work or project that looked too big at first. What methods did you employ to guarantee its effective completion and how did you approach it?

Answer: In a former position, I was tasked with an assignment that demanded thorough data analysis and timely reporting. Despite feeling overwhelmed at first, I tackled the project by dividing it into manageable tasks. Moreover, I devised a comprehensive schedule to ensure the project stayed on course. By prioritizing crucial components and collaborating with team members who possessed specialized skills in certain aspects, we successfully accomplished the task together in an efficient manner. With effective time management skills and dedicated effort from our team’s collaboration, we met the deadline and had exceptional results.

## Q13. Have you ever solved a problem without managerial input? What was the outcome and how did you handle it?

Answer: In a previous position, I encountered a technical challenge that disrupted our operations. As the leader of the team, I took charge by collecting information and analyzing the problem. Together with my team, we conducted a brainstorming session to come up with potential solutions and collaborated with the IT department to resolve it. Our proactive approach helped minimize any further disruptions and enabled us to restore normalcy within 24 hours.

## Q14. How do you respond when your supervisor asks for your opinion or recommendation?

Answer: When my supervisor asks for my input, I make sure to offer a thoughtful response. To start, I evaluate the circumstances and take into account any pertinent details while also considering possible consequences. Then, I communicate my perspective directly and succinctly and back it up with evidence or illustrations. Furthermore, I remain receptive to constructive feedback, promoting an environment of cooperation where ideas can be shared for the best course of action.

## Q15. How do you assess a solution’s effectiveness?

Answer: Evaluating the effectiveness of a solution involves a systematic assessment procedure. To begin, specific metrics and key performance indicators are established in accordance with the nature and goals of the problem at hand. These indicators are continuously monitored, comparing data before and after implementation to detect any positive changes or discrepancies. Gathering feedback from individuals involved, such as team members and end-users, offers valuable perspectives on how well the solution is performing in practical settings. Consistent reviews and necessary adjustments guarantee and support long-term objectives effectively.

## Q16. Describe how you learn from your experiences.

Answer: Once a project or task is completed, I take time to conduct a thorough evaluation. By looking back at both achievements and difficulties encountered, I identify key factors that contributed to success or hindered progress. This introspection allows me to identify areas for development and fine-tune my approach for future ventures. Furthermore, getting feedback from my colleagues and supervisors offers unique viewpoints that contribute to a more holistic understanding of the experience.

## Q17. Do you consider yourself a great problem solver?

Answer: I possess strong problem-solving abilities. My approach to challenges is proactive, breaking down complex problems into manageable parts. By examining the underlying causes and utilizing both creativity and critical thinking, I have a history of developing successful solutions. Moreover, I am open to collaborating with others and appreciate diverse viewpoints that contribute to comprehensive problem-solving approaches. While there is always room for growth, my past achievements showcase my determination to confront obstacles head-on and devise innovative resolutions.

Also Read: Behavioral Interview Questions .

## Problem-Solving Interview Questions: Common Mistakes to Avoid

Below are relevant tips to aid you in answering problem-solving interview questions.

- Avoid Giving Easy Responses- Individuals who opt for easier responses are considered to lack critical thinking.
- Avoid Giving Hasty Responses- Take your time in addressing the issue at hand and make sure you have a thorough understanding of it. If there are any unclear points, ask for clarification before giving your response. This shows that you value accuracy and precision.
- Avoid Taking Too Much on One Question- It is important to be brief and thorough when responding within a reasonable timeframe.

When answering an analytical question during an interview, endeavor to demonstrate the right mindset for solving problems. Problem-solving interview questions are an opportunity for you to showcase your analytical skills, creativity, and ability to handle challenges. You can make the right impression by preparing thoroughly, practicing different types of questions, and emphasizing your problem-solving ability.

Drop us a comment below if this blog has been helpful to you. Also, check out how to ace interviews with proven tips .

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Shobha Saini, the Head of Human Resources at Internshala, has maintained a stellar track record in employee relations and talent acquisition. With eight exceptional years of experience, she specializes in strategic planning, policy-making, and performance management. A multi-talented individual, she has played a major role in strategizing HR practices in the organization.

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