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Multiplying fractions word problems

Including estimating.

These grade 5 word problems involve the multiplication of common fractions by other fractions or whole numbers. Some problems ask students between what numbers does the answer lie? Answers are simplified where possible.

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Fraction Multiplication Word Problems Worksheets

Our printable worksheets on multiplying fractions word problems task grade 4 through grade 7 students with reading and solving realistic scenarios by performing fraction multiplication. The problems feature both common and uncommon denominators, so the budding problem-solving stars must follow the correct procedure to obtain the products. Equipped with answer keys, these pdf resources are available in customary and metric units. Try some multiplying fractions word problems worksheets for free!

Multiplying Fractions by Whole Numbers Word Problems

Impel the eager beavers in 4th grade and 5th grade to multiply fractions by whole numbers through word problems. Kids are required to multiply proper fractions and improper fractions by whole numbers correctly.

• Download the set

Multiplying Fractions by Cross-Cancelling Word Problems

Say a whole-hearted yes to our no-prep printable worksheets on fraction multiplication that have you fully covered! Interpret the word problems and multiply fractions with a special emphasis on cross cancelling.

Multiplying Mixed Numbers Word Problems

Multiplying mixed numbers may initially feel incomprehensible, but practice makes the pain melt away. Let grade 6 and grade 7 kids convert the mixed numbers into fractions and work out the products.

Multiplying Mixed Numbers and Fractions Word Problems

Let not the challenges of obtaining solutions for problems befall you! Our pdf worksheets on multiplying fractions word problems, equipped with answer key for a quick self-validation, help ease into the process.

Themed Fraction Multiplication Word Problems

Revive 5th grade, 6th grade, and 7th grade students' problem-solving fortunes with our themed word problems, featuring a good mix of like fractions, unlike fractions, whole numbers, and mixed numbers!

Related Worksheets

» Multiplying Fractions on a Number Line

» Multiplying Fractions by Whole Numbers

» Multiplying Fractions with Cross Cancelling

» Multiplying Mixed Numbers

» Fraction Word Problems

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Multiplying Fractions

Multiply the tops, multiply the bottoms.

There are 3 simple steps to multiply fractions

1. Multiply the top numbers (the numerators ).

2. Multiply the bottom numbers (the denominators ).

3. Simplify the fraction if needed.

Example: 1 2 × 2 5

Step 1 . Multiply the top numbers:

1 2  ×  2 5   =   1 × 2     =   2  

Step 2 . Multiply the bottom numbers:

1 2  ×  2 5   =   1 × 2 2 × 5   =   2 10

Step 3 . Simplify the fraction :

Here you can see it with pizza ...

Do you see that half of two-fifths is two-tenths? Do you also see that two-tenths is simpler as one-fifth?

With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

Another Example: 1 3 × 9 16

1 3  ×  9 16   =   1 × 9     =   9  

1 3  ×  9 16   =   1 × 9 3 × 16   =   9 48

Step 3 . Simplify the fraction:

9 48 = 3 16

(This time we simplified by dividing both top and bottom by 3)

♫ "Multiplying fractions: no big problem, Top times top over bottom times bottom. "And don't forget to simplify, Before it's time to say goodbye" ♫

Fractions and Whole Numbers

What about multiplying fractions and whole numbers?

Make the whole number a fraction, by putting it over 1.

Example: 5 is also 5 1

Then continue as before.

Example: 2 3  ×  5

Make 5 into 5 1 :

2 3  ×  5 1

Now just go ahead as normal.

Multiply tops and bottoms:

2 3  ×  5 1   =   2 × 5 3 × 1   =   10 3

The fraction is already as simple as it can be.

Answer = 10 3

Or you can just think of the whole number as being a "top" number:

Example: 3 ×  2 9

3    ×  2 9   =   3 × 2 9   =   6 9

Mixed Fractions

You can also read how to multiply mixed fractions

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4.3: Multiply and Divide Fractions

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Learning Objectives

By the end of this section, you will be able to:

• Simplify fractions
• Multiply fractions
• Find reciprocals
• Divide fractions

Be Prepared 4.3

Before you get started, take this readiness quiz.

Find the prime factorization of 48 . 48 . If you missed this problem, review Example 2.48.

Be Prepared 4.4

Draw a model of the fraction 3 4 . 3 4 . If you missed this problem, review Example 4.2.

Be Prepared 4.5

Find two fractions equivalent to 5 6 . 5 6 . If you missed this problem, review Example 4.14.

Simplify Fractions

In working with equivalent fractions, you saw that there are many ways to write fractions that have the same value, or represent the same part of the whole. How do you know which one to use? Often, we’ll use the fraction that is in simplified form.

A fraction is considered simplified if there are no common factors, other than 1 , 1 , in the numerator and denominator . If a fraction does have common factors in the numerator and denominator, we can reduce the fraction to its simplified form by removing the common factors.

Simplified Fraction

A fraction is considered simplified if there are no common factors in the numerator and denominator.

For example,

• 2 3 2 3 is simplified because there are no common factors of 2 2 and 3 . 3 .
• 10 15 10 15 is not simplified because 5 5 is a common factor of 10 10 and 15 . 15 .

The process of simplifying a fraction is often called reducing the fraction . In the previous section, we used the Equivalent Fractions Property to find equivalent fractions. We can also use the Equivalent Fractions Property in reverse to simplify fractions. We rewrite the property to show both forms together.

Equivalent Fractions Property

If a , b , c a , b , c are numbers where b ≠ 0 , c ≠ 0 , b ≠ 0 , c ≠ 0 , then

a b = a · c b · c and a · c b · c = a b . a b = a · c b · c and a · c b · c = a b .

Notice that c c is a common factor in the numerator and denominator . Anytime we have a common factor in the numerator and denominator, it can be removed.

Simplify a fraction.

• Step 1. Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers.
• Step 2. Simplify, using the equivalent fractions property, by removing common factors.
• Step 3. Multiply any remaining factors.

Example 4.19

Simplify: 10 15 . 10 15 .

To simplify the fraction, we look for any common factors in the numerator and the denominator.

Try It 4.37

Simplify: 8 12 8 12 .

Try It 4.38

Simplify: 12 16 12 16 .

To simplify a negative fraction, we use the same process as in Example 4.19. Remember to keep the negative sign.

Example 4.20

Simplify: − 18 24 . − 18 24 .

Try It 4.39

Simplify: − 21 28 . − 21 28 .

Try It 4.40

Simplify: − 16 24 . − 16 24 .

After simplifying a fraction, it is always important to check the result to make sure that the numerator and denominator do not have any more factors in common. Remember, the definition of a simplified fraction: a fraction is considered simplified if there are no common factors in the numerator and denominator .

When we simplify an improper fraction, there is no need to change it to a mixed number.

Example 4.21

Simplify: − 56 32 . − 56 32 .

Try It 4.41

Simplify: − 54 42 . − 54 42 .

Try It 4.42

Simplify: − 81 45 . − 81 45 .

• Step 3. Multiply any remaining factors

Sometimes it may not be easy to find common factors of the numerator and denominator. A good idea, then, is to factor the numerator and the denominator into prime numbers. (You may want to use the factor tree method to identify the prime factors.) Then divide out the common factors using the Equivalent Fractions Property.

Example 4.22

Simplify: 210 385 . 210 385 .

Try It 4.43

Simplify: 69 120 . 69 120 .

Try It 4.44

Simplify: 120 192 . 120 192 .

We can also simplify fractions containing variables. If a variable is a common factor in the numerator and denominator , we remove it just as we do with an integer factor.

Example 4.23

Simplify: 5 x y 15 x . 5 x y 15 x .

Try It 4.45

Simplify: 7 x 7 y . 7 x 7 y .

Try It 4.46

Simplify: 9 a 9 b . 9 a 9 b .

Multiply Fractions

A model may help you understand multiplication of fractions. We will use fraction tiles to model 1 2 · 3 4 . 1 2 · 3 4 . To multiply 1 2 1 2 and 3 4 , 3 4 , think 1 2 1 2 of 3 4 . 3 4 .

Start with fraction tiles for three-fourths. To find one-half of three-fourths, we need to divide them into two equal groups. Since we cannot divide the three 1 4 1 4 tiles evenly into two parts, we exchange them for smaller tiles.

We see 6 8 6 8 is equivalent to 3 4 . 3 4 . Taking half of the six 1 8 1 8 tiles gives us three 1 8 1 8 tiles, which is 3 8 . 3 8 .

1 2 · 3 4 = 3 8 1 2 · 3 4 = 3 8

Manipulative Mathematics

Example 4.24.

Use a diagram to model 1 2 · 3 4 . 1 2 · 3 4 .

First shade in 3 4 3 4 of the rectangle.

We will take 1 2 1 2 of this 3 4 , 3 4 , so we heavily shade 1 2 1 2 of the shaded region.

Notice that 3 3 out of the 8 8 pieces are heavily shaded. This means that 3 8 3 8 of the rectangle is heavily shaded.

Therefore, 1 2 1 2 of 3 4 3 4 is 3 8 , 3 8 , or 1 2 · 3 4 = 3 8 . 1 2 · 3 4 = 3 8 .

Try It 4.47

Use a diagram to model: 1 2 · 3 5 . 1 2 · 3 5 .

Try It 4.48

Use a diagram to model: 1 2 · 5 6 . 1 2 · 5 6 .

Look at the result we got from the model in Example 4.24. We found that 1 2 · 3 4 = 3 8 . 1 2 · 3 4 = 3 8 . Do you notice that we could have gotten the same answer by multiplying the numerators and multiplying the denominators?

This leads to the definition of fraction multiplication. To multiply fractions, we multiply the numerators and multiply the denominators. Then we write the fraction in simplified form.

Fraction Multiplication

If a , b , c , a , b , c , and d d are numbers where b ≠ 0 b ≠ 0 and d ≠ 0 , d ≠ 0 , then

a b · c d = a c b d a b · c d = a c b d

Example 4.25

Multiply, and write the answer in simplified form: 3 4 · 1 5 . 3 4 · 1 5 .

There are no common factors, so the fraction is simplified.

Try It 4.49

Multiply, and write the answer in simplified form: 1 3 · 2 5 . 1 3 · 2 5 .

Try It 4.50

Multiply, and write the answer in simplified form: 3 5 · 7 8 . 3 5 · 7 8 .

When multiplying fractions, the properties of positive and negative numbers still apply. It is a good idea to determine the sign of the product as the first step. In Example 4.26 we will multiply two negatives, so the product will be positive.

Example 4.26

Multiply, and write the answer in simplified form: − 5 8 ( − 2 3 ) . − 5 8 ( − 2 3 ) .

Another way to find this product involves removing common factors earlier.

We get the same result.

Try It 4.51

Multiply, and write the answer in simplified form: − 4 7 ( − 5 8 ) . − 4 7 ( − 5 8 ) .

Try It 4.52

Multiply, and write the answer in simplified form: − 7 12 ( − 8 9 ) . − 7 12 ( − 8 9 ) .

Example 4.27

Multiply, and write the answer in simplified form: − 14 15 · 20 21 . − 14 15 · 20 21 .

Try It 4.53

Multiply, and write the answer in simplified form: − 10 28 · 8 15 . − 10 28 · 8 15 .

Try It 4.54

Multiply, and write the answer in simplified form: − 9 20 · 5 12 . − 9 20 · 5 12 .

When multiplying a fraction by an integer, it may be helpful to write the integer as a fraction. Any integer, a , a , can be written as a 1 . a 1 . So, 3 = 3 1 , 3 = 3 1 , for example.

Example 4.28

Multiply, and write the answer in simplified form:

ⓐ 1 7 · 56 1 7 · 56

ⓑ 12 5 ( −20 x ) 12 5 ( −20 x )

Try It 4.55

• ⓐ 1 8 · 72 1 8 · 72
• ⓑ 11 3 ( −9 a ) 11 3 ( −9 a )

Try It 4.56

• ⓐ 3 8 · 64 3 8 · 64
• ⓑ 16 x · 11 12 16 x · 11 12

Find Reciprocals

The fractions 2 3 2 3 and 3 2 3 2 are related to each other in a special way. So are − 10 7 − 10 7 and − 7 10 . − 7 10 . Do you see how? Besides looking like upside-down versions of one another, if we were to multiply these pairs of fractions, the product would be 1 . 1 .

The reciprocal of the fraction a b a b is b a , b a , where a ≠ 0 a ≠ 0 and b ≠ 0 , b ≠ 0 ,

A number and its reciprocal have a product of 1 . 1 .

a b · b a = 1 a b · b a = 1

To find the reciprocal of a fraction, we invert the fraction. This means that we place the numerator in the denominator and the denominator in the numerator.

To get a positive result when multiplying two numbers, the numbers must have the same sign. So reciprocals must have the same sign.

To find the reciprocal, keep the same sign and invert the fraction. The number zero does not have a reciprocal. Why? A number and its reciprocal multiply to 1 . 1 . Is there any number r r so that 0 · r = 1 ? 0 · r = 1 ? No. So, the number 0 0 does not have a reciprocal.

Example 4.29

Find the reciprocal of each number. Then check that the product of each number and its reciprocal is 1 . 1 .

• ⓐ 4 9 4 9
• ⓑ − 1 6 − 1 6
• ⓒ − 14 5 − 14 5
• ⓓ 7 7

To find the reciprocals, we keep the sign and invert the fractions.

Try It 4.57

Find the reciprocal:

• ⓐ 5 7 5 7
• ⓑ − 1 8 − 1 8
• ⓒ − 11 4 − 11 4
• ⓓ 14 14

Try It 4.58

• ⓐ 3 7 3 7
• ⓑ − 1 12 − 1 12
• ⓒ − 14 9 − 14 9
• ⓓ 21 21

In a previous chapter, we worked with opposites and absolute values. Table 4.1 compares opposites, absolute values, and reciprocals.

Example 4.30

Fill in the chart for each fraction in the left column:

To find the opposite, change the sign. To find the absolute value, leave the positive numbers the same, but take the opposite of the negative numbers. To find the reciprocal, keep the sign the same and invert the fraction.

Try It 4.59

Fill in the chart for each number given:

Try It 4.60

Divide Fractions

Why is 12 ÷ 3 = 4 ? 12 ÷ 3 = 4 ? We previously modeled this with counters. How many groups of 3 3 counters can be made from a group of 12 12 counters?

There are 4 4 groups of 3 3 counters. In other words, there are four 3 3 s in 12 . 12 . So, 12 ÷ 3 = 4 . 12 ÷ 3 = 4 .

What about dividing fractions? Suppose we want to find the quotient: 1 2 ÷ 1 6 . Figure 4.5. Notice, there are three 1 6 1 6 tiles in 1 2 , 1 2 , so 1 2 ÷ 1 6 = 3 . 1 2 ÷ 1 6 = 3 .

Example 4.31

Model: 1 4 ÷ 1 8 . 1 4 ÷ 1 8 .

We want to determine how many 1 8 1 8 s are in 1 4 . 1 4 . Start with one 1 4 1 4 tile. Line up 1 8 1 8 tiles underneath the 1 4 1 4 tile.

There are two 1 8 1 8 s in 1 4 . 1 4 .

So, 1 4 ÷ 1 8 = 2 . 1 4 ÷ 1 8 = 2 .

Try It 4.61

Model: 1 3 ÷ 1 6 . 1 3 ÷ 1 6 .

Try It 4.62

Model: 1 2 ÷ 1 4 . 1 2 ÷ 1 4 .

Example 4.32

Model: 2 ÷ 1 4 . 2 ÷ 1 4 .

We are trying to determine how many 1 4 1 4 s there are in 2 . 2 . We can model this as shown.

Because there are eight 1 4 1 4 s in 2 , 2 ÷ 1 4 = 8 . 2 , 2 ÷ 1 4 = 8 .

Try It 4.63

Model: 2 ÷ 1 3 2 ÷ 1 3

Try It 4.64

Model: 3 ÷ 1 2 3 ÷ 1 2

Let’s use money to model 2 ÷ 1 4 Figure 4.6. So we can think of 2 ÷ 1 4 2 ÷ 1 4 as, “How many quarters are there in two dollars?” One dollar is 4 4 quarters, so 2 2 dollars would be 8 8 quarters. So again, 2 ÷ 1 4 = 8 . 2 ÷ 1 4 = 8 .

Using fraction tiles, we showed that 1 2 ÷ 1 6 = 3 . 1 2 ÷ 1 6 = 3 . Notice that 1 2 · 6 1 = 3 1 2 · 6 1 = 3 also. How are 1 6 1 6 and 6 1 6 1 related? They are reciprocals. This leads us to the procedure for fraction division.

Fraction Division

If a , b , c , a , b , c , and d d are numbers where b ≠ 0 , c ≠ 0 , b ≠ 0 , c ≠ 0 , and d ≠ 0 , d ≠ 0 , then

a b ÷ c d = a b · d c a b ÷ c d = a b · d c

To divide fractions, multiply the first fraction by the reciprocal of the second.

We need to say b ≠ 0 , c ≠ 0 b ≠ 0 , c ≠ 0 and d ≠ 0 d ≠ 0 to be sure we don’t divide by zero.

Example 4.33

Divide, and write the answer in simplified form: 2 5 ÷ ( − 3 7 ) . 2 5 ÷ ( − 3 7 ) .

Try It 4.65

Divide, and write the answer in simplified form: 3 7 ÷ ( − 2 3 ) . 3 7 ÷ ( − 2 3 ) .

Try It 4.66

Divide, and write the answer in simplified form: 2 3 ÷ ( − 7 5 ) . 2 3 ÷ ( − 7 5 ) .

Example 4.34

Divide, and write the answer in simplified form: 2 3 ÷ n 5 . 2 3 ÷ n 5 .

Try It 4.67

Divide, and write the answer in simplified form: 3 5 ÷ p 7 . 3 5 ÷ p 7 .

Try It 4.68

Divide, and write the answer in simplified form: 5 8 ÷ q 3 . 5 8 ÷ q 3 .

Example 4.35

Divide, and write the answer in simplified form: − 3 4 ÷ ( − 7 8 ) . − 3 4 ÷ ( − 7 8 ) .

Try It 4.69

Divide, and write the answer in simplified form: − 2 3 ÷ ( − 5 6 ) . − 2 3 ÷ ( − 5 6 ) .

Try It 4.70

Divide, and write the answer in simplified form: − 5 6 ÷ ( − 2 3 ) . − 5 6 ÷ ( − 2 3 ) .

Example 4.36

Divide, and write the answer in simplified form: 7 18 ÷ 14 27 . 7 18 ÷ 14 27 .

Try It 4.71

Divide, and write the answer in simplified form: 7 27 ÷ 35 36 . 7 27 ÷ 35 36 .

Try It 4.72

Divide, and write the answer in simplified form: 5 14 ÷ 15 28 . 5 14 ÷ 15 28 .

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Section 4.2 Exercises

Practice makes perfect.

In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers.

15 20 15 20

12 18 12 18

− 40 88 − 40 88

− 63 99 − 63 99

− 108 63 − 108 63

− 104 48 − 104 48

120 252 120 252

182 294 182 294

− 168 192 − 168 192

− 140 224 − 140 224

11 x 11 y 11 x 11 y

15 a 15 b 15 a 15 b

− 3 x 12 y − 3 x 12 y

− 4 x 32 y − 4 x 32 y

14 x 2 21 y 14 x 2 21 y

24 a 32 b 2 24 a 32 b 2

In the following exercises, use a diagram to model.

1 2 · 2 3 1 2 · 2 3

1 2 · 5 8 1 2 · 5 8

1 3 · 5 6 1 3 · 5 6

1 3 · 2 5 1 3 · 2 5

In the following exercises, multiply, and write the answer in simplified form.

2 5 · 1 3 2 5 · 1 3

1 2 · 3 8 1 2 · 3 8

3 4 · 9 10 3 4 · 9 10

4 5 · 2 7 4 5 · 2 7

− 2 3 ( − 3 8 ) − 2 3 ( − 3 8 )

− 3 4 ( − 4 9 ) − 3 4 ( − 4 9 )

− 5 9 · 3 10 − 5 9 · 3 10

− 3 8 · 4 15 − 3 8 · 4 15

7 12 ( − 8 21 ) 7 12 ( − 8 21 )

5 12 ( − 8 15 ) 5 12 ( − 8 15 )

( − 14 15 ) ( 9 20 ) ( − 14 15 ) ( 9 20 )

( − 9 10 ) ( 25 33 ) ( − 9 10 ) ( 25 33 )

( − 63 84 ) ( − 44 90 ) ( − 63 84 ) ( − 44 90 )

( − 33 60 ) ( − 40 88 ) ( − 33 60 ) ( − 40 88 )

4 · 5 11 4 · 5 11

5 · 8 3 5 · 8 3

3 7 · 21 n 3 7 · 21 n

5 6 · 30 m 5 6 · 30 m

−28 p ( − 1 4 ) −28 p ( − 1 4 )

−51 q ( − 1 3 ) −51 q ( − 1 3 )

−8 ( 17 4 ) −8 ( 17 4 )

14 5 ( −15 ) 14 5 ( −15 )

−1 ( − 3 8 ) −1 ( − 3 8 )

( −1 ) ( − 6 7 ) ( −1 ) ( − 6 7 )

( 2 3 ) 3 ( 2 3 ) 3

( 4 5 ) 2 ( 4 5 ) 2

( 6 5 ) 4 ( 6 5 ) 4

( 4 7 ) 4 ( 4 7 ) 4

In the following exercises, find the reciprocal.

− 5 17 − 5 17

− 6 19 − 6 19

−13 −13

−19 −19

−1 −1

Fill in the chart.

In the following exercises, model each fraction division.

1 2 ÷ 1 4 1 2 ÷ 1 4

1 2 ÷ 1 8 1 2 ÷ 1 8

2 ÷ 1 5 2 ÷ 1 5

3 ÷ 1 4 3 ÷ 1 4

In the following exercises, divide, and write the answer in simplified form.

3 4 ÷ 2 3 3 4 ÷ 2 3

4 5 ÷ 3 4 4 5 ÷ 3 4

− 4 5 ÷ 4 7 − 4 5 ÷ 4 7

− 3 4 ÷ 3 5 − 3 4 ÷ 3 5

− 7 9 ÷ ( − 7 9 ) − 7 9 ÷ ( − 7 9 )

− 5 6 ÷ ( − 5 6 ) − 5 6 ÷ ( − 5 6 )

3 4 ÷ x 11 3 4 ÷ x 11

2 5 ÷ y 9 2 5 ÷ y 9

5 8 ÷ a 10 5 8 ÷ a 10

5 6 ÷ c 15 5 6 ÷ c 15

5 18 ÷ ( − 15 24 ) 5 18 ÷ ( − 15 24 )

7 18 ÷ ( − 14 27 ) 7 18 ÷ ( − 14 27 )

7 p 12 ÷ 21 p 8 7 p 12 ÷ 21 p 8

5 q 12 ÷ 15 q 8 5 q 12 ÷ 15 q 8

8 u 15 ÷ 12 v 25 8 u 15 ÷ 12 v 25

12 r 25 ÷ 18 s 35 12 r 25 ÷ 18 s 35

−5 ÷ 1 2 −5 ÷ 1 2

−3 ÷ 1 4 −3 ÷ 1 4

3 4 ÷ ( −12 ) 3 4 ÷ ( −12 )

2 5 ÷ ( −10 ) 2 5 ÷ ( −10 )

−18 ÷ ( − 9 2 ) −18 ÷ ( − 9 2 )

−15 ÷ ( − 5 3 ) −15 ÷ ( − 5 3 )

1 2 ÷ ( − 3 4 ) ÷ 7 8 1 2 ÷ ( − 3 4 ) ÷ 7 8

11 2 ÷ 7 8 · 2 11 11 2 ÷ 7 8 · 2 11

Everyday Math

Baking A recipe for chocolate chip cookies calls for 3 4 3 4 cup brown sugar. Imelda wants to double the recipe.

ⓐ How much brown sugar will Imelda need? Show your calculation. Write your result as an improper fraction and as a mixed number.

ⓑ Measuring cups usually come in sets of 1 8 , 1 4 , 1 3 , 1 2 , 1 8 , 1 4 , 1 3 , 1 2 , and 1 1 cup. Draw a diagram to show two different ways that Imelda could measure the brown sugar needed to double the recipe.

Baking Nina is making 4 4 pans of fudge to serve after a music recital. For each pan, she needs 2 3 2 3 cup of condensed milk.

• ⓐ How much condensed milk will Nina need? Show your calculation. Write your result as an improper fraction and as a mixed number.
• ⓑ Measuring cups usually come in sets of 1 8 , 1 4 , 1 3 , 1 2 , 1 8 , 1 4 , 1 3 , 1 2 , and 1 1 cup. Draw a diagram to show two different ways that Nina could measure the condensed milk she needs.

Portions Don purchased a bulk package of candy that weighs 5 5 pounds. He wants to sell the candy in little bags that hold 1 4 1 4 pound. How many little bags of candy can he fill from the bulk package?

Portions Kristen has 3 4 3 4 yards of ribbon. She wants to cut it into equal parts to make hair ribbons for her daughter’s 6 6 dolls. How long will each doll’s hair ribbon be?

Writing Exercises

Explain how you find the reciprocal of a fraction.

Explain how you find the reciprocal of a negative fraction.

Rafael wanted to order half a medium pizza at a restaurant. The waiter told him that a medium pizza could be cut into 6 6 or 8 8 slices. Would he prefer 3 3 out of 6 6 slices or 4 4 out of 8 8 slices? Rafael replied that since he wasn’t very hungry, he would prefer 3 3 out of 6 6 slices. Explain what is wrong with Rafael’s reasoning.

Give an example from everyday life that demonstrates how 1 2 · 2 3 1 2 · 2 3 is 1 3 . 1 3 .

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?

Trending Post : Teaching Fractions with Food

Multiplying Fractions Word Problems | 10 Real Life Examples | PDF

Multiplying fractions word problems.

I guess maybe some students get it from their parents. After all, I know that I have been known to grumble about things I learned in school, but never used in real life. I’m sure when it comes to word problems for multiplying fractions, that phrase may have passed your lips too.

But, we do multiply fractions in real life and the real world sometimes. For example, recipes! Recipes and adjusting, maybe cutting a recipe in half or doubling it, those are real world examples of multiplying fractions.

Most schools begin introducing fractions around 3rd grade, with multiplying fractions word problems beginning in 6th grade.

Here are 10 multiplying fractions word problems to work on multiplying fractions using real-life examples.

Have you ever heard, “I will never use this”?

It is important for children to see how math is used in everyday life. And word problems are one way to do this.

Multiplying Fractions

Multiplying Fractions seems like a foreign concept to many students, but it is a concept we use.

Have you ever wanted to only make 1/2 of a recipe? If so, you have probably multiplying fractions…..especially if the recipe called for 3/4 a cup of flour.

So today, we are going to finish up our multiplying fraction unit with some word problems. I am doing the activity in the post as well as some of the fraction games and activities below.

Grab my other free multiplying fractions by fractions activities.

• How to Multiply Fractions by Fractions – Step by Step Instructions with Free Printable
• Here is a Multiplying Fractions BINGO Game That’s Perfect for Extra Practice
• 3 Cut and Paste Worksheets For Multiplying Fractions Practice
• Free Printable Fraction Game For Multiplying Fractions
• Many More on my TeachersPayTeachers page for Multiplying Fractions

Preparing the Fractions Real World Problems

These task cards are easy to prepare.

• Print off on copy paper.
• Have children cut them out and glue them in their math journal.
• Finally, provide them pencils, glue, and colored pencils. and you are ready to go.

Multiplying Fractions Word Problems Example

Rachel’s  Famous  Cookies sold  2/3 as many sugar cookies as peanut butter cookies. If they sold 1/4  of a box of peanut butter cookies, how many boxes of sugar cookies did they sell?

The first step is to look at we know. We know that they sold 1/4 a box of peanut butter cookies. But they only sold 2/3 of the 1/4 when it came to the sugar cookies.

So if we want to start with a diagram, we can begin by drawing a box of cookies and coloring in 1/4.

Many students require a multisensory approach to learning. It’s not just enough to talk about something and hear it. They have to see it. This activity works as a visual graphic organizer of sorts, so that the student can visualize what is going on.

Next, we can color in 2/3.

Finally, we look and see what part overlaps, and this is the answer! Two out of the 12 squares overlap, so our answer is 2/12 or 1/6 when the fraction is simplified . But using the squares on the paper and coloring with overlap, we have completed our first multiplying fractions word problem.

Using Fractions in Real Life

I’m a firm believer that children should not be given multiplying fractions word problems that require the same operation each time.

That is not real life, and that does teach them to learn what needs to be done to solve the problem. We need to give them the confidence that they can apply this knowledge to different situations and word problems.

That’s why I am including more than that in the multiplying fractions word problems worksheets.

So even though this printable is for practicing multiplying fractions with word problems there are a few word problems where multiplication is not used. Here is one example.

Luciana gave 1/4 of the cake to one friend, and 1/3 another friend. How much of the cake is left if she started with a whole cake?

This word problem has the children subtracting to figure out the answer.

• We know that Luciana started with a whole cake, which equals one. So we want to begin by drawing a square.
• The next thing we have to figure out is how many parts we need to divide it up into. Since we now we will be subtracting 1/4 and 1/3 we will need to get the Least Common Multiple. The multiples of three and four are…..

4: 4, 8, 12

3: 3, 6, 9, 12

As you can see 12 is the least common multiple. So our square needs to have 12 equal parts.

3. Next, we will need to find equivalent fractions for both of our fractions.

1/4 x 3/3 = 3/12 and 1/3 x 4/4 = 4/12.

4. Now all that is left is to subtract 3 part and then 4 parts.

5. Finally, we can see that there 5/12 of the cake left.

Word Problems are an important part of math instruction, and how we do math in everyday life. Enjoy working through these real life problems with your children.

The printable that accompanies this activity is below. Here you go, your free multiplying fractions word problems PDF. This free printable includes multiplying fractions word problems with answers.

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Long division

Multiplying and dividing rational numbers

Multiplying and dividing fractions

Here you will learn about multiplying and dividing fractions , including calculations involving whole numbers, proper and improper fractions, and mixed numbers.

Students will first learn about multiplying and dividing fractions as a part of number and operations in fractions in elementary school. They continue to build on this knowledge as a part of the number system in middle school.

What is multiplying and dividing fractions?

Multiplying and dividing fractions is multiplying or dividing to solve an equation when one or more of the numbers is written as a fraction. The product and quotient are often fractions. Fractions can be multiplied or divided using models or an algorithm.

Let’s start with multiplying fractions.

For example,

\cfrac{1}{4} \times \cfrac{2}{3}

Using models:

In the model, \cfrac{2}{3} is yellow and \cfrac{1}{4} is blue.

The product is where the fractions overlap in green.

The model shows \cfrac{2}{3} of \cfrac{1}{4}, so \cfrac{1}{4} \times \cfrac{2}{3}=\cfrac{2}{12}.

Using the algorithm:

To multiply fractions , you multiply the numerators together, and multiply the denominators together: \cfrac{1}{4} \times \cfrac{2}{3}=\cfrac{2}{12}.

You can also divide fractions with a model or an algorithm.

\cfrac{1}{2}\div \cfrac{2}{3}

Think of this equation as how many \cfrac{2}{3} fit into \cfrac{1}{2}.

In the model, \cfrac{1}{2} is orange and \cfrac{2}{3} is yellow.

To divide into equal groups, use the equivalent fractions \cfrac{3}{6} and \cfrac{4}{6}.

The quotient is the final fraction formed when \frac{3}{6} is put into a group of \cfrac{4}{6}.

Three out of the four parts are filled, so \cfrac{3}{6}\div \cfrac{4}{6} = \cfrac{3}{4}.

KEEP the first fraction, FLIP the second fraction, CHANGE to multiplication.

\cfrac{1}{2} \div \cfrac{2}{3}

Keep the dividend (first fraction): \cfrac{1}{2}

Take the reciprocal of the divisor (flip the second fraction): \cfrac{2}{3} → \cfrac{3}{2}

Change to multiplication: \cfrac{1}{2} \times \cfrac{3}{2}

Multiply the fractions: \cfrac{1}{2} \times \cfrac{3}{2}=\cfrac{3}{4}

\cfrac{1}{2} \div \cfrac{2}{3}=\cfrac{3}{4}

Since \cfrac{1}{2} is smaller than \cfrac{2}{3}, the answer makes sense. A smaller number divided by a larger number, will have a quotient of less than 1.

Note that, unlike when you add and subtract fractions, you do not need a common denominator to multiply and divide fractions when using the algorithm .

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Common Core State Standards

How does this relate to 4th grade math, 5th grade math, and 6th grade math?

• Grade 4 – Number and Operations – Fractions (4.NF.B.4b) ​​Understand a multiple of \cfrac{a}{b} as a multiple of \cfrac{1}{b}, and use this understanding to multiply a fraction by a whole number.
• Grade 5 – Number and Operations – Fractions (5.NF.B.4b) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
• Grade 6 – Number System (6.NS.A) Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

How to multiply with fractions

In order to multiply fractions with models:

• Draw one fraction horizontally and the other vertically.
• Connect the fractions all the way across with 2 different colors.
• Count the overlap.

If possible, simplify or convert to a mixed number.

In order to multiply fractions, whole numbers and mixed numbers with the algorithm:

Convert whole numbers and mixed numbers to improper fractions.

Multiply the numerators together.

Multiply the denominators together.

In order to solve multiplying fraction word problems:

Create an equation to model the problem.

[FREE] Fraction Operations Check for Understanding Quiz (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

Multiplying and dividing fractions examples

Example 1: multiplying a fraction by a fraction with a model.

Solve \cfrac{3}{5} \times \cfrac{1}{8} with a model.

Draw a rectangle. Divide one side into fifths.

Divide the other side into eighths.

2 Connect the fractions all the way across with 2 different colors.

Shade in \cfrac{3}{5} with yellow and \cfrac{1}{8} with blue.

3 Count the overlap.

The model shows \cfrac{1}{8} of \cfrac{3}{5}, so \cfrac{3}{5} \times \cfrac{1}{8}=\cfrac{3}{40}, because there are 3 green squares and the whole has 40 squares in total.

4 If possible, simplify or convert to a mixed number.

3 and 40 only have a common factor of 1, so the fraction cannot be simplified.

So, \; \cfrac{3}{5} \times \cfrac{1}{8}=\cfrac{3}{40}

Example 2: multiplying a fraction by a fraction with the algorithm

Solve \cfrac{1}{3} \times \cfrac{5}{6}.

There are no whole numbers or mixed numbers that need to be converted.

\cfrac{1}{3} \times \cfrac{5}{6}=\cfrac{5}{}

\cfrac{1}{3} \times \cfrac{5}{6}=\cfrac{5}{18}

5 and 18 only have a factor of 1, so the fraction cannot be simplified.

So, \cfrac{1}{3} \times \cfrac{5}{6}=\cfrac{5}{18}.

Example 3: multiplying a whole number by a fraction with the algorithm

Solve \cfrac{6}{10} \times 3.

Write 3 as an improper fraction, 3=\cfrac{3}{1}.

\cfrac{6}{10} \times \cfrac{3}{1}=\cfrac{18}{}

\cfrac{6}{10} \times \cfrac{3}{1}=\cfrac{18}{10}

The numerator is greater than the denominator, so the improper fraction can be converted to a mixed number.

\cfrac{18}{10}=1 \cfrac{8}{10}

The product can be simplified. Both 8 and 10 have a common factor of 2.

\cfrac{8 \; \div \; 2}{10 \; \div \; 2}=\cfrac{4}{5}

So, \cfrac{6}{10} \times \cfrac{3}{1}=1 \cfrac{4}{5}.

Example 4: multiplying a mixed number by a fraction with the algorithm

Solve \cfrac{5}{12} \times 2 \cfrac{3}{4}.

Convert the mixed number to an improper fraction.

2 \cfrac{3}{4}=\cfrac{11}{4}

\cfrac{5}{12} \times \cfrac{11}{4}=\cfrac{55}{}

\cfrac{5}{12} \times \cfrac{11}{4}=\cfrac{55}{48}

\cfrac{55}{48}=1 \cfrac{7}{48}

The product cannot be simplified. 7 and 48 only have a common factor of 1.

So, \cfrac{5}{12} \times \cfrac{11}{4}=\cfrac{55}{48} or 1 \cfrac{7}{48}.

Example 5: word problem multiplying with fractions

Mr. Sanchez has a rectangular patio in his back yard that measures 2 \cfrac{2}{5}m by 4 \cfrac{1}{2}m. What is the area of Mr. Sanchez’s patio?

Area of a rectangle is l \times w, so use 2 \cfrac{2}{5} \times 4 \cfrac{1}{2} to solve.

Convert the mixed numbers to improper fractions.

2 \cfrac{2}{5}=\cfrac{12}{5} \quad and \quad 4 \cfrac{1}{2}=\cfrac{9}{2}

\cfrac{12}{5} \times \cfrac{9}{2}=\cfrac{108}{}

\cfrac{12}{5} \times \cfrac{9}{2}=\cfrac{108}{10}

\cfrac{108}{10}=10 \cfrac{8}{10}

The product can be simplified. 8 and 10 have a common factor of 2.

So, \cfrac{12}{5} \times \cfrac{9}{2}=\cfrac{108}{10} or 10 \cfrac{4}{5}.

How to divide with fractions

In order to divide fractions, whole numbers, and mixed numbers with the algorithm:

• Change the whole numbers and mixed numbers to improper fractions.

Take the reciprocal (flip) of the divisor (second fraction).

Change the division sign to a multiplication sign.

Multiply the fractions together.

In order to solve dividing fraction word problems:

Change any mixed numbers to an improper fraction.

Take the reciprocal (flip) of the divisor (second fractions).

Example 6: dividing a fraction by a fraction

Divide the numbers \cfrac{1}{3} \div \cfrac{1}{6}.

\cfrac{1}{6} → \cfrac{6}{1}

\cfrac{1}{3} \times \cfrac{6}{1}

\cfrac{1}{3} \times \cfrac{6}{1}=\cfrac{6}{3}

\cfrac{6}{3}=2.

This can also be solved with a model.

You can think of this equation as how many \cfrac{1}{6} fit into \cfrac{1}{3}.

In the model, \cfrac{1}{3} is yellow and \cfrac{1}{6} is orange.

To divide into equal groups, the fractional pieces need to be the same size.

Use \cfrac{2}{6} and \cfrac{1}{6} to solve.

The quotient is the final fraction formed when \cfrac{2}{6} is put into groups of \cfrac{1}{6}.

Two groups of \cfrac{1}{6} are in \cfrac{2}{6}, so \cfrac{2}{6} \div \cfrac{1}{6}=2.

Example 7: dividing a fraction by a whole number

Divide the numbers \cfrac{1}{5} \div 4.

\cfrac{4}{1} → \cfrac{1}{4}

Change the division sign to the multiplication sign.

\cfrac{1}{5} \times \cfrac{1}{4}

\cfrac{1}{5} \times \cfrac{1}{4}=\cfrac{1}{20}

\cfrac{1}{20} is in its simplest form and cannot be changed into a mixed number.

This can also be solved with a model. \cfrac{1}{5} divided into equal groups of 4 creates twentieths.

Example 8: dividing a mixed number by a mixed number

Divide the numbers 2 \cfrac{3}{4} \div 1 \cfrac{1}{12}.

Change the mixed number to an improper fraction.

2 \cfrac{3}{4}=\cfrac{11}{4} \quad and \quad 1 \cfrac{1}{12}=\cfrac{13}{12}

\cfrac{13}{12} → \cfrac{12}{13}

\cfrac{11}{4} \times \cfrac{12}{13}

\cfrac{11}{4} \times \cfrac{12}{13}=\cfrac{132}{52}

If possible, simplify or convert to a mixed number (mixed fraction).

\cfrac{132}{52}=2 \cfrac{28}{52}

The fraction can be simplified. Both 28 and 52 have a factor of 4.

\cfrac{28 \; \div \; 4}{52 \; \div \; 4}=\cfrac{7}{13}

So, \cfrac{11}{4} \times \cfrac{12}{13}=\cfrac{132}{52} or 2 \cfrac{7}{13}.

Example 9: word problem dividing with fractions

Each cupcake needs \cfrac{1}{4} cup of icing. How many cupcakes can be decorated with 12 cups of icing?

12 \div \cfrac{1}{4}= \; ?

The whole number 12 should be changed to an improper fraction.

12=\cfrac{12}{1}

\cfrac{1}{4} → \cfrac{4}{1}

\cfrac{12}{1} \times \cfrac{4}{1}

\cfrac{12}{1} \times \cfrac{4}{1}=\cfrac{48}{1}

\cfrac{48}{1}=48 which is a whole number.

12 cups of icing will decorate 48 cupcakes.

Teaching tips for multiplying and dividing fractions

• For elementary students, multiplying and dividing fractions can be a challenging topic. This type of multiplication and division does not always lend itself well to the idea of repeated addition or sharing into equal groups, which are ideas students rely on for whole number multiplication and division. As much as possible, use hands-on visual models and/or digital models so that students can understand what multiplication and division of fractions is. Taking time to do this in the beginning will benefit students when they begin to encounter word problems and real world situations with fractions.
• Highlight patterns within and between multiplication and division of fractions as students are learning. Encourage students to be pattern-seekers themselves. This will help them make sense of the steps involved in multiplying and dividing fractions and understand why the algorithms work.
• Use a variety of activities when teaching multiplying and dividing fractions, instead of relying on just practice worksheets.

Our favorite mistakes

Related fractions operations lessons

• Fractions operations
• Adding fractions
• Subtracting fractions
• Adding and subtracting fractions
• Multiplying fractions
• Dividing fractions
• Reciprocal math
• Fraction word problems
• Multiplicative inverse
• Interpret fractions as division

Practice multiplying and dividing fractions questions

1. Solve \cfrac{3}{4} \times \cfrac{2}{5}.

To solve using a model, draw a rectangle. Divide one side into fourths.

Divide the other side into fifths.

Shade in \cfrac{3}{4} with yellow and \cfrac{2}{5} with blue.

The model shows \cfrac{2}{5} of \cfrac{3}{4}, so \cfrac{3}{4} \times \cfrac{2}{5}=\cfrac{6}{20}, because there are 6 green squares and the whole has 20 squares in total.

The product can be simplified.

Both 6 and 20 have a factor of 2, so they can be divided by 2\text{:} \; \cfrac{6 \; \div \; 2}{20 \; \div \; 2}=\cfrac{3}{10}.

So, \cfrac{3}{4} \times \cfrac{2}{5}=\cfrac{6}{20} or \cfrac{3}{10}.

2. Solve \cfrac{3}{8} \times \cfrac{4}{10}.

Multiply the numerators together: \cfrac{3}{8} \times \cfrac{4}{10}=\cfrac{12}{}.

Then, multiply the denominators together: \cfrac{3}{8} \times \cfrac{4}{10}=\cfrac{12}{80}.

The product can be simplified. 12 and 80 have a common factor of 4, so they can each be divided by 4\text{:} \; \cfrac{12 \; \div \; 4}{80 \; \div \; 4}=\cfrac{3}{20}.

So, \cfrac{3}{8} \times \cfrac{4}{10}=\cfrac{12}{80} or \cfrac{3}{20}.

3. Solve 3 \times \cfrac{4}{6}.

Then, multiply the numerators together: \cfrac{3}{1} \times \cfrac{4}{6}=\cfrac{12}{}.

Then, multiply the denominators together: \cfrac{3}{1} \times \cfrac{4}{6}=\cfrac{12}{6}.

So, \cfrac{3}{1} \times \cfrac{4}{6}=\cfrac{12}{6} or 2.

4. Solve 2 \cfrac{5}{12} \times 1 \cfrac{1}{2}. Write the product as a mixed number in lowest terms.

2 \cfrac{5}{12}=\cfrac{29}{12} \quad and \quad 1 \cfrac{1}{2}=\cfrac{3}{2}

Then, multiply the numerators together: \cfrac{29}{12} \times \cfrac{3}{2}=\cfrac{87}{}.

Then, multiply the denominators together: \cfrac{29}{12} \times \cfrac{3}{2}=\cfrac{87}{24}.

Both 15 and 24 have a factor of 3, so they can be divided by 3\text{:} \; \cfrac{15 \; + \; 3}{24 \; \div \; 3}=\cfrac{5}{8}. So, \cfrac{29}{12} \times \cfrac{3}{2}=\cfrac{87}{24} or 3 \cfrac{5}{8}.

5. Solve \cfrac{3}{10} \div \cfrac{1}{5}. Write the product in lowest terms.

Keep the dividend (first fraction): \cfrac{3}{10}

Take the reciprocal of the divisor (flip the second fraction): \cfrac{1}{5} → \cfrac{5}{1}

Change to multiplication: \cfrac{3}{10} \times \cfrac{5}{1}

Multiply the fractions: \cfrac{3}{10} \times \cfrac{5}{1}=\cfrac{15}{10}

Simplify and convert to a mixed number: \cfrac{15}{10}=1 \cfrac{5}{10}=1 \cfrac{1}{2}

You can think of this equation as how many \cfrac{1}{5} fit into \cfrac{3}{10}.

In the model, \cfrac{3}{10} is yellow and \cfrac{1}{5} is orange.

Use \cfrac{3}{10} and \cfrac{2}{10} to solve.

The quotient is the final fraction formed when \cfrac{3}{10} is put into groups of \cfrac{2}{10}.

The three yellow tenths, fit into a group of 2 tenths, with one out of two in the second group, so \cfrac{3}{10} \div \cfrac{2}{10}=1 \cfrac{1}{2}.

6. Solve \cfrac{7}{8} \div 3.

Keep the dividend (first fraction): \cfrac{7}{8}

Take the reciprocal of the divisor (flip the second fraction): \cfrac{3}{1} → \cfrac{1}{3}

Change to multiplication: \cfrac{7}{8} \times \cfrac{1}{3}

Multiply the fractions: \cfrac{7}{8} \times \cfrac{1}{3}=\cfrac{7}{24}

Simplify and convert to a mixed number: \cfrac{7}{24} is in its lowest terms.

7. Solve 1\cfrac{5}{6}\div 2\cfrac{2}{3}. Write the product in lowest terms.

Change the mixed numbers to improper fractions:

1 \cfrac{5}{6}=\cfrac{11}{6} \quad and \quad 2 \cfrac{2}{3}=\cfrac{8}{3}

Keep the dividend (first fraction): \cfrac{11}{6}

Take the reciprocal of the divisor (flip the second fraction): \cfrac{8}{3} → \cfrac{3}{8}

Change to multiplication: \cfrac{11}{6} \times \cfrac{3}{8}

Multiply the fractions: \cfrac{11}{6} \times \cfrac{3}{8}=\cfrac{33}{48}

Change back into a mixed number:

In \cfrac{33}{48}, the numerator is less than the denominator, so it will not be a mixed number.

Simplify: \cfrac{33 \; \div \; 3}{48 \; \div \; 3}=\cfrac{11}{16}, so the answer in lowest terms is \cfrac{11}{16}.

8. Jenny is making bracelets. She uses 1 \cfrac{3}{4} \, \text{ft} of string for each bracelet. How many complete bracelets can she make with 20 \, \text{ft} of string?

3 bracelets

10 bracelets

11 bracelets

20 bracelets

Create the equation 20 \div 1 \cfrac{3}{4} = \; ?

Keep the dividend (first fraction): 20 = \cfrac{20}{1}

Take the reciprocal of the divisor (flip the second fraction): \cfrac{7}{4} → \cfrac{4}{7}

Change to multiplication: \cfrac{20}{1} \times \cfrac{4}{7}

Multiply the fractions: \cfrac{20}{1} \times \cfrac{4}{7}=\cfrac{80}{7}

Change back into a mixed number: \cfrac{80}{7}=11 \cfrac{3}{7}

Simplify: \cfrac{3}{7} is in lowest terms, so the answer is 11 \cfrac{3}{7}.

Jenny can make 11 complete bracelets.

Multiplying and dividing fractions FAQs

For multiplying fractions, you multiply the numerators together and the denominators together, but you do not take the reciprocal of either fraction. For dividing fractions, you multiply by using the reciprocal of the divisor (the second fraction).

Students should know and use the following vocabulary… ◌ Numerator: the top number ◌ Denominator: the bottom number ◌ Product: the answer when multiplying ◌ Quotient: the answer when dividing

Although you can encourage students to do it, lowest terms is not a requirement for their understanding of this skill. Students can successfully multiply and divide fractions without using the greatest common factor (GCF) to simplify the products to their lowest terms. However, each state has different expectations of when students should use lowest terms. Refer to state standards for clarification.

The next lessons are

• Algebraic expression

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• Fifth Grade lessons
• How to multiply fractions word problems

" class="arrow-title-img"> How to multiply fractions word problems

• INTRODUCTION
• Step 1 IDENTIFY THE PROBLEM
• Step 2 STRATEGIZE
• Step 3 SET UP
• Step 4 PROVIDE A SOLUTION
• Step 5 CHECK YOUR WORK
• Examples Examples on how to multiply fractions word problems

Get more contents on this skill...

Here is a simple guide on how to multiply fraction word problems in Grade 5 . This exciting step-by-step guide will offer a well-structured and less complex way of multiplying fraction word problems effortlessly.

In addition, we are here to encourage fifth graders to better understand the relationships between the quantities described by the problem. Thus, making it easier for them to multiply all fraction word problems they encounter.

Most importantly, your kids will aptly transfer the skills they’ll learn from this guide to tackle tasks that include structurally similar but more challenging word problems.

When representing and solving our super exciting word problems, your kids will discover that it is easy to differentiate between irrelevant and relevant information in any fraction multiplication word problem.

Steps on how to solve multiplication of fractions word problems

The purpose of these steps on how to solve multiplication of fractions word problems is to actively engage 5th graser’s minds to understand and solve word problems effortlessly and effectively.

Besides, we believe that providing them with sufficient guidance on how to multiply fractions word problems will unravel the diverse difficulties most learners face when they encounter complex multiplying fractions word problems.

As a result, we have attached some exciting examples below to show them how the process works.

Step 1: IDENTIFY THE PROBLEM

To identify the problem, we’ll first figure out the important fractions and keywords in the word problem. Use these keywords to determine whether the problem involves multiplication or requires any other operation.

However, when multiplying fractions, we look for common keywords such as “of,” “times,” “product of,” “how many,” “how much,” etc.

Note : One key Element for learners to understand is that they should not always rely on keywords alone . That is to say; the same keyword can have different meanings in different word problems . For this reason, we reiterate on the importance of reading the question very carefully to understand the situation that the word problem is describing , then figure out exactly which operation to use

Step 2: STRATEGIZE OR GATHER RELEVANT INFORMATION

How will you solve or tackle the problem?

• As discussed in step 1 above, the keyword(s) in the word problem will enable you to determine if you need to multiply or perform any other operation.
• Note that you must not rely only on keywords . Also, try to understand the situation that the problem is describing .
• After knowing which operation you will perform, construct short expressions/sentences representing the given word problem.

Step 3: CREATE THE EQUATION

Here, we need to compose a numerical expression /a mathematical equation representing the information in the word problem.

Step 4: PROVIDE A SOLUTION

From step 3 above, multiply the numerators and the denominators across. Remember that when multiplying fractions, a common denominator is not needed. Simplify the fraction if possible. Moreover, do not forget to add the unit of measurement to your final answer.

Step 5: CHECK YOUR WORK

Lastly, check if your answer makes sense. For instance, estimate the answer and see if it is close to what you expected. However, if the answer is not what you expected, go back to step one and start all over again.

Find more practices with these tests online

• Multiply numbers ending in zeros word problems
• Multiplying by one digit numbers word problems
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Multiplying two fractions

Multiplying by one digit numbers

Multiply numbers ending in zeroes

Examples on how to multiply fractions word problems

Example one.

Step 1: You see that the important fractions here are and 3. The keyword found in the word problem is “triple.”

Step 2: How will you solve the problem? This problem asks you to triple the original recipe. So, from the situation the problem is describing and its keyword(s), It shows that you have to perform a multiplication operation .

Now, we have to construct short sentences to represent the given word problem.

• Fraction of the cup of corn flour that the recipe calls for =
• Number of times Barbra wants to increase the recipe = 3 times
• Therefore, the quantity of flour that she used = fraction of the cup of corn flour that the recipe calls for × the number of times Barbra wants to increase the recipe

Step 3: At this point, write down a numerical equation to represent the bolded sentence in step 2 above to solve this word problem:

Step 4: From Step 3 above,

• First, convert the whole number above into a fraction by dividing the whole number by 1.
• Then, multiply the numerators across and also multiply the denominators across. Remember that when multiplying fractions, a common denominator is not needed.
• Simplify the fraction if possible.
• Do not forget to add the unit of measurement to your final answer.

So, Barbra will use cup of corn flour.

Step 5: Finally, check if your answer makes sense. For instance, estimate the answer and see if it is close to what you expected. However, if the answer is not what you expected, go back to step one and start all over again.

Example Two

Step 1: You see that, after reading the word problem very carefully, you’ll figure out that the most important fractions here are and . As you read further, the keyword in the word problem is “of.”

Step 2: How will you solve the problem? This problem asks you to find of the original portion of shawarma that Lucy ate. From the situation the problem is describing and its keyword, it shows that you have to perform a multiplication operation .

Now, set up short sentences to represent the given word problem.

• Fraction of the shawarma Grace left =
• Fraction of the shawarma Lucy ate =
• Therefore, the fraction of the shawarma that she ate = the fraction of the shawarma Grace left in the fridge × the fraction of the shawarma Lucy ate

Step 3: Then, write down a numerical equation for each bolded sentence in step 2 above to solve this word problem:

So Lucy ate of the shawarma

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• \frac{1}{2}\cdot\frac{8}{7}
• \frac{-\frac{1}{5}}{\frac{7}{4}}
• descending\:order\:\frac{1}{2},\:\frac{3}{6},\:\frac{7}{2}
• decimal\:to\:fraction\:0.35
• What is a mixed number?
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• How can I compare two fractions?
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• To add or subtract fractions with different denominators, convert the fractions to have a common denominator. Then you can add or subtract the numerators of the fractions, leaving the denominator unchanged.

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Multiplying Fractions in Context - Worded Problems

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

18 November 2022

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Easy Finger Math Tricks to Help Kids Solve Problems

While using your fingers isn't the fastest way to recall a multiplication fact while doing a problem, finger math tricks can help kids figure out how to answer the problem at hand — and as they work on their math, they will eventually learn all the facts by repetition.

Note that before your child can understand other finger tricks, they must be able to count by 2s, 5s, and 10s and multiply by 2s, 3s, and 4s.

Quick Finger Math Tricks for Threes and Fours

The tricks for multiplying by threes and fours are really a matter of counting out the answer on your fingers. As your children count out the answer repeatedly, they'll memorize it and then be able to move on to larger numbers.

Multiplying by Three

Did you realize that all of your fingers have three segments? Therefore, you can figure out anything from 3 x 1 to 3 x 10 by counting the segments on each finger. To start:

• Hold up the number of fingers you're going to multiply by 3. For example, if the problem is 3 x 4 — hold up four fingers.
• Count each segment on each finger you're holding up, and you should come up with 12 — which is the correct answer.

Multiplying by Four

Multiplying by four is the same as multiplying by two — twice. To start:

• Hold up the number of fingers to correspond with the number you are multiplying by four. For example, if you are multiplying 4 x 6 — hold up six fingers.
• Count each finger by two, moving from left to right. Then count each finger again, continuing to count by twos, until you've counted every finger twice.

Helpful Hack To keep track of the fingers you've counted twice, sometimes it's easier to put your finger down as you count the first time, and back up as you count the second time.

Finger Math Tricks for Multiplying by 6, 7, 8, and 9

While numbers one through five are easy for most kids to remember, six and up often pose a problem. This handy trick will make it a little easier to work those problems out.

Multiplying 6, 7, 8, and 9 by Hand

To begin, assign each finger a number. For example, your thumbs represent 6, your index fingers each represent 7, etc. This will remain the same throughout the finger math hack.

Your left hand will represent the first number that you are multiplying and your right hand will represent the second number you are multiplying. In this example, we are multiplying 7 x 8. 

To Determine the Part of Your Answer:

• On your left hand, put down the finger that represents the number you are multiplying as well as any fingers whose number value is less than this figure. In this example, you are multiplying 7 x 8, so the left hand will represent 7. You will drop your index finger (number 7) and your thumb (number 6).
• Similarly, the right hand will represent eight, so you will drop down your middle finger (number 8), your index finger (number 7), and your thumb (number 6).
• Now, just multiply the fingers that are still pointed upwards. In this case, you will have three fingers on your left hand and two on your right, so you will multiply 3 x 2 to get 6. This is the first part of your answer!

To Determine the Second Part of Your Answer:

• Keeping your fingers in the same positions, count how many fingers are folded down. In the 7 x 8 example, you should have five fingers folded. 
• You will count each of these in quantities of ten. So, 10, 20, 30, 40, 50.
• 50 is your answer.

To Determine Your Final Answer:

• Add your two numbers together. In this example, you would add 6 + 50, which gives you 56!

Another Finger Math Trick Just for Nine

There is a trick that works separately, just for multiplying by the number nine.

• To start, hold up all ten fingers, with your palms facing you.
• Assign each finger a number, starting with your left-hand thumb and ending with your right-hand thumb. The left-hand thumb will be one, the left-hand index finger will be two, and so on until you reach the number 10 for your right-hand thumb.
• To tackle a problem, put down the corresponding finger of the number you're multiplying by nine. For example, if you are multiplying 9 x 8, you'd put down the eighth finger (which will be on your right hand).
• Count all the fingers to the left of the finger you have folded down. This will give you 7. This is the first digit of your answer.
• Count all the fingers to the right of the finger you have folded down. This will give you 2. This is the second digit of your answer.
• Put the numbers together! Your answer is 72.

Finger Multiplication Tricks Can Make Math Easy and Fun

While the hope is that your kids will eventually memorize their multiplication charts , using some quick hand tricks for multiplication and letting them count things out on their fingers is not a bad way to learn. It keeps frustration at bay since the answer is always a fingertip away, and the repetition of having to figure it out will help cement those facts into their brains.