simplifying fractions problem solving year 6

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Simplifying Fractions Worksheet

Welcome to our Simplifying Fractions Worksheet page. Here you will find a wide range of graded printable fraction worksheets which will help your child to practice converting fractions to their simplest form.

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Simplifying Fractions Worksheet page

We have a selection of worksheets designed to help your child understand how to simplify fractions.

The sheets are graded so that the easier ones are at the top.

The first sheet in the section is supported and the highest common factor is already provided.

The last two sheets are the hardest and is a great challenge for more able mathematicians.

Using these sheets will help your child to:

• practice simplifying a range of fractions;
• apply their times tables knowledge.

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

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

Quicklinks to...

How to simplify fractions, simplifying fractions worksheets.

• More related Math resources

Simplifying Fractions Online Quiz

Simplifying fractions is also sometimes called reducing fractions to their simplest (or lowest) form.

This involves dividing both the numerator and denominator by a common factor to reduce the fraction to the equivalent fraction with the smallest possible numerator and denominator.

The printable fraction page below contains more support, examples and practice about simplifying fractions.

The Simplifying Fractions calculator will also show you how worked examples of how to simplify a fraction if you are really stuck!

• How to Simplify Fractions support page
• Simplify Fractions Practice Zone

• Simplify Fraction Calculator

These sheets get progressively harder, with sheet 1 being the easiest and sheet 6 being the hardest.

Sheet 7 involves simplifying fractions with negative numerators, negative denominators or both.

• Simplifying Fractions Sheet 1 (supported)
• PDF version
• Simplifying Fractions Sheet 2
• Simplifying Fractions Sheet 3
• Simplifying Fractions Sheet 4
• Simplifying Fractions Sheet 5
• Simplifying Fractions Sheet 6 (harder)
• Simplifying Fractions Sheet 7 (includes negative numbers)

Simplifying Fractions Walkthrough Video

This short video walkthrough shows several problems from our Simplifying Fractions 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!

More Recommended Math Resources

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

Learning Fractions Math Help Page

Here you will find the Math Salamanders free online Math help pages about Fractions.

There is a wide range of help pages including help with:

• fraction definitions;
• equivalent fractions;
• converting improper fractions;
• how to add and subtract fractions;
• how to convert fractions to decimals and percentages;
• how to simplify fractions.
• Learning Fractions Support
• Math Fraction Games

Here is our collection of Math games involving fractions.

These games are suitable for kids aged from 3rd grade and upwards.

Playing games is a great way to learn fraction skills in a fun way.

Fraction equivalence, fraction to decimal conversion and properties of fractions are all explored in our fun games to play.

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'.

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This quick quiz tests your understanding and skill at simplifying fractions.

Fun Quiz Facts

• This quiz has been attemped 1,235 times last academic year. The average (mean) score is 8.8 out of 14 marks.
• Can you beat the mean score?

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Compare and order fractions

Your child will compare fractions and put them in size order.

They will be able to do this with proper fractions (i.e. fractions less than one) and fractions that are greater than one (i.e. improper fractions or mixed numbers ). For example:

 is greater than   is greater than 

Calculate with mixed numbers and fractions with different denominators

Your child will learn to add and subtract fractions with different denominators  (bottom numbers). They will do this by finding equivalent fractions that have the same denominator. For example:

 +   =   +   = 

They will use objects, diagrams, and symbols to solve problems with mixed numbers and fractions, and to explain how they have solved a problem.

Multiply and simplify proper fractions

Your child will be able to multiply pairs of proper fractions (i.e. fractions smaller than 1) together, and then write the answer in its simplest form.

 ×   =   = 

Your child will use objects, diagrams, and symbols in their calculations.

Divide proper fractions by whole numbers

Proper fractions are fractions with a value of less than 1. Your child will be able to divide these kinds of fractions by whole numbers. For example:

Your child will do this using objects, diagrams, and symbols.

Understand the link between fractions, division, and decimals

To find    of 36cm, you would divide 36 by 4 (36cm ÷ 4 = 9 cm).   If you know  of an unknown length is 36cm and you want to find the whole length, you would multiply 36 by 4 (36cm × 4 = 144cm).

Use numbers with 3 decimal places

Your child will understand the value of each digit in numbers with 3 decimal places. They will also be able to multiply and divide numbers by 10, 100, and 1000, giving answers up to 3 decimal places. For example:

9 ÷ 1000 = 0.009   0·734 × 100 = 73.4

Your child will divide decimal numbers by 1-digit whole numbers. At first, they will learn this in practical contexts involving measures and money (for example, 0.65m ÷ 5 = 0.13m).

Multiply numbers with decimal places

Your child will learn to multiply 1-digit numbers with up to 2 decimal places by whole numbers. For example:

2.75 × 2 = 5.5

They will start with simple examples, such as 0.4 × 2 = 0.8, in practical contexts such as using money.

Use written division methods where appropriate

Your child will use written division methods (like long division and short division) in cases where the answer has up to 2 decimal places. You can find out more about these methods on our YouTube channel: see How to do long division and How to do short division .

Round numbers to estimate answers

Your child will round numbers and estimate answers to check their answers to decimal calculations. For example:

2.56 × 5.3 ≈ 2.5 × 5 = 12.5   So, when your child works out the question exactly, they will expect their result to be roughly 12.5. If they get an answer like 1350, they will know something has gone wrong!

Use equivalences between simple fractions, decimals, and percentages

How to help at home

There are lots of ways you can help your child to understand fractions. Here are just a few ideas.

1. Help your child calculate with fractions

They could separate the whole numbers and the fractional parts:

First, add the whole numbers: 3 + 2 = 5.   Then, add the fractional parts:  +   =  .   Finally, add the whole number and fractional parts together to create a mixed number: 5 .

They could turn each mixed number into an improper fraction, then add the improper fractions together, and finally convert the answer back into a mixed number:

First, convert 3   into an improper fraction:  .   Then, convert 2   into an improper fraction:  .   Then, add the improper fractions together:    +      =   .   Finally, turn the answer back into a mixed number:    = 5   .

The same strategies can be applied to subtracting fractions using mixed numbers.

2. Multiply and divide with fractions

In this example, the half is shown on the left by splitting the shape vertically into two equal pieces. The same shape will then be drawn to represent quarters , this time split horizontally into four equal pieces. The diagrams will then be added together to divide the shape into eighths:

The answer can be found where the half and the quarter overlap to make one eighth :

Fraction Calculations in School

3. Calculate with decimals

Your child will continue to practise adding and subtracting with decimal numbers up to 3 decimal places. They will have to understand the effect of multiplying and dividing decimal numbers by 10, 100, 1000, and so on.

Place value charts are a great way to visualise these changes:

Help your child to understand that dividing by 10 means getting ten times smaller, dividing by 100 means getting a hundred times smaller, and so on. The same concept applies to multiplication, but the other way around.

Calculate with numbers that have 3 decimal places in the real world. For example, when you fill the car with petrol, ask your child to tell you what the number is by explaining how many tenths, hundredths, or thousandths it has. Can they round the total price or the total amount of petrol to the nearest whole number, tenth, or hundredth? For example:

If you have 56.784 litres of petrol, you could round to the nearest litre (57L), tenth (56.8L), or hundredth (56.78L).

Money and measures are great for practising using numbers with 2 decimal places. You could show your child your shopping receipt with the total hidden. Ask your child to work out the total cost of the shopping receipt. How much change you would be given if you paid using, for instance, a £10 note?

4. Link fractions, decimals, and percentages

It is important your child understands that decimals and percentages are just other ways to show fractions.

Fraction, Decimal, and Percentage Treasure Hunt

Practise matching percentages, decimals, and fractions on a fun treasure hunt.

5. Multiply fractions and mixed numbers by whole numbers

Your child will multiply proper fractions and mixed numbers by whole numbers.

6. Percentages

Your child will continue to work with percentages. Talk about how ‘percent’ means ‘number of parts per hundred’.

Sales at the shops can provide great real-life opportunities to work with percentages. For example, you could ask your child to help you work out the sale price of an item. If there is 30% off a T-shirt and the full price is £9.99, what is 30% of the full price and what is the sale price?

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Simplifying Fractions for Grade 6

Equivalent fractions math worksheets.

These grade 6 math worksheets provide practice in simplifying fractions , recognizing equivalent fractions and converting fractions to and from mixed numbers.  

Sample Grade 6 Simplifying Fractions Worksheet

More fractions worksheets

Explore all of our fractions worksheets , from dividing shapes into "equal parts" to multiplying and dividing improper fractions and mixed numbers.

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Mastery Fractions Worksheets - Year 6

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

1 December 2016

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Useful for teaching!

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These are great but are there any answer keys?

Brill - thank you.

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Fraction word problems for year 6

A fraction word problems worksheet for year 6. Children are asked to simplify fractions, to add and subtract fractions, to multiply fractions, to divide fractions and to solve problems to find fractions of amounts. Calculations feature proper fractions and include those with different denominators

This one-page problem solving maths worksheet is linked to national curriculum objectives and is ideal for classroom and home learning. Answers are included.

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Simplify fractions: Reasoning and Problem Solving

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Year 6 Fractions A – Equivalent fractions and simplifying – Lesson 1

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Description

In this lesson, children will learn how to simplify fractions into their lowest form and learn how to find the highest common factor. There is a teaching presentation and a differentiated resources with a range of fluency, reasoning and problem solving questions.

Mathematics Year 6:  use common factors to simplify fractions

Differentiation: There are three levels of differentiation in this pack: ‘working towards,’ ‘expected’ and ‘greater depth’.

Level of this Pack: Age: 10-11  England & Wales: Year 6  Scotland: Primary 6  Rep. Ireland: Fifth Class  Australia: Grade 5  USA: Grade 5

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Linked resources:

Year 6 Maths Display Poster – The Fractions Song

Year 6 Fractions A – Equivalent fractions on a number line – Lesson 2

Year 6 Fractions A – Compare & Order (Denominator) – Lesson 3

Year 6 Fractions A – Compare & Order (numerator) – Lesson 4

Year 6 Fractions A – Add and subtract simple fractions – Lesson 5

Year 6 Fractions A – Add and subtract fractions (2) – Lesson 6

Year 6 Fractions A – Add mixed numbers – Lesson 7

Year 6 Fractions B – Mixed questions with fractions – Lesson 5

Year 6 Fractions B – Fraction of an amount – Lesson 6

Year 6 Fractions B – Fraction of an amount – finding the whole – Lesson 7

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Simplify Fractions Year 6 Fractions Free Resource Pack

Step 1: Simplify Fractions Year 6 Resources

Simplify Fractions Year 6 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Autumn Block 3.

What's included in the pack?

This pack includes:

• Simplify Fractions Year 6 Teaching PowerPoint.
• Simplify Fractions Year 6 Varied Fluency with answers.
• Simplify Fractions Year 6 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 6: (6F2)  Use common factors to simplify fractions; use common multiples to express fractions in the same denomination

Differentiation:

Varied Fluency Developing Questions to support simplifying fractions using denominators which are multiples of the numerator. Bar models or fraction walls used in every question. Expected Questions to support simplifying fractions using highest common factors of the numerator and denominator. Involving multiples of any number up to 12 x 12. Some pictorial support given. Greater Depth Questions to support simplifying fractions using highest common factors of the numerator and denominator. Involving multiples of numbers up to 12 x 12 and introducing multiples of 20 and 25. No pictorial support.

Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing Complete the missing parts of a simplified fraction using denominators which are multiples of the numerator. Visual image provided for support. Expected Complete the missing parts of a simplified fraction using the highest common factor of the numerator and denominator. A selection of factors provided. Involving multiples of any number up to 12 x 12. Greater Depth Find two different ways to complete the missing parts of a simplified fraction and identify the highest common factor. Involving multiples of any number up to 12 x 12.

Questions 2, 5 and 8 (Problem Solving) Developing Solve the word problem using knowledge of how to simplify fractions using denominators which are multiples of the numerator. Pictorial support given. Expected Solve the word problem using knowledge of how to simplify fractions using highest common factors of the numerator and denominator. Involves multiples of any number up to 12 x 12. Some pictorial support given. Greater Depth Solve the word problem using knowledge of how to simplify fractions using highest common factors of the numerator and denominator. Involves multiples of any number up to 12 x 12 and introducing multiples of 20 and 25. No pictorial support given.

Questions 3, 6 and 9 (Reasoning) Developing Identify whether a fraction has been simplified correctly using denominators which are multiples of the numerator. Pictorial support given. Expected Identify whether a fraction has been simplified correctly using highest common factors of the numerator and denominator. Involving multiples of any number up to 12 x 12. Some pictorial support given. Greater Depth Identify whether a fraction has been simplified correctly using highest common factors of the numerator and denominator. Involving multiples of any number up to 12 x 12 and introducing multiples of 20 and 25. No pictorial support given.

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