multiplying fractions problem solving year 5

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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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Unit 6: Multiply fractions

About this unit.

Why have just one way to multiply fractions when you can have four? Learn how to use number lines, the fraction model, the area model, and word problems to multiply fractions like a pro.

Multiplication as scaling

• Multiplication as scaling with fractions (Opens a modal)
• Fraction multiplication as scaling examples (Opens a modal)
• Fraction multiplication as scaling Get 5 of 7 questions to level up!

Multiplying fractions and whole numbers

• Multiplying fractions by whole numbers on a number line (Opens a modal)
• Multiplying unit fractions and whole numbers (Opens a modal)
• Multiplying fractions and whole numbers visually (Opens a modal)
• Multiplying fractions and whole numbers (Opens a modal)
• Multiply fractions and whole numbers visually Get 5 of 7 questions to level up!
• Multiply fractions and whole numbers Get 5 of 7 questions to level up!

Multiplying fractions

• Multiplying 2 fractions: fraction model (Opens a modal)
• Multiplying 2 fractions: number line (Opens a modal)
• Multiplying 2 fractions: 5/6 x 2/3 (Opens a modal)
• Represent fraction multiplication with visuals Get 3 of 4 questions to level up!
• Multiplying fractions with visuals Get 3 of 4 questions to level up!
• Multiplying fractions Get 5 of 7 questions to level up!

Multiplying mixed numbers

• Multiplying mixed numbers (Opens a modal)
• Multiply mixed numbers Get 3 of 4 questions to level up!

Area of rectangles with fraction side lengths

• Finding area with fractional sides 1 (Opens a modal)
• Finding area with fractional sides 2 (Opens a modal)
• Area of rectangles with fraction side lengths Get 3 of 4 questions to level up!

Multiplying fractions word problems

• Multiplying fractions word problem: muffins (Opens a modal)
• Multiplying fractions word problem: laundry (Opens a modal)
• Multiplying fractions word problem: bike (Opens a modal)
• Multiply fractions: FAQ (Opens a modal)
• Multiply fractions word problems Get 3 of 4 questions to level up!

Your child will also order fractions whose denominators are all multiples of the same number. For example:

Put the fractions   ,   ,   ,   , and     in order from least to greatest.   ,  ,  ,  ,  .

Identify equivalent fractions

Use mixed numbers and improper fractions

Your child will recognise mixed numbers and improper fractions , and will be able to convert one to the other.

Add and subtract fractions with denominators that are multiples of the same number

Your child will use drawings, diagrams, and symbols to add and subtract fractions with the same denominator, and denominators that are multiples of the same number. For example:

  +     =   .     +     =     =   .

Multiply proper fractions and mixed numbers by whole numbers

Children will use objects and diagrams to:

Read and write decimal numbers as fractions

Your child will be able to understand the equivalence between decimals and fractions. For example:

Use tenths, hundredth, thousandths, and their decimal equivalents

They will be able to mentally add and subtract tenths, as well as mixed numbers that have one-digit whole numbers and tenths.

Round numbers to one decimal place

Your child will round numbers with two decimal places up or down to the nearest whole number. For example, 3.45 will round down to 3.

They will also round numbers with two decimal places up or down to one decimal place. For example, 2.67 will round up to 2.7.

Compare numbers with three decimal places

Your child will learn to read, write, order and compare decimal numbers with up to three decimal places.

For example, they will be able to:

• read and write numbers with three decimal places (for example, 1.454, 1.764, 1.654, 1.453)
• put them in order (for example, 1.453, 1.454, 1.654, 1.764)
• compare them (for example, 1.453 < 3.454).

Solve problems involving numbers with three decimal places

Understand and use percentages.

Your child will know that percentages, decimals, and fractions are different ways of expressing proportions.

They will make connections between percentages, fractions, and decimals. For example:

100% = 1   1% =    = 0·01   50% =    = 0·5   25% =    = 0·25

Your child will also recognise the percent symbol (%) and understand that ‘percent’ means ‘number of parts per hundred’. They will be able to write percentages as a fraction with denominator 100, and as a decimal fraction.

Compare percentages to fractions and decimals

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. Explore mixed numbers and improper fractions

Mixed numbers and improper fractions can be difficult for your child to grasp at first.

It often helps children to learn about these types of fractions visually. Diagrams can help their understanding:

Fraction Calculations in School

Ask your child to gather a number of pizza slices to make an improper fraction. Can they use these slices to show a mixed fraction? Can your child write down a mathematical way to reach the same answer?

2. Add and subtract fractions

Adding fractions.

In Year 5, your child will continue to add and subtract fractions. They will now be expected to add and subtract fractions whose denominators are multiples of the same number. For example:

 +   = ? First they will need to find the lowest common denominator (i.e. the smallest multiple of the two numbers). The lowest common denominator here is 8, because it is the smallest number both 4 and 8 will divide into equally. Your child will then have to multiply the numerator and the denominator by 2 to represent   in eighths: Your child will now be able to add the fractions:    +   =   –   = 

Subtracting fractions

Your child will follow a similar process to subtract fractions like these. For example:

  –    = ?   Your child will first need to find the   lowest common denominator , which is 12. So,     will become     as the numerator and the denominator will each be multiplied by 4. The     will become     as the numerator and the denominator will each be multiplied by 3. Your child will then be able to subtract     from     to leave   .    –   =   –   =   

More practice

You could practise calculating with fractions using the pizza cutouts in the Fraction Calculations in School booklet.

3. Multiply fractions by whole numbers

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

4. Investigate decimals

Show your child a number with 3 decimal places and ask them to tell you how many tenths, hundredths, or thousandths it has. For example, the number 4·203 has two tenths, zero hundredths, and three thousandths.

Place value charts can help your child to better understand decimal numbers:

Look for examples of these numbers in the real world and point them out to your child.

For example, when filling the car with petrol, ask your child to tell you what the number is by explaining how many tenths, hundredths, or thousandths it has. You could also ask them to round the total price or the total amount of petrol up or down to the nearest whole number, tenth, or hundredth. For instance, if you used 56.784 litres of petrol, you could ask your child to round this to the nearest litre (57L), tenth (56.8L), or hundredth (56.78L).

5. Investigate percentages

In Year 5, your child will be introduced to 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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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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Multiply Unit Fractions by an Integer Lesson

This Year 5 Multiply Unit Fractions by an Integer lesson covers the prior learning of adding 2 or more fractions, before moving onto the main skill of multiplying unit fractions by an integer.

The lesson starts with a prior learning worksheet to check pupils’ understanding. The interactive lesson slides recap the prior learning before moving on to the main skill. Children can then practise further by completing the activities and can extend their learning by completing an engaging extension task.

National Curriculum Objective Mathematics Year 5: (5F5) Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

Mathematics Year 5: (5F2a) Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5 + 4/5 = 6/5 = 1 1/5 ]

Mathematics Year 5: (5F2b) Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

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Lesson Slides

These lesson slides guides pupils through the prior learning of adding 2 or more fractions, before moving onto the main skill of multiply unit fractions by an integer. There are a number of questions to check pupils' understanding throughout.

Modelling PowerPoint

This powerpoint can be used to model the questions that the children will complete on the Varied Fluency and Reasoning & Problem Solving worksheets as part of this lesson.

These are the same as the lesson slides on Classroom Secrets. You can assign this as an activity for pupils to access individually in school or remotely from home.

1 Prior Learning

This worksheet recaps prior learning of adding 2 or more fractions, before moving onto the main skill of multiplying unit fractions by an integer.

Interactive Activity

This Year 4 Add 2 or More Fractions Game checks pupils' understanding of adding 2 or more fractions together where the denominators are the same.

2 Practical Activities

Supporting Activity

This the Multiply Unit Fractions by an Integer supporting activities sheet contains suggestions for additional tasks you might wish to use to support pupils' understanding of the concepts taught in the lesson.

2 Varied Fluency

This differentiated worksheet includes varied fluency questions for pupils to practise the main skill of this lesson.

Interactive Animation Activity

This Year 5 Multiply Unit Fractions by an Integer Interactive Animation supports pupils’ understanding of multiplying fractions including where the answer needs to be converted into a mixed number.

2 Reasoning & Problem Solving

This multiply unit fractions by an integer extension task includes a challenge activity which can be used to further pupils' understanding of the concepts taught in the multiply unit fractions by an integer lesson.

Mixed Practice

This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of multiply unit fractions by an integer.

This differentiated worksheet includes reasoning and problem solving questions to support the teaching of this step.

Discussion Problem

This worksheet includes two discussion problems which can be used in pairs or small groups to further pupils' understanding of the concepts taught in this lesson.

Interactive Challenge Activity

This Year 5 Multiply Unit Fractions by an Integer Maths Challenge checks pupils' understanding of multiplying unit fractions within a problem solving context. Pupils will sort the fractions based on the given criteria.

This differentiated worksheet includes varied fluency and reasoning and problem solving questions to support the teaching of this step.

2 Additional Activities

Consolidation Pack

These Fractions worksheets are fantastic at helping your pupils practice their reasoning and problem solving skills. This pack contains two different question types for Year 5 Spring Block 2.

Home Learning Pack

This Spring week 9 Maths pack contains varied fluency, reasoning and problem solving worksheets

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KS2 Maths: Multiplying and dividing fractions

BBC Teach > Primary Resources > KS2 Maths > Calculations - Mathematical challenges

NARRATION: Back in the deepest, darkest depths of time, there lived a great mathemagician called Hypatia. Numbers fell under her spell one by one. With them, Hypatia could do anything. Now Hypatia is looking for people to share her powers with. She has forged a mathematical maze. Only true mathemagicians can solve the puzzles and find their way out. Join two young explorers, Olivia and Hassan, to solve the puzzles, escape the maze and become the greatest mathemagicians of all time.

Multiplying and dividing fractions.

OLIVIA: Hassan?

HASSAN: Olivia?

ARCHIMEDES: Archimedes!

HASSAN: Ah! Ohhh.

ARCHIMEDES: We made it to the Crystal Cave. Grab some gems.

HASSAN: Wow, that's amazing! Wow!

OLIVIA: Wow!

HYPATIA: The cave holds many secrets.Perhaps this equation will help your escape. 2/5 times 5/8.

OLIVIA: Hmm, I'm sure we can work something out.

HYPATIA: Hmm, I'll be curious to see.

ARCHIMEDES: Let's take a look at an example. We multiply the top numbers, the numerators, together. Then we multiply the bottom numbers, the denominators, with each other. We can see that 15/63 is a smaller fraction than either of our two original numbers.

HASSAN: Hey, look at those grids! When we are multiplying fractions, we are essentially multiplying a portion by a portion, creating something even tinier.

ARCHIMEDES: Exactly. And 15/63 is difficult to work with, so by using the common factor of three, we can simplify our product to 5/21.

HYPATIA: When multiplying fractions by integers, by whole numbers, things are slightly different, as you will see.

ARCHIMEDES: Yeah, we take our grid and copy it four times. 3/4 times four is the same as 3/4 multiplied by 4/1. Three times four is 12, and four times one is four. 12 divided by four is three. Or, if you want to think of it this way, we take our grid and copy it four times. Then we add all these sections together, resulting in three completed grids, three completed wholes.

OLIVIA: So our answer's simply three?

ARCHIMEDES: Exactly.

OLIVIA: Hmm.

ARCHIMEDES: Take 1/6 divided by five. We're breaking up 1/6 of a whole into parts that are five times smaller. Through doing that, the total number of parts that make up the whole is increasing, so to reflect that, we now actually need to multiply the denominator of our number by the whole number. And six times five is 30, giving us 1/30.

Oh, nice outfits! Shall we solve the equation?

HASSAN: Oh we can't move. These are really heavy.

OLIVIA: But we have a present for you guys.

HYPATIA: Oh wow

ARCHIMEDES: Thank you.

HASSAN: We found 15/5 of magic gems and were able to push them together to make three magic gems.

ARCHIMEDES: Oh so, what maths were you using there?

OLIVIA: We were using maths?

HASSAN: Oh, we were multiplying fractions together!

OLIVIA: Oh!

HASSAN: Oh, and that must be the same for our magic gems. 15 magic gems is the same as 15/1 which we multiply with 1/5, to make 15/5.

OLIVIA: 15/5 is equal to three, because 15 divided by five is three.

HYPATIA: You guys are getting good at this. But how about my puzzle? Can you solve it? Or have you decided to stay here forever?

OLIVIA: Hmm, I think the answer is 2/8.

HASSAN: And I think the answer is 1/4.

HYPATIA: You are both right. We can divide both the numerator and the denominator of 2/8 by two, to make 1/4, meaning they are equivalent.

ARCHIMEDES: When we have multiple options for simplifying, we always go for the one that results in the smallest digit for the denominator.

OLIVIA: Woo!

HASSAN: Ha!

OLIVIA AND HASSAN: Thank you.

ARCHIMEDES: Was that the only exit?

HYPATIA: Uh-oh!

ARCHIMEDES: Oh no.

HYPATIA: Now young mathemagicians, it is your turn. Follow in Hassan and Olivia's footsteps and become mathemagicians. Something divided by four is 7/24. 5/20 divided by something is 5/80. What are the missing fractions and integers?

Video summary

In a mysterious crystal cave, Olivia and Hassan get to work dividing and multiplying fractions in order to find their way out.

Archimedes has ²⁄₅ of an emerald and asks how much he would have left if he gave ¹⁄₂ to Hypatia.

After working out the division of this fraction, Olivia and Hassan get to work to divide and multiply fractions.

With a little help from Archimedes, Olivia and Hassan then learn how to multiply and divide more complex fractions.

This short animated film is from the BBC Teach series, Hypatia's Mathematical Maze.

Teacher Notes

Before watching the film:

Prior to this lesson you may wish to introduce pupils to other relevant topics, for example:

• Multiplication and division
• Comparing and ordering fractions
• Simplification of fractions

During watching the film:

Depending on the focus of your lesson, you may wish to pause the film at certain points to check for understanding, asking questions such as:

• What is the difference between an integer and a fraction?
• How else can you represent the fractions?
• How would we simplify the fractions that Olivia and Hassan have?
• What different stages will you use to answer Hypatia’s final question?

Final question: Something divided by four is seven twenty-fourths. Five twentieths divided by something is five eightieths. What are the missing fractions and integers? ? ÷ 4 = ⁷⁄₂₄ 5⁄₂₀ ÷ ? = 5⁄₈₀

Answer to the final question: 7⁄₆ ÷ 4 = ⁷⁄₂₄ 5⁄₂₀ ÷ 4 = 5⁄₈₀

Following on from the film:

• Use bar models to represent dividing the fractions into further pieces.
• Use examples where the pupils have to explain their thinking in terms of factors, multiples, commutativity and equivalent fractions e.g. Which is larger? ⅘ ÷ 3 or 4⁄₃ ÷ 5? What is larger, ⅔ ÷ 5 or 4⁄₆ ÷ 5?
• ¹⁄₂ ÷ 2 = ¹⁄₂ x ¹⁄₂
• ¹⁄₂ ÷ 4 = ¹⁄₂ x ³⁄₄
• ¹⁄₂ ÷ 3 = ¹⁄₂ x ¹⁄₃
• ¹⁄₂ ÷ 5 = ¹⁄₂ x ¹⁄₅

This short film is suitable for teaching maths at KS2 in England, Wales and Northern Ireland and 2nd Level in Scotland.

More from this series:

Adding and subtracting using mental methods

In a mythical temple full of obstacles, Olivia and Hassan learn simple mental maths and apply it to work out the passcode to open the door.

Adding and subtracting using written methods

Having been transported to a floating library, Olivia and Hassan's ability to solve large equations using written methods is tested.

How and why we round numbers

Olivia and Hassan are taught how to round to the nearest 1000, 10,000, and 100,000 when a disgruntled magic carpet demands money from them.

Using addition and subtraction in multi-step problems

Inside a giant computer created before the age of mathemagicians, Olivia and Hassan are faced with a multi-step problem to reach the labyrinth’s next stage.

Multiplying by 10, 100 and 1000

When Olivia and Hassan find themselves on the roof of an enormous skyscraper they learn how to multiply by 10, 100 and 1000 and work out the number of windows on the building.

Mental multiplication

While exploring a jungle, Olivia and Hassan learn the true nature of square numbers as being created when two of the same number are multiplied together.

Factors, multiples and primes

Trapped in a desert together with Archimedes, Olivia and Hassan learn what common factors, multiples, and prime numbers are.

Multiplying using written methods

Finding themselves in space, Olivia and Hassan watch mathemagician Hypatia perform long multiplications in the sky by bending the stars.

Dividing using written methods

Olivia and Hassan learn how to perform long division in order to free gridlocked traffic on a bridge.

Recognising and comparing fractions

Olivia and Hassan are enjoying themselves in a world made out of pizza and learn how to work with numerators and denominators in fractions.

Adding and subtracting fractions

Amongst the ruins of an ancient city, Olivia and Hassan learn how to add and subtract fractions.

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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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