# Solve Fractions and Multiples Problems

In this worksheet, students will be asked to solve a range of fractions and multiples problems. These problems will involve unequal sharing and grouping using knowledge of fractions and multiples.

Key stage:  KS 2

Curriculum topic:   Ratio and Proportion

Curriculum subtopic:   Solve Fraction/Multiples Problems

Difficulty level:

### QUESTION 1 of 10

In this activity, you will use your knowledge of fractions and multiples to solve a range of problems.

Let's work through one together.

I ate ¼ of a pie and served ⅛ later to my guests.

What fraction was served to my guests?

1st step: Convert

Convert ¼ to eighths so both fractions have the same denominator and then will be easier to work with

¼ both numbers should be multiplied by 2 to convert to eighths as 4 x 2 = 8

So I ate  and I saved ⅛ a total of ⅜

2nd step: Subtract

The total pie was originally a whole =

So ⅝  of the pie was served to guests

James has a bag of marbles.

There were 56 in the bag.

He gave away &frac38; of them.

How many are left?

In a pet shop, 3/12 of the pets are fish and 1/6 are rabbits.

Which type of pet is there more of?

Rabbits

Fish

Sam has an amazing collection of stickers.

He gives 2/5 to his sister and 3/8 to his best friend.

Who does he give the most stickers to?

Rabbits

Fish

Two contestants are competing in a grape eating challenge.

Rich has eaten  and Sally has gobbled ⅝ of hers.

Who is currently leading the contest?

Write the name in the box.

Lucy and Max have identical cars.

Lucy has used  of the petrol in her car.

Max has used  of the fuel in his.

Who has more fuel left in their car?

Kim and Tom swam in a swimming gala.

Kim swam &frac58; of a mile.

Tom swam &frac23; of a mile.

Can you match each fraction to its equivalent?

This will then clearly show you who has swum the furthest.

## Column B

Swam furthest distance
Tom
Swam smaller distance
15 ⁄24
5 ⁄8
Kim
2 ⁄3
16 ⁄24

Dad gave his two children the same amount of pocket money.

Alisha spent ⅚ on a new top.

Jez spent on a game.

Can you match each fraction to its equivalent?

This will then clearly show you who has the most pocket money remaining.

## Column B

Spent most pocket money
Alisha
Spent least pocket money
45 ⁄54
5 ⁄6
42 ⁄54
7 ⁄9
Jez

Karina took 5/12 of the sweets and Ivy took 3/8 of the sweets.

What fraction of the sweets did they take between them?

Write your answer as a fraction, use a '/' and do not leave a space between numbers.

Someone has snuck into the kitchen and eaten 3/10 of John's cake.

How much cake is still left?

Write your answer as a fraction, use a '/' and do not leave a space between numbers.

Last year, Miss Smith weighed 60 kg.

This year she weighs 2/5 more.

How much does Miss Smith weigh this year?

• Question 1

James has a bag of marbles.

There were 56 in the bag.

He gave away &frac38; of them.

How many are left?

EDDIE SAYS
First, we need to find 1/8 of 56 56 ÷ 8 = 7 1/8 = 7 Then 7 x 3 to find 3/8 = 21 56 - 21 = 35 Therefore there are 35 marbles left
• Question 2

In a pet shop, 3/12 of the pets are fish and 1/6 are rabbits.

Which type of pet is there more of?

Fish
EDDIE SAYS
To find the answer to this fraction problem, we needed to convert both fractions to a common denominator. We can convert 1/6 into 12ths 1/6 = 2/12 So, 3/12 of the pets are fish and 2/12 pets are rabbits. Therefore, there are more fish than rabbits.
• Question 3

Sam has an amazing collection of stickers.

He gives 2/5 to his sister and 3/8 to his best friend.

Who does he give the most stickers to?

EDDIE SAYS
To solve this type of fraction problem, we need to ensure both fractions have a common denominator by finding the lowest common multiple. The lowest common multiple of 5 and 8 is 40. 2/5 = 16/40 3/8= 15/40 Therefore, Sam gave his sister the most stickers.
• Question 4

Two contestants are competing in a grape eating challenge.

Rich has eaten  and Sally has gobbled ⅝ of hers.

Who is currently leading the contest?

Write the name in the box.

Rich
rich
EDDIE SAYS
How did you find this one? To directly compare the fractions, we needed to find the common denominator by using the lowest common multiple. The lowest common multiple of 10 and 8 is 80. 7/10 = 56/80 5/8 = 50/80 Therefore, Rich is currently leading the contest.
• Question 5

Lucy and Max have identical cars.

Lucy has used  of the petrol in her car.

Max has used  of the fuel in his.

Who has more fuel left in their car?

Lucy
lucy
EDDIE SAYS
Again, in order to directly compare the fractions, we need to find the common denominator by using the lowest common multiple. The lowest common multiple of 7 and 9 is 63. 4/7 = 36 /63 5/9 = 35/63 Therefore, Lucy has the most fuel left in her car.
• Question 6

Kim and Tom swam in a swimming gala.

Kim swam &frac58; of a mile.

Tom swam &frac23; of a mile.

Can you match each fraction to its equivalent?

This will then clearly show you who has swum the furthest.

## Column B

Swam furthest distance
Tom
Swam smaller distance
Kim
5 ⁄8
15 ⁄24
2 ⁄3
16 ⁄24
EDDIE SAYS
5/8 = 15/24 2/3 = 16/24 Therefore, Tom swam furthest and Kim swam the lesser distance. Are you feeling more confident? Your focus is great, four more questions to go...
• Question 7

Dad gave his two children the same amount of pocket money.

Alisha spent ⅚ on a new top.

Jez spent on a game.

Can you match each fraction to its equivalent?

This will then clearly show you who has the most pocket money remaining.

## Column B

Spent most pocket money
Alisha
Spent least pocket money
Jez
5 ⁄6
45 ⁄54
7 ⁄9
42 ⁄54
EDDIE SAYS
5/6 = 45/54 7/9 = 42/54 You can now see, Alisha has spent the most pocket money.
• Question 8

Karina took 5/12 of the sweets and Ivy took 3/8 of the sweets.

What fraction of the sweets did they take between them?

Write your answer as a fraction, use a '/' and do not leave a space between numbers.

19/24
EDDIE SAYS
To solve this problem, we need to first convert the fractions into the same denominator by using the lowest common multiple. The lowest common multiple of 12 and 8 is 24. 5/12= 10/24 3/8 = 9/24 By adding both of the fractions together, we then know that Karina and Ivy took a total of 19/24 of the sweets. You’re making great progress!
• Question 9

Someone has snuck into the kitchen and eaten 3/10 of John's cake.

How much cake is still left?

Write your answer as a fraction, use a '/' and do not leave a space between numbers.

11/30
EDDIE SAYS
To solve this problem, we first need to convert the fractions into the same denominator by using the lowest common multiple. The lowest common multiple of 10 and 3 is 30. 3/10 = 9/30 1/3 = 10/30 By adding both of the fractions together, we then know that a total of 19/30 of the cake has been eaten. This means 11/30 of the cake remains. Poor John!
• Question 10

Last year, Miss Smith weighed 60 kg.

This year she weighs 2/5 more.

How much does Miss Smith weigh this year?

EDDIE SAYS
To find out Miss Smith's weight, we firstly needed to find 1/5 of 60. 60 ÷ 5 = 12 1/5 = 12 2/5 = 24 So, 60 + 24 = 84kg Great work, you've completed another activity! How about attempting another one so you feel super confident?
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