Solving problems with fractions

Home learning focus

Learn how to solve problems involving fractions.

This includes:

  • two examples
  • one quiz
  • two activities to apply your learning


Problem solving with fractions

When problem solving with fractions it may seem tricky to start with. Remember:

  • look at the question: what is it asking you to find out?
  • apply what you know: think about what you have learnt /know about fractions.
  • refresh your memory with these guides on fractions from KS2 maths.

Here are some examples:

Example 1

James runs \(\frac{1}{7}\) of a mile, three times a week. Alisha runs \(\frac{1}{9}\) of a mile, four times a week.

James thinks he runs further than Alisha. Is he correct? Prove it using the steps in the slideshow below!

The question is asking us to compare how far James and Alisha run. James runs 1/7 of a mile three times a week and Alisha runs 1/9 of a mile, four times a week.

1 of 5

Example 2

Complete this calculation using the digit cards. Remember each digit card can only be used once.

In this example, we are looking to create a mixed number fraction using the digit cards given.

Step 1:

When multiplying fractions by an integer (whole number), the denominator ( bottom number of a fraction) stays the same.
So we know that it must be \(\frac{4}{5} \) x ? = ? \(\frac{?}{5}\)

Step 2

When problem solving, mathematicians often use a method called trial and error to try and solve a problem. We can use this method to try and solve this problem.

Let's pick the digit card 2 as the number we are going to multiply by and see if it works. \(\frac{4}{5} \) x 2 = \(\frac{8}{5}\) = 1 \(\frac{3}{5}\)

Although this calculation is correct, it doesn't solve our problem as there isn't a 1 digit card.

Let's pick a different digit card: 3

\(\frac{4}{5} \) x 3 = \(\frac{12}{5}\) = 2 \(\frac{2}{5}\)

Yes - this is one possible answer to solve our calculation. Can you find another possible answer?

When you're multiplying fractions by an integer (or a whole number) you multiply the numerator of the fraction by the whole number, whilst the denominator of the fraction stays the same.


Activity 1

Have a go at using your problem solving skills with this quiz! You may need a paper and pen to help you jot down your working out.

Activity 2

You may need a piece of paper and pen for this activity.

Can you solve the calculation in two different ways using the numbers given below.

\(\frac{7}{10}\) x ? = ? \(\frac{?}{?}\)

8 , 5 , 1 , 12 , 3 , 6 , 10 , 2

Each number can only be used once in a calculation.

Check your answers here.

Activity 3

Use your problem solving skills with fractions to solve this problem:

Tom eats \(\frac{1}{6}\) of a pizza. Harry then ate some more. When Danny comes to eat some pizza, he finds that there is only \(\frac{3}{15}\) of the pizza left. Danny argues that Harry has eaten more than his third of the pizza.

Is Danny right? Justify your answer with your working out.

Check your answer here.

There's more to learn

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7 - 11 Maths
This Term's Topics - Maths
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