# 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

# Learn

### 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!

## 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.

# Practise

## 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.