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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?

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.

Check your answer here.

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