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How to work out a fraction of an amount

Part of MathsFractions

Key points

  • To find a fraction of an amount, divide by the and multiply by the .
  • A can be used to help explain a problem and support the working out.
  • Sometimes the fractional amount is given and the whole must be worked out. In this case the process is reversed. Divide by the numerator and multiply by the denominator.
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How to find a fraction of an amount

How to find a fraction of an amount:

  1. Divide the amount by the denominator.

  2. Multiply the answer by the numerator.

The multiplication and division can be done in any order. Division is usually done first as the calculation can be easier.

To find a fraction of an amount using a :

  1. Draw a bar to represent the total amount.

  2. Split the bar into the number of parts given by the denominator.

  3. Find the value of 1 part by dividing the amount by the number of parts.

  4. Multiply the answer by the numerator.

Examples

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  1. Example 1. A bar model showing 80 across.

    The bar represents the total amount, 80

Question

Work out \( \frac{3}{10} \) of 560

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How to find the amount from a given fraction

To find the original amount from a fraction of that amount:

  1. Divide by the numerator to find the (one part).
  2. Multiply by the denominator to find the original amount (the whole).

Examples

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  1. Example 1. Three quarters of question mark equals twenty-four. A bar model is underneath divided into four equal parts. Three of the part s are highlighted and show they add to twenty-four. The whole length of the bar is then labelled underneath with a question mark.

    3⁄4 of a number is 24. Find the value of the number.

Question

\( \frac{3}{5} \) of a number is 36. What is the number?

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Practise finding a fraction of an amount

Try this quiz to practise finding a fraction of an amount. You may need a pen and paper to solve some of these problems.

Quiz

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Real-world maths

A woman wearing a black hijab working on a sketch on a desk with lots of paper and architectural blueprints.
Architects may use fractions when working on a building design.

Architects use fractions when drawing design plans, such as a floor plan that is\( \frac{1}{50} \)the size of the real building.

For example, if the location of an electrical socket needs to be moved, the distance it moves on the plan uses a calculation that involves finding a fraction of an amount.

For a change made on the design, the architect will have to work out what the real measurement is to ensure accuracy in the actual building.

A woman wearing a black hijab working on a sketch on a desk with lots of paper and architectural blueprints.
Architects may use fractions when working on a building design.
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Game - Divided Islands

Using your maths skills, help to build bridges and bring light back to the islands in this free game from ý Bitesize.

Play the Divided Islands game!
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More on Fractions

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