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Division in a given ratio

Part of MathsRatio

Key points

  • Division in a given is also known as sharing in a given ratio.

  • Similar processes are used when dividing an amount in a ratio and finding a fraction of an amount.

  • To divide in a given ratio:

    • can be used to support understanding
    • a numerical method without bar models can also be used

  • Understanding the link between ratios and fractions is a valuable skill to practise.

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Understanding the link between ratios and fractions

Examples

To understand the link between a and a fraction, it is important to know that:

  • the ratio represents the parts that make up the whole

  • the total of the parts gives the of the fractions

  • each part of the ratio gives the for that fractional part

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  1. Example 1: A diagram of nine circles. Five are shaded blue; four are shaded orange.

    There are nine circles. 4 circles are orange and 5 circles are blue. Find the fraction of orange circles, the fraction of blue circles and the ratio of orange to blue circles.

Question

The ratio of the number of green to orange to blue circles is 4 : 2 : 1

What fraction of the circles are orange?

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Using bar models to divide in a given ratio

To divide in a using :

  1. Draw a to represent the whole and split it into the total number of parts.

  2. Find the value of one part by dividing the whole by the total number of parts.

  3. Calculate the value of each share of the ratio by multiplying the number of parts in each share of the ratio by the value of one part.

Examples

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  1. Example 1: A bar labelled forty with an arrow pointing to each end.

    The bar represents the whole. Divide 40 in the ratio 5 : 3

Question

There are 30 dogs (German Shepherds, Golden Retrievers and Labradors) at a doggy day care centre in the ratio 1 : 5 : 4. How many Labradors are there?

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How to divide in a given ratio – numerical method

To divide an amount in a given :

  1. the parts of the ratio to get the total number of parts.

  2. Find the value of one part by dividing the amount by the total number of parts.

  3. Find the value of each share in the ratio by multiplying the number of parts in each share by the value of one part.

Examples

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  1. Example 1: Six-hundred. Four to three to five.

    Divide 600 in the ratio 4 : 3 : 5

Question

Divide 72 in the ratio 7 : 3 : 8

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Practise division in a given ratio

Quiz

Practise division in a given ratio in this quiz. You may need a pen and paper to complete these questions.

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Real-world maths

Video

Ratios are often used in jobs where liquids must be mixed in the correct proportions.

Watch the video to see how a hairdresser needs to mix a hair colour dye solution and a developer in a specific ratio to achieve a particular shade safely. The ratio can vary depending on the types of products being mixed.

Ratio proportions need to be just right when dyeing hair or a client’s hair may get damaged.

A 200 ml blend of colour and developer is required for a client. The required shade uses colour and developer in the ratio 2 : 3

200 ml is divided in the ratio 2 : 3

The hairdresser needs to mix 80 ml of colour and 120 ml of developer.

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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 ±«Óătv Bitesize.

Play the Divided Islands game!
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More on Ratio

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