Share in a ratio

Objective. Divide an amount in a stated ratio.

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2. Worked example
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Learn: the key idea

Sharing an amount in a given ratio means splitting a total quantity into parts proportional to the numbers in the ratio. First add the parts of the ratio to find the total number of shares, then divide the amount by this total to find the value of one share, and finally multiply by each part of the ratio. For example, to share £40 in the ratio 3:5, add 3+5=8 shares, divide £40 by 8 to get £5 per share, then multiply: 3×5=£15 and 5×5=£25. Checking that the shares add back up to the original total confirms the answer.

Worked example

Share £72 between Amir and Beth in the ratio 5:4.

1 $Add the parts of the ratio: 5+4=9.$
2 $Divide the total by the number of shares: 72\div9=8.$
3 $Multiply each part by the value of one share: 5\times8=40 and 4\times8=32.$
4 $Check the shares add to the total: 40+32=72.$

Answer: Amir £40, Beth £32

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Common mistake. Pupils sometimes divide the total by the number of ratio terms rather than the sum of the parts, dividing £40 by 2 instead of 8 for a 3:5 ratio. Always add the parts of the ratio first before dividing.

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