Sharing an Amount to a Given Ratio

There are three common methods for sharing an amount to a given ratio.  Depending on the age group and ability range I am teaching I would choose one approach over the other two.

The three methods are:

  1. Using fractions
  2. Unitary method
  3. Using a table

In this blog I will demonstrate each of the three methods for the same problem.

Nikki and Gemma share £36 in the ratio 4 : 5.

Work out how much Nikki and Gemma each receive.

Sharing an Amount to a Given Ratio Using fractions

Change the shares for each person in to a fraction.

Nikki’s Share = 4/(4+5) = 4/9

Gemma’s Share = 5/(4+5) = 5/9

Calculate each fraction of the total amount.

Nikki receives £36 × 4/9 = £16.  Gemma receives £35 × 5/9 = £20.

I use this approach when teaching more able students as it reinforces the link between ratio and proportion.  The fractions are seen as proportions of the total amount.

Sharing an Amount to a Given Ratio Using the Unitary Method

The unitary method emphasises the need to find the value of one share by dividing the total amount by the total number of shares.  This can be taught illustratively or with clear writing frames.

Unitary method using boxes to illustrate the value of a single share.

Sharing an Amount to a Given Ratio

The illustrative approach represents each share as a box.  Each box contains an equal proportion of the total amount.   Illustrating the shares as boxes helps the younger and less able students to visualise the importance of finding one share and using that to split the amount correctly.

Unitary method using writing frames to find the value of a single share

Unitary Method using Writing Frames

Step 1: Find the total number of shares:  4 + 5 = 9.

Step 2: Find the value of one share:  £36 ÷ 9 = £4 per share

Step 3: Multiply each part of the ratio by the value of one share.

Nikki = 4 shares × £4 = £16, Gemma = 5 shares × £4 = £20

The written unitary method is my most common approach for teaching how to share an amount to a ratio as it breaks the problem down into three intuitive stages.

Sharing an Amount to a Given Ratio Using a Table

The first column of the table uses the ratio given in the question.  Subsequent columns are multiples of the first column.  This method works well when the total shares is a factor of the amount.

Sharing an Amount to a Ratio

I use this method for lower ability students and those in key stage 3.  It reinforces multiples and patterns while providing a visual representation of the increasing shares.

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