Sharing an Amount to a Given Ratio

July 9, 2021

Differentiated Learning Objectives

• All students should be able to share to a ratio where the total shares are a factor of the amount.
• Most students should be able to share to a ratio by calculating the value of a single share.
• Some students should be able derive and simplify a ratio involving three terms and share to any amount.

There are three standard 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 of 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 into 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 proportions of the total amount.

Sharing an Amount to a Given Ratio Using the Unitary Method

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

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

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 visualize the importance of finding one share and splitting the amount correctly.

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

Click here to view the video.

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 share is a factor of the amount.

I

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.

Additional Resources

Problem Solving

Ratio

Problem Solving with Ratio. There are five problems that link to money, fractions and probability.

Revision

Sharing to a Ratio

Revision lesson on sharing to a ratio for exam students.

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About Mr Mathematics

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.