Sharing and Changing Quantities in a Ratio

15 min

Let's begin

Byiringiro and Keza looked after the school vegetable garden and sold the cabbages for 24 000 Frw. Byiringiro worked 3 days and Keza worked 5 days, so they agree to share the money in the ratio 3 : 5. How much should each of them get?

Sharing an amount in a given ratio

Think of the money cut into equal parts: Byiringiro gets 3 parts and Keza gets 5 parts.

Byiringiro: ■ ■ ■
Keza: ■ ■ ■ ■ ■

Step 1: add the parts. 3 + 5 = 8 parts altogether.
Step 2: find the value of one part. 24 000 ÷ 8 = 3 000 Frw.
Step 3: multiply. Byiringiro: 3 × 3 000 = 9 000 Frw. Keza: 5 × 3 000 = 15 000 Frw.
Step 4: check. 9 000 + 15 000 = 24 000 Frw. Correct.

When you know one share

The ratio of boys to girls in a choir is 4 : 5, and there are 20 boys. How many girls are there?
4 parts = 20 boys, so 1 part = 20 ÷ 4 = 5.
Girls = 5 parts = 5 × 5 = 25. The whole choir has 20 + 25 = 45 singers.

Three-part ratios

A family shares 50 000 Frw of savings among three children in the ratio 2 : 3 : 5.
Parts: 2 + 3 + 5 = 10. One part: 50 000 ÷ 10 = 5 000 Frw.
Shares: 10 000 Frw, 15 000 Frw and 25 000 Frw. Check: 10 000 + 15 000 + 25 000 = 50 000.

Increasing or decreasing in a ratio

To increase 600 in the ratio 5 : 3, multiply by 53: 600 × 5 ÷ 3 = 1 000.
To decrease 1 500 in the ratio 3 : 5, multiply by 35: 1 500 × 3 ÷ 5 = 900.

The ratio of increase compares the new amount with the old one. A moto fare rose from 400 Frw to 500 Frw: new : old = 500 : 400 = 5 : 4. A price that falls from 1 200 Frw to 900 Frw has a ratio of decrease of 900 : 1 200 = 3 : 4.

Explore

In the Proportion Playground simulation, mix red and blue paint in different ratios and see which mixes give exactly the same colour.

Tip

Add the parts, find one part, multiply. Then always check that the shares add up to the whole amount.

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Try it yourself

Share 3 600 Frw in the ratio 1 : 2.
Share 45 mangoes in the ratio 4 : 5.
The ratio of boys to girls is 2 : 3. There are 18 girls. How many boys are there?
Share 60 000 Frw in the ratio 1 : 2 : 3.
Increase 800 in the ratio 5 : 4.

Answers

3 parts, one part = 1 200 Frw. The shares are 1 200 Frw and 2 400 Frw.
9 parts, one part = 5. The shares are 20 and 25 mangoes.
3 parts = 18, so one part = 6. Boys = 2 × 6 = 12.
6 parts, one part = 10 000 Frw. The shares are 10 000, 20 000 and 30 000 Frw.
800 × 5 ÷ 4 = 1 000.

Quick check

Share 36 000 Frw in the ratio 4 : 5. Put the steps in order.

Tap the cards in the right order.

What you learned today

To share in a ratio: add the parts, divide to find one part, then multiply.
If you know one share, use it to find the value of one part first.
To change an amount in the ratio new : old, multiply by the fraction new/old.

Sources and credits

Grade 6, Unit 2, Lesson 15: Part-Part-Whole Ratios, by Illustrative Mathematics and Open Up Resources (IM 6–8 Math), provided by Illustrative Mathematics / Kendall Hunt, licensed under CC BY 4.0. Adapted by Ganzaa.
Proportion Playground, version 1.0.1. Simulation by PhET Interactive Simulations, University of Colorado Boulder, licensed under CC BY 4.0 (https://phet.colorado.edu)
The section on increasing and decreasing in a given ratio. Written by Ganzaa.

1Sharing an amount in a given ratio

2When you know one share

3Three-part ratios

4Increasing or decreasing in a ratio

5Explore