Equivalent ratios

Objective. Scale ratios up and down to find missing values.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

Equivalent ratios express the same proportion between quantities, obtained by multiplying or dividing every part of a ratio by the same number. For example, the ratio 2:5 is equivalent to 6:15, since both parts have been multiplied by 3. Equivalent ratios are used to find a missing value when one quantity is known: if the ratio of flour to sugar is 2:5 and you have 10 units of sugar, dividing 10 by 5 then multiplying 2 by that same scale factor of 2 gives 4 units of flour. The scale factor connecting two equivalent ratios is always consistent across every part.

Worked example

The ratio of red to blue counters is 3:7. If there are 21 blue counters, find an equivalent ratio to work out how many red counters there are.

1 $Find the scale factor linking 7 to 21: 21\div7=3.$
2 $Apply the same scale factor to the red part: 3\times3=9.$
3 $Write the equivalent ratio: 9:21.$
4 $Check by dividing both parts by 3, giving back 3:7.$

Answer: 9 red counters

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Pupils sometimes apply a different scale factor to each part of the ratio, breaking the proportion. Always find one single scale factor from the known pair, and apply it consistently to the other part.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard