Simplify ratios, including ones with different units, decimals and fractions, write them in the form 1 : n or n : 1, and link ratios with fractions.
What you will learn
- Simplify a ratio fully, including one with three parts
- Simplify ratios with different units, decimals or fractions
- Write a ratio in the form 1 : n or n : 1
- Turn a ratio into a fraction of the whole, and a fraction into a ratio
Simplify by dividing every part
A ratio compares amounts.
Divide every part by the same number, and keep going until the only common factor is 1.
- 24 : 36
- the highest common factor of 24 and 36 is 12
- 24 ÷ 12 = 2 and 36 ÷ 12 = 3
- 24 : 36 = 2 : 3
Three parts work the same way: 40 : 60 : 100 = 2 : 3 : 5 (divide by 20). The order matters: 2 : 3 is not the same as 3 : 2.
Ratios are equivalent when they simplify to the same ratio. You make an equivalent ratio by multiplying or dividing every part by the same number: 2 : 3 = 4 : 6 = 10 : 15. Adding the same number to each part does not work: 2 : 3 and 3 : 4 are different ratios. To test whether 18 : 27 and 10 : 15 are equivalent, simplify both: each is 2 : 3, so they are.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Simplify by dividing every part
- Units, decimals and fractions
- Ratios and fractions
- Try it: Simplify with the ratio tool
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Every part, Equivalent, Same unit
In this unit: Ratio and proportion
Convert units and use scales, write and simplify ratios, share amounts in a ratio, compare best buys and exchange rates, and solve direct and inverse proportion problems.
- Units, conversions and scales
- Writing and simplifying ratios
- Sharing and using ratios
- Best buys, recipes and exchange rates
- Direct and inverse proportion