Ratio · Year 9
In Year 9 you get fluent with: ratios and fractions.
A ratio compares the sizes of two or more quantities: 3 : 5 means “for every 3 of the first there are 5 of the second”. Ratios are used in recipes, maps, mixing paint and sharing money fairly.
Key facts
- Simplify a ratio by dividing every part by the same number (their HCF): 12 : 18 = 2 : 3.
- Write the quantities in the same units before simplifying: 50 cm : 2 m = 50 : 200 = 1 : 4.
- Sharing in a ratio: add the parts. Divide the total by the number of parts to find one part. Then multiply.
- If you know one share, use it to find one part: in 3 : 5, if the 3 parts are 24, one part is 8.
- In the ratio a : b, the first quantity is a/(a + b) of the total.
- A map scale of 1 : 25,000 means 1 cm on the map is 25,000 cm (250 m) in real life.
Worked examples
Example 1
Share £120 in the ratio 3 : 5.
Answer: £45 and £75