Writing and simplifying ratios
- A ratio compares quantities. 3 : 2 means that for every 3 of the first, there are 2 of the second.
- Simplify by dividing both parts by their highest common factor: 12 : 18 = 2 : 3.
- Use the same units first: 50 cm : 2 m = 50 : 200 = 1 : 4.
- The form 1 : n divides both parts by the first part: 4 : 10 = 1 : 2.5.
Sharing in a ratio
- Add the parts, find one part, then multiply. Share £60 in the ratio 2 : 3: there are 5 parts, 1 part = £12, so the shares are £24 and £36.
- If you know one share: in the ratio 3 : 5 the smaller share is 12, so 1 part = 4 and the larger share is 20.
- If you know the difference: in the ratio 2 : 7 the difference is 35, so 5 parts = 35, 1 part = 7, and the numbers are 14 and 49.
Ratios and fractions
- In the ratio 2 : 3, the first part is 2/5 of the total and the second part is 3/5.
- If 3/8 of a class are boys, the ratio of boys to girls is 3 : 5.
Using ratios
- Recipes: a recipe for 4 people uses 300 g of flour, so for 6 people use 300 ÷ 4 × 6 = 450 g.
- Combining ratios: if a : b = 2 : 3 and b : c = 4 : 5, make the b parts the same: 8 : 12 and 12 : 15, so a : b : c = 8 : 12 : 15.
Key terms
- Ratio
- A comparison of two or more quantities, written with colons, such as 3 : 2.
- Simplest form
- A ratio whose parts have no common factor other than 1.
- Part
- One share of the total in a ratio problem.
- Unit ratio
- A ratio written as 1 : n or n : 1.
- Equivalent ratios
- Ratios that simplify to the same ratio, such as 2 : 3 and 8 : 12.