1. GCSE Mathematics Ratio & Proportion

2. Aims To simplify ratios To write ratios in unitary form To compare ratios and fractions

3. What is a Ratio What is a ratio?

4. Notation This is read as 2 to 3. It means that for every 2 units of the first quantity there are 3 units of the second. 2 : 3

5. Maps For example scales on a map 1:2000

6. Scale Models Scale models 1:25

7. Recipes If you had a recipe that used 100g of margarine to 250g of flour, the ratio of margarine to flour is 100 : 250.

8. Ratios There are a few ways of expressing ratios. Simplest Form Unitary Form Equivalent Form

9. Simplest Form If a ratio is in its simplest form the numbers do not share a common factor. The numbers are whole numbers. Simplifying ratios is similar to simplifying fractions.

10. Question Write down the ratio 100 : 250 in its simplest form. : 25 : 100250 ÷ 50

11. Question Write down a ratio that is equivalent to 2 : 5

12. Question Write down the ratio 2 : ½ in its simplest form. : 2x 22 x ½ : 2½ x2 : 41

13. Question Write down the ratio 1.1 : 0.2 in its simplest form. : 1.1 x 100.2 x 10 : 1.10.2 x10 : 112

14. Unitary Form Ratios expressed in unitary form are either of the form 1 : n Or n : 1 In these cases n may be a fraction or a decimal

15. Unitary Form Write the ratio 6 : 10 in the form 1 : n : 6 ÷ 610 ÷ 6 : 610 ÷ 6 : 1 This side needs to be 1

16. Unitary Form Write the ratio 6 : 10 in the form n : 1 : 6 ÷ 1010 ÷ 10 : 610 ÷ 10 : 0.61 This side needs to be 1

17. Question Write the ratio 40 : 10 1.In its simplest form 2.In the form 1 : n

18. Solutions Write the ratio 40 : 10 In its simplest form 4 : 1 In the form 1 : n 1 : 0.25 Divide both sides by 10 Divide both sides by 40