1. Ratio & Proportion according to Lawrence Potter The contents of this presentation are drawn from the Reading “Mathematics minus Fear” by Lawrence Potter (Marion Boyars Publishers Ltd 2006).

2. Ratio

3. Ratio and Proportion3 A “Rusty Nail” is one part Drambuie to 3 parts Scotch Whiskey. How much of each is needed to make a 100 mL “shot”? One part Drambuie and three parts Scotch makes four parts altogether. Drambuie makes up ¼ of 100 mL (i.e. 25 mL) and Scotch makes up ¾ of 100 mL (i.e. 75 mL). Check: 25 : 75 = 1 x 25 : 3 x 25 = 1 : 3 and 25 mL + 75 mL = 100 mL. So need 25 mL Drambuie + 75 mL Scotch to make a 100 mL Rusty Nail.

4. Ratio and Proportion4 The 'poor man's screwdriver' is one part vodka, and two parts orange drink mix, such as Gatorade. How much vodka is needed to make up a 1.5 litre jug of “poor man’s screw-driver” mix for a party? (a) 250 mL (b) 333 mL (c) 500 mL (d) 750 mL (e) 1 000 mL

5. Ratio and Proportion5 The 'poor man's screwdriver' is one part vodka, and two parts orange drink mix, such as Gatorade. How much vodka is needed to make up a 1.5 litre jug of “poor man’s screw-driver” mix for a party? (a) - (b) - (c) 500 mL (d) - (e) - One part out of three is vodka. 1 / 3 x 1 500 mL = 500 mL

6. Ratio and Proportion6 Proportion

7. Ratio and Proportion7 A car uses 30 litres of fuel for a journey of 400 Km. At this rate, how much fuel would be needed for a trip of 550 Km? 30 / 400 = x / 550 x = 30 / 400 x 550 x = 16500 / 400 x = 165 / 4 = 41.25 litres

8. Ratio and Proportion8 A car uses 25 litres of fuel for a journey of 300 Km. At this rate, how much fuel would be needed for a trip of 480 Km? (a) 30 litres (b) 35 litres (c) 36 litres (d) 40 litres (e) 45 litres

9. Ratio and Proportion9 A car uses 25 litres of fuel for a journey of 300 Km. At this rate, how much fuel would be needed for a trip of 480 Km? (a) - (b) - (c) - (d) 40 litres (e) - x = 25 x 480 / 300 = 40 L

10. Ratio and Proportion10 For 11 people, I will need 5.5 (= 11 / 2 ) times the quantities needed for 2 people. For example, I will need 5.5 x 4 = 22 onions. How many tomatoes are required?

11. Ratio and Proportion11 For 11 people, I will need 5.5 (= 11 / 2 ) times the quantities needed for 2 people. For example, I will need 5.5 x 4 = 22 onions. How many tomatoes are required? 5.5 x 6 = 33 tomatoes

12. Ratio and Proportion12 20 : 5 is equivalent to 4 : 1. 4 shares to the dog and 1 share to the cat makes 5 shares altogether. 575 g divided into 5 shares gives 115g for each “share”. The dog gets 4 x 115 g = 460 g. The cat gets 1 x 115 g = 115 g. Check: 460 g + 115 g = 575 g

13. Ratio and Proportion13 If the dog weighed 20 Kg, but the cat weighed only 3 Kg, how much would the cat receive of the 575 g tin of pet food? (a) 75 g (b) 100 g (c) 115 g (d) 125 g (e) 130 g

14. Ratio and Proportion14 If the dog weighed 20 Kg, but the cat weighed only 3 Kg, how much would the cat receive of the 575 g tin of pet food? (a) 75 g (b) - (c) - (d) - (e) - The cat receives 3 parts out of 23 ( = 20 + 3 ). 575 g divided into 23 parts gives 25 g per part. 3 x 25 g = 75 g This means the dog gets 20 x 25 g = 500 g. Check: 75 + 500 = 575

15. Ratio and Proportion15 For every 2 who are happy, 7 look unhappy. If there are 36 (= 2 x 18) happy people, there must be 7 x 18 (i.e. 126) people who look unhappy and should look for a better job!

16. Ratio and Proportion16 On a street map, 1 millimetre represents 25 metres. How many centimetres on the map is equivalent to a real distance of 1 Kilometre? (a) 0.4 centimetres (b) 4.0 centimetres (c) 40 centimetres (d) 400 centimetres (e) 25 centimetres

17. Ratio and Proportion17 On a street map, 1 millimetre represents 25 metres. How many centimetres on the map is equivalent to a real distance of 1 Kilometre? (a) - (b) 4.0 centimetres (c) - (d) - (e) - 1 mm 25 m 1 Km = 1 000 m = 40 x 25 m Therefore need 40 x 1 mm on the map to represent 40 x 25 m real distance. 40 mm = 4.0 cm

18. References: http://en.wikipedia.org/wiki/Scale_(map) http://en.wikipedia.org/wiki/Proportional ity_(mathematics)