1. 1 Press Ctrl-A ©G Dear 2008 – Not to be sold/Free to use Rates Stage 6 - Year 11 General Mathematics Preliminary

2. 2 Rates (1/5) It is the comparison of two (or more) quantities of a different type. km/h Kilometres per hour kg/ha Kilograms per hectare DistanceTimeMassArea mg/L Milligrams per litre MassVolume L/h Litres per hour VolumeTime

3. 3 Simplifying Rates (2/5) To simplify rates we divide the first number by the second. Eg 1: 600 km in 5 hours 600 ÷ 5= 120 km/h Eg 2: 50 tonne in 10 hectares 50 ÷ 10= 5 t/ha

4. 4 Converting Rates (3/5) To convert rates we multiply (or divide) each number separately. Eg 1: Convert 72 km/h to m/s x 1000 (to convert to meters) = 72 000 m/h x 60 = 72 000 m/ 3600 s = 72 000 ÷ 3600 = 20 m/s (to convert to seconds)

5. 5 Converting Rates (4/5) To convert rates we multiply (or divide) each number separately. Eg 2: Convert 7500 mL/1500g to L/kg ÷ 1000 (to convert to litres) = 7.5 L/1500g ÷ 1000 = 7.5 L/ 1.5 kg = 7.5 ÷ 1.5 = 5 L/kg (to convert to kilograms)

6. 6 Using Rates (5/5) A recipe for banana cake (for 6 people) includes 2 bananas, 500g of flour and 100 mL of olive oil. Convert it for 9 people. Multiplication Factor =9÷ 6= 1.5 Bananas =2x 1.5 = 3 Bananas Flour =500x 1.5 = 750 g Olive oil =100x 1.5 = 150 mL