1. Per means for each. A phrase that contains the word ‘per’ is called a RATE. Example :Sean walks at 5 km per hour (km/hr) This means that if Sean walked at this speed for one hour he would travel 5km. Rates

2. We are often interested in rates Miles per gallon Goals per game £’s spent per day Calories per day Words per minute Rates Why are we interested in rates?

3. Example : Sean walks at 5 km per hour (km/hr) How far would he walk in : (a)4 hours(b)Half an hour (a) 20km Rates 15 44 x 5 = HoursDistance walked (b) 2.5km 15 0.50.5 x 5 = HoursDistance walked

4. Finding the Rate Example : For 5 hours’ work Jennifer is paid £30. Calculate her rate of pay per hour. Answer : 5 hours  £30 1 hour  £30 ÷ 5 =£6 This means that Jennifer is paid a ‘rate’ of £6 per hour

5. Finding the Rate Example : Nicola gets paid £48 000 pounds a year. What is her monthly rate of pay. Answer : 12 months  £48 000 1 month  £48 000 ÷ 12 =£4 000 This means Nicola gets paid £4 000 per month

6. Direct Proportion “.. When you double the number of cakes you double the cost.” CakesCost Two quantities, (for example, number of cakes and total cost) are said to be in DIRECT PROPORTION, if : Example :The cost of 6 cakes is £4.20. find the cost of 5 cakes. 6  4.20 1  4.20 ÷ 6 = 0.70 5  0.70 x 5 = £3.50

7. Direct Proportion £$ Example :On holiday I exchanged £30 for $45. How many $ will I get for £50. 30  45 1  45 ÷ 3 0 = 1.5 50  1.5 x 50 = $75 What name do we give to this value Exchange rate

8. Direct Proportion PencilsCost Sometimes it is easier to find the cost of 10,100 or 1000 items rather than 1. Example :300 pencils cost £6. How much will 200 cost. 300  £6.00 100  £6.00 ÷ 3 = £2.00 200  £2.00 x 2 = £4.00

9. Proportion MenHours Inverse proportion is when one quantity increases and the other decreases. The two quantities are said to be INVERSELY PROPORTIONAL or (INDIRECTLY PROPORTIONAL) to each other. Example :If it takes 3 men 8 hours to build a wall. How long will it take 4 men. 3  8 1  4  Inverse Proportion Are we expecting more or less Less Time !!! 3 x 8= 24 24 ÷ 4= 6 hours

10. 1  8  Proportion MenMonths Example :It takes 10 men 12 months to build a house. How long should it take 8 men. 10  12 Inverse Proportion Are we expecting more or less More time !!! 12 x 10 = 120 120 ÷ 8 = 15 months

11. Ratios can be used to compare different quantities Example : There are 2 triangles and 3 rectangles. The ratio of triangles to rectangles is said to be 2 : 3 Note: The ratio of rectangles to triangles is said to be 3 : 2 Ratio Simplifying a ratio ?

12. Simplifying a ratio is like simplifying fractions Fraction : Ratio : Ratio Simplifying a ratio ? 6868 == 3434 6 : 8 = = 3 : 4 Divide top and bottom by highest common factor

13. Ratio Calculations Example :The ratio of boys to girls is 4:5. If there are 16 boys, how many girls are there. boys girls 45 1620 x 4 x 4 Ratio

14. Ratio Calculations Example :The ratio of cars to buses is 3:7. If there are 49 buses, how many cars are there? cars buses 37 2149 x 7 x 7 Ratio

15. Ratio Calculations Ratio Example :The ratio of goals to games for a footballer is 1 : 4. If he plays 52 games, how many goals would he be expected to score? goals games 14 1352 x 13 x 13

16. Ratio & Proportion Example :Bill and Ben share a raffle win of £400 in the ratio 3:5. How much does each get ? Proportional Division Step 1 :Since the ratio is 3:5, there are : 3+5 = 8 shares Step 2 :Each share is worth : Step 3 :Bill gets 3 x 50 = £150 Ben gets 5 x 50 = £250 Check ! 150 + 250 = 400

17. Ratio & Proportion Example :Ryan and Ross share 24 cakes in the ratio 3:1. How many cakes does each get ? Proportional Division Step 1 :Since the ratio is 3:1, there are : 3+1 = 4 shares Step 2 :Each share is worth : Step 3 :Ryan gets 3 x 6 = 18 Ross gets 1 x 6 = 6 Check ! 18 + 6 = 24