1. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Simplifying Ratios Ratio Calculations Ratio & Proportion www.mathsrevision.com Direct Proportion Graph of Direct Proportion Inverse Proportion Proportional Division Proportion

2. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com

3. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Understand the term ratio.. 1. We are learning what a ratio is and explain how we can sometimes simplify them. Ratio & Proportion 2.Calculate and simplify basic ratios showing appropriate working. What is a ratio ?

4. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion Ratios can be used to compare different quantities What is a ratio ? 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 MNU 3-08a MNU 4-08a

5. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion Simplifying a ratio is like simplifying fractions Simplifying a ratio ? Fraction : Ratio : MNU 3-08a MNU 4-08a

6. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion Sometimes we need to multiply to simplify Simplifying a ratio ? Ratio : MNU 3-08a MNU 4-08a

7. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion When working with ratios, the two units MUST be the same Simplifying a ratio ? Ratio : MNU 3-08a MNU 4-08a

8. 1-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 1&2 Ch41 (page 158) www.mathsrevision.com Ratio & Proportion Simplifying a ratio ?

9. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 9 6 8

10. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Remember and apply tabular method to work out ratios. 1 We are learning to do ratio calculations. Ratio & Proportion 2.Show appropriate working. Ratio Calculations

11. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion 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 MNU 3-08a MNU 4-08a

12. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion 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 MNU 3-08a MNU 4-08a

13. 1-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 3 Ch41 (page 160) www.mathsrevision.com Ratio & Proportion Ratio Calculations MNU 3-08a MNU 4-08a

14. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 9 6 8

15. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. We are learning to calculate proportional division by using shares. 1. Calculate one share. Ratio & Proportion Proportional Division 2. Solve problems using shares. 3. Show appropriate working.

16. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 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 MNU 3-08a MNU 4-08a

17. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 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 MNU 3-08a MNU 4-08a

18. 1-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 4 Ch41 (page 161) www.mathsrevision.com Ratio & Proportion Proportional Division MNU 3-08a MNU 4-08a

19. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com

20. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1 We are learning the term proportion. 1. Understand the idea of proportion. Ratio & Proportion 2. Solve simple proportional problems. Proportion

21. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion Example :The cost of 5 cakes is £4.00. Find the cost of one. Cost of one is simply : If you know the total cost of several items, you can easily find the cost per item. Proportion MNU 3-08a MNU 4-08a

22. 1-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 5 Ch41 (page 163) www.mathsrevision.com Ratio & Proportion Proportion MNU 3-08a MNU 4-08a

23. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com

24. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. We are learning the term Direct Proportion. 1. Understand the idea of Direct Proportion. Ratio & Proportion 2. Solve simple proportional problems. Direct Proportion

25. Example :The cost of 6 cakes is £4.20. Find the cost of 5 cakes. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & 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 : Direct Proportion 6  4.20 1  4.20 ÷ 6 = 0.70 5  0.70 x 5 = £3.50 Easier method CakesPence 6  420 5 Are we expecting more or less (less) MNU 3-08a MNU 4-08a

26. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion £ $ 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 = $75 What name do we give to this value Exchange rate Easier method £$ 30  45 50 Are we expecting more or less (more) MNU 3-08a MNU 4-08a

27. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion Pencils Cost Sometimes it is easier to find the cost of 10,100 or 1000 items rather than 1. Direct Proportion 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 Easier method PencilPence 300  600 200 Are we expecting more or less (less) MNU 3-08a MNU 4-08a

28. 1-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 6 Ch41 (page 164) www.mathsrevision.com Ratio & Proportion Direct Proportion MNU 3-08a MNU 4-08a

29. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com

30. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. We are learning how Direct Proportion Graph is always a straight line. 1. Understand that Direct Proportion Graph is a straight line. Ratio & Proportion 2. Construct Direct Proportion Graphs. Direct Proportion Graphs

31. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion The table below shows the cost of packets of “Biscuits”. Direct Proportion Graphs We can construct a graph to represent this data. What type of graph do we expect ? MNU 3-08a MNU 4-08a

32. 1-Aug-15Created by Mr. Lafferty Maths Dept. Direct Proportion Graphs Notice that the points lie on a straight line passing through the origin This is true for any two quantities which are in Direct Proportion.

33. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion Direct Proportion Graphs KeyPoint Two quantities which are in DIRECT PROPORTION always lie on a straight line passing through the origin. MNU 3-08a MNU 4-08a

34. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion Example : Plot the points in the table below. Are they in direct proportion? Direct Proportion Graphs We plot the points (1,3), (2,6), (3,19), (4,12)X1234y36912 MNU 3-08a MNU 4-08a

35. 1-Aug-15Created by Mr. Lafferty Maths Dept. 1 www.mathsrevision.com Ratio & Proportion Plotting the points (1,3), (2,6), (3,9), (4,12) Direct Proportion Graphs 01234 10 11 12 2 3 4 5 6 7 8 9 Since we have a straight line passing through the origin x and y are in direct proportion. x y MNU 3-08a MNU 4-08a

36. 1-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 7 Ch41 (page 166) www.mathsrevision.com Ratio & Proportion Direct Proportion MNU 3-08a MNU 4-08a

37. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com x x x x x x x x y

38. MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. We are learning the term Inverse Proportion. 1. Understand the idea of Inverse Proportion. Ratio & Proportion 2. Solve simple inverse proportion problems. Inverse Proportion

39. Example :If it takes 3 workers 8 hours to build a wall. How long will it take 4 men. 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion MenHours Inverse proportion is when one quantity doubles and the other halves. The two quantities are said to be INVERSELY PROPORTIONAL or (INDIRECTLY PROPORTIONAL) to each other. 3  8 1  3 x 8 = 24 hours 4  24 ÷ 4 = 6 hours Inverse Proportion Easier method Workers Hours 3  8 4 Are we expecting more or less (less) MNU 3-08a MNU 4-08a

40. 8  120 ÷ 8 = 15 months 1-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Ratio & Proportion MenMonths Example : It takes 10 workers 12 months to build a house. How long should it take 8 men. 10  12 1  12 x 10 = 120 Inverse Proportion Easier method Workersmonths 10  12 8 Are we expecting more or less (more) MNU 3-08a MNU 4-08a

41. 1-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 8 Ch41 (page 168) www.mathsrevision.com Ratio & Proportion Direct Proportion MNU 3-08a MNU 4-08a

42. 1-Aug-15Created by Mr. Lafferty Maths Dept. Mixed Problems Exercise 9 Ch41 (page 168) www.mathsrevision.com Ratio & Proportion MNU 3-08a MNU 4-08a