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Rate and Proportion

S4. Rate and Proportion. Rates and Finding Rates. Direct Proportion. Direct Proportion graphs. www.mathsrevision.com. Inverse Proportion. S4. Starter Questions. www.mathsrevision.com. Rates. S4. Learning Intention. Success Criteria. To understand the term ‘rate’ and calculate it.

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Rate and Proportion

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  1. S4 Rate and Proportion Rates and Finding Rates Direct Proportion Direct Proportion graphs www.mathsrevision.com Inverse Proportion Created by Mr. Lafferty @www.mathsrevision.com

  2. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  3. Rates S4 Learning Intention Success Criteria • To understand the term ‘rate’ and calculate it. • To explain the term ‘rate’ is and how to find the rate. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  4. Rates S4 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) www.mathsrevision.com This means that if Sean walked at this speed for one hour he would travel 5km. Created by Mr. Lafferty @www.mathsrevision.com

  5. Rates S4 • We are often interested in rates • Miles per gallon • Goals per game • £’s spent per day • Calories per day • Words per minute www.mathsrevision.com Why are we interested in rates? www.mathsrevision.com

  6. Rates S4 Example : Sean walks at 5 km per hour (km/hr) How far would he walk in : (a) 4 hours (b) Half an hour www.mathsrevision.com (a) 4 x 5 = 20km (b) 5 x 0.5 = 2.5 km Created by Mr. Lafferty @www.mathsrevision.com

  7. Finding the Rate S4 Example : For 5 hours’ work Jennifer is paid £30. Calculate her rate of pay per hour. Answer : 5 hours  £30 www.mathsrevision.com 1 hour  £30 ÷ 5 = £6 This means that Jennifer is paid a ‘rate’ of £6 per hour Created by Mr. Lafferty @www.mathsrevision.com

  8. Finding the Rate S4 Example : 3 litres of paint covers a fence area of 36 m2 How much will 1 litre cover. Answer : 3 litres  36 www.mathsrevision.com 1 litre  36 ÷ 3 = 12m2 This means that 12m2 requires 1 litre of paint. Created by Mr. Lafferty @www.mathsrevision.com

  9. Finding the Rate S4 Example : Nicola gets paid £48 000 pounds a year. What is her monthly rate of pay. Answer : 12 months  £48 000 www.mathsrevision.com 1 month  £48 000 ÷ 12 = £4 000 This means Nicola gets paid £4 000 per month Created by Mr. Lafferty @www.mathsrevision.com

  10. Finding the Rate S4 Now try Ex 1 Ch 2 (page 26) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  11. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  12. Direct Proportion S4 Learning Intention Success Criteria 1. Understand the idea of Direct Proportion. • 1. To explain the term Direct Proportion. 2. Solve simple proportional problems. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  13. Direct Proportion S4 Two quantities, (for example, number of cakes and total cost) are said to be in DIRECT PROPORTION, if : Are we expecting more or less “ .. When you double the number of cakes you double the cost.” Easier method Cakes Pence 6 420 5 Example : The cost of 6 cakes is £4.20. find the cost of 5 cakes. www.mathsrevision.com Cakes Cost 6  4.20 (less) 1  4.20 ÷ 6 = 0.70 5  0.70 x 5 = £3.50 Created by Mr. Lafferty Maths Dept.

  14. Direct Proportion S4 Example : On holiday I exchanged £30 for $45. How many $ will I get for £50. Are we expecting more or less What name do we give to this value Exchange rate £ $ Easier method £ $ 30 45 50 30  45 www.mathsrevision.com 1  45 ÷ 30 = 1.5 50  1.5 x 50 = $75 (more) Created by Mr. Lafferty Maths Dept.

  15. Direct Proportion S4 Sometimes it is easier to find the cost of 10,100 or 1000 items rather than 1. Are we expecting more or less Example : 300 pencils cost £6. How much will 200 cost. Easier method Pencil Pence 300 600 200 Pencils Cost 300  £6.00 www.mathsrevision.com 100  £6.00 ÷ 3 = £2.00 200  £2.00 x 2 = £4.00 (less) Created by Mr. Lafferty Maths Dept.

  16. Direct Proportion S4 Now try Ex 2 Ch2 (page 28) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  17. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  18. Proportion Direct Proportion Graphs S4 Learning Intention Success Criteria 1. Understand that Direct Proportion Graph is a straight line. • 1. To explain how Direct Proportion Graph is always a straight line. 2. Construct Direct Proportion Graphs. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  19. Proportion Direct Proportion Graphs S4 The table below shows the cost of packets of “Biscuits”. www.mathsrevision.com We can construct a graph to represent this data. What type of graph do we expect ? Created by Mr. Lafferty Maths Dept.

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

  21. Proportion Direct Proportion Graphs S4 KeyPoint Two quantities which are in DIRECT PROPORTION always lie on a straight line passing through the origin. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  22. Proportion Direct Proportion Graphs S4 Example : Plot the points in the table below. Are they in direct proportion? www.mathsrevision.com We plot the points (1,3) , (2,6) , (3,19) , (4,12) Created by Mr. Lafferty Maths Dept.

  23. y x Proportion Direct Proportion Graphs S4 12 Plotting the points (1,3) , (2,6) , (3,9) , (4,12) 11 10 9 8 7 Since we have a straight line passing through the origin x and y are in direct proportion. 6 www.mathsrevision.com 5 4 3 2 1 Created by Mr. Lafferty Maths Dept. 0 1 2 3 4

  24. Proportion Direct Proportion S4 Now try TJ Extension booklet www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  25. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  26. Proportion Inverse Proportion S4 Learning Intention Success Criteria 1. Understand the idea of Inverse Proportion. • 1. To explain the term Inverse Proportion. 2. Solve simple inverse proportion problems. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  27. Proportion Inverse Proportion S4 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. Are we expecting more or less Easier method Workers Hours 3 8 4 Example : If it takes 3 men 8 hours to build a wall. How long will it take 4 men. (Less time !!) www.mathsrevision.com Men Hours 3  8 (less) 1  3 x 8 = 24 hours 4  24 ÷ 4 = 6 hours Created by Mr. Lafferty Maths Dept.

  28. Proportion Inverse Proportion S4 Example : It takes 10 men 12 months to build a house. How long should it take 8 men. Are we expecting more or less Men Months Easier method Workers months 10 12 8 10  12 www.mathsrevision.com 1  12 x 10 = 120 8  120 ÷ 8 = 15 months (more) Created by Mr. Lafferty Maths Dept.

  29. Proportion Inverse Proportion S4 Now try TJ Extension Booklet www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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