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Unformatted text preview: Ratio & Proportion
Simplifying Ratios Ratio Calculations Proportional Division Proportion Direct Proportion Graph of Direct Proportion Inverse Proportion
13 Feb 2012 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Starter Questions
1. 3x + 5 = 17 2 . C a lc ula t e 2 0 % o f 2 2 0 3. How many signif icant number s
(a) 123 (b) 202 (c) 0. 09 www.mathsrevision.com 4. Car depr eciat es by 20% in it s f ir st year . I f it was bought new f or 10 000. How much is it wor t h now.
Created by Mr. Lafferty Maths Dept. 13 Feb 2012 Ratio & Proportion
What is a ratio ?
Learning Intention Success Criteria 1. Understand the term ratio. . 2. Calculate and simplify basic ratios. www.mathsrevision.com 1. To understand what a ratio is and explain how we can sometimes simplify them. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
What is a ratio ? Ratios can be used to compare different quantities www.mathsrevision.com 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
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Simplifying a ratio ? Simplifying a ratio is like simplifying fractions www.mathsrevision.com Fraction : 6 6 3 = 2 = 8 8 4
2 Ratio : 6 : 8 = 6 : 8 = 3 : 4
2 2 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Simplifying a ratio ? Sometimes we need to multiply to simplify www.mathsrevision.com Ratio : 1 1 : 5 = 3 : 5 3 = 1 : 15 3 3 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Simplifying a ratio ? When working with ratios, the two units MUST be the same Ratio : www.mathsrevision.com 1 h o ur : 4 0 m inut e s 4 = 15 m inut e s : 4 0 m inut e s = 3 m inut e s : 8 m inut e s
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Simplifying a ratio ? www.mathsrevision.com Now try Exercise 1&2 Ch41 (page 158) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
1. 3x + 5 = 17 9 8 6 www.mathsrevision.com 2 . C a lc ula t e t h e a r e a o f t h e s h a p e . 3. How many signif icant number s
(a) 0. 13 (b) 0. 02 (c) 1. 0 9 4. 3 2 + 4 3
Created by Mr. Lafferty Maths Dept. 13 Feb 2012 Ratio & Proportion
Ratio Calculations
Learning Intention Success Criteria 1. Use tabulating method to work out ratios. 2. Show appropriate working. www.mathsrevision.com 1. To show how to do ratio calculations. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 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 x 4 4 16 girls 5 20 x 4 www.mathsrevision.com
13 Feb 2012 Created by Mr. Lafferty Maths Dept. 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 x 7 3 21 buses 7 49 x 7 www.mathsrevision.com
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Ratio Calculations www.mathsrevision.com Now try Exercise 3 Ch41 (page 160) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
1. 6x + 5 = 59 9 8 6 www.mathsrevision.com 2 . C a lc ula t e t h e a r e a o f t h e s h a p e . 3. Round t o 2 decimal places.
(a) 0. 853 (b) 0. 356 (c) 1 . 995 4. 5 1 + 2 4
Created by Mr. Lafferty Maths Dept. 13 Feb 2012 Ratio & Proportion
Proportional Division
Learning Intention Success Criteria 1. Work out equal number of shares for a ratio. 2. Solve problems using shares. 3. Show appropriate working. www.mathsrevision.com 1. Explain how to work out proportional division by using shares. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Proportional Division Example : Bill and Ben share a raffle win of 400 in the ratio 3:5. How much does each get ? www.mathsrevision.com 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
13 Feb 2012 Created by Mr. Lafferty Maths Dept. 50 8 400
Check ! 150 + 250 = 400 Ratio & Proportion
Proportional Division Example : Ryan and Ross share 24 cakes in the ratio 3:1. How many cakes does each get ? www.mathsrevision.com 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
13 Feb 2012 Created by Mr. Lafferty Maths Dept. 6 4 24
Check ! 18 + 6 = 24 Ratio & Proportion
Proportional Division www.mathsrevision.com Now try Exercise 4 Ch41 (page 161) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
1. Simplf y t he r at io 13 : 52 2 . Calculat e 3. 2. 5 % of 400 www.mathsrevision.com I got $ 650 f or 100. How much would I get f or 2. Put in or der , smallest f ir st . 0. 25, 0. 19, 0. 01, 0. 026 4. 5.
13 Feb 2012 Find t he value of x 7x +2. 5 = 20
Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Proportion
Learning Intention Success Criteria 1. Understand the idea of proportion. www.mathsrevision.com 1. To explain the term proportion. 2. Solve simple proportional problems. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Proportion If you know the total cost of several items, you can easily find the cost per item. www.mathsrevision.com Example : The cost of 5 cakes is 4.00. Find the cost of one. Cost of one is simply : 0 .8 0 5 4 .0 0 = 8 0 p 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Proportion www.mathsrevision.com Now try Exercise 5 Ch41 (page 163) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
1. Simplf y t he r at io 85 : 25 www.mathsrevision.com 2 . Calculat e 3. 6. 5% of 300 Find t he mean, median and mode f or 25, 20, 55, 20 4 . C a lc ula t e 13 Feb 2012 4 5 5 8
Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Direct Proportion
Learning Intention Success Criteria 1. Understand the idea of Direct Proportion. 2. Solve simple proportional problems. www.mathsrevision.com 1. To explain the term Direct Proportion. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Direct Proportion 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." Example : The cost of 6 cakes is 4.20. Easier method Find the cost of 5 cakes. Cakes Pence Cakes Cost 6 420 6 4.20 (less) 5 1 4.20 6 = 0.70 5 420 = 350 = 3.50 5 0.70 x 5 = 3.50 13 Feb 2012 www.mathsrevision.com 6 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Direct Proportion Example : Are we expecting more or less On holiday I exchanged 30 for $45. How many $ will I get for 50. $ 45 45 30 = 1.5 1.5 x 50 = $75 www.mathsrevision.com What name do we give to this value Exchange rate 30 Easier method 1 $ 30 50 45 (more) 50
13 Feb 2012 50 45 = $75 30 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Direct Proportion 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. Pencils Cost Easier method 300 6.00 Pencil Pence 100 6.00 3 = 2.00 300 600 200 2.00 x 2 = 4.00 (less) 200
13 Feb 2012 www.mathsrevision.com 200 600 = 400 = 4 300 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Direct Proportion www.mathsrevision.com Now try Exercise 6 Ch41 (page 164) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
1. Simplf y t he r at io 95 : 35 www.mathsrevision.com 2 . Calculat e 3. 2. 5% of 500 Find t he mean, median and mode f or 5, 2, 5, 8 4 . C a lc ula t e 3
13 Feb 2012 1 1 1 2 2
Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Direct Proportion Graphs
Learning Intention Success Criteria 1. Understand that Direct Proportion Graph is a straight line. 2. Construct Direct Proportion Graphs. www.mathsrevision.com 1. To explain how Direct Proportion Graph is always a straight line. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Direct Proportion Graphs The table below shows the cost of packets of "Biscuits". www.mathsrevision.com No . o f Pkt s Co s t ( p) 1 20 2 40 3 60 4 80 5 6 10 0 12 0 We can construct a graph to represent this data. What type of graph do we expect ?
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Dir ect Pr opor t ion
14 0 12 0 10 0 80 60 40 20 0 0
13 Feb 2012 Notice that the points lie Direct Proportion Graphs on a straight line passing through the origin This is true for any two quantities which are in Direct Proportion.
1 2
Created by Mr. Lafferty Maths Dept. 3 4 5 6 No. of Packet s Ratio & Proportion
Direct Proportion Graphs www.mathsrevision.com KeyPoint
Two quantities which are in DIRECT PROPORTION always lie on a straight line passing through the origin.
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Direct Proportion Graphs Example : Plot the points in the table below. Are they in direct proportion? www.mathsrevision.com X y 1 3 2 6 3 9 4 12 We plot the points (1,3) , (2,6) , (3,19) , (4,12) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Direct Proportion Graphs y 12 Plotting the points 11 10 (1,3) , (2,6) , (3,9) , (4,12) 9 8 7 Since we have a straight line 6 passing through the origin 5 x and y are in 4 direct proportion. 3 2 1
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion www.mathsrevision.com 0 1 2 3 4 x Ratio & Proportion
Direct Proportion www.mathsrevision.com Now try Exercise 7 Ch41 (page 166) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
1. Simplf y t he r at io 95 : 35 y x x x www.mathsrevision.com 2 . Calculat e 0. 5 + 1. 45 + 0. 06 3. I s t her e a cor r elat ion bet ween t he t wo quanit ies. I f so descr ibe it . x xx x x 4 . C a lc ula t e 13 Feb 2012 1 2 1 4
Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Inverse Proportion
Learning Intention Success Criteria 1. Understand the idea of Inverse Proportion. 2. Solve simple inverse proportion problems. www.mathsrevision.com 1. To explain the term Inverse Proportion. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Inverse Proportion Inverse proportion is when one quantity doubles and the other halves. The two quantities are said Are we expecting to be INVERSELY PROPORTIONAL more or less or (INDIRECTLY PROPORTIONAL) to each other. Example : If it takes 3 workers 8 hours to build a wall. How long will it take 4 men. Easier method Workers Hours Men Hours 3 8 3 8 (less) 4 1 3 x 8 = 24 hours 13 Feb 2012 www.mathsrevision.com 3 8 = 6 hours 4 4 24 4 = 6 hours Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Inverse Proportion Example : It takes 10 workers 12 months to build a house. Are we expecting How long should it take 8 men. more or less Men Months 10 12 Easier method 1 12 x 10 = 120 Workersmonths 120 8 = 15 months 10 8 12 (more) 8
13 Feb 2012 www.mathsrevision.com 10 12 = 15 months 8 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Direct Proportion www.mathsrevision.com Now try Exercise 8 Ch41 (page 168) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Ratio & Proportion
Mixed Problems Exercise 9 Ch41 (page 168) www.mathsrevision.com
13 Feb 2012 Created by Mr. Lafferty Maths Dept. ...
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