Ratio Proportion www mathsrevision com MNU 3 08

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Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Simplifying Ratios Ratio Calculations Proportional Division Proportion Direct Proportion Graph of Direct Proportion Inverse Proportion 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a 10

Starter Questions www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion What is a ratio ? www. mathsrevision. com MNU 3 -08

Ratio & Proportion What is a ratio ? www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Learning Intention Success Criteria 1. We are learning what a ratio is and explain how we can sometimes simplify them. 10 -Nov-20 1. Understand the term ratio. . 2. Calculate and simplify basic ratios showing appropriate working. Created by Mr. Lafferty Maths Dept.

Ratio & Proportion What is a ratio ? MNU 3 -08 a MNU 4

Ratio & Proportion What is a ratio ? MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com 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 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Simplifying a ratio ? www. mathsrevision. com MNU 3 -08 a

Ratio & Proportion Simplifying a ratio ? www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Simplifying a ratio is like simplifying fractions Fraction : Ratio : 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Simplifying a ratio ? www. mathsrevision. com MNU 3 -08 a

Ratio & Proportion Simplifying a ratio ? www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Sometimes we need to multiply to simplify Ratio : 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Simplifying a ratio ? www. mathsrevision. com MNU 3 -08 a

Ratio & Proportion Simplifying a ratio ? www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a When working with ratios, the two units MUST be the same Ratio : 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Simplifying a ratio ? Now try Exercise 1&2

Ratio & Proportion www. mathsrevision. com Simplifying a ratio ? Now try Exercise 1&2 Ch 41 (page 158) 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com 9

Starter Questions MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com 9 8 6 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Ratio Calculations www. mathsrevision. com MNU 3 -08 a MNU 4

Ratio & Proportion Ratio Calculations www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Learning Intention 1 10 -Nov-20 Success Criteria We are learning to do ratio calculations. 1. Remember and apply tabular method to work out ratios. 2. Show appropriate working. Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Ratio Calculations www. mathsrevision. com MNU 3 -08 a MNU 4

Ratio & Proportion Ratio Calculations www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Example : The ratio of boys to girls is 4: 5. If there are 16 boys, how many girls are there. boys girls x 4 10 -Nov-20 4 5 16 20 Created by Mr. Lafferty Maths Dept. x 4

Ratio & Proportion Ratio Calculations www. mathsrevision. com MNU 3 -08 a MNU 4

Ratio & Proportion Ratio Calculations www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Example : The ratio of cars to buses is 3: 7. If there are 49 buses, how many cars are there. cars buses x 7 10 -Nov-20 3 7 21 49 Created by Mr. Lafferty Maths Dept. x 7

Ratio & Proportion Ratio Calculations www. mathsrevision. com MNU 3 -08 a MNU 4

Ratio & Proportion Ratio Calculations www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Now try Exercise 3 Ch 41 (page 160) 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com 9

Starter Questions MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com 9 8 6 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportional Division www. mathsrevision. com MNU 3 -08 a MNU 4 -08

Ratio & Proportional Division www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Learning Intention Success Criteria 1. We are learning to calculate proportional division by using shares. 1. Calculate one share. 2. Solve problems using shares. 3. Show appropriate working. 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportional Division www. mathsrevision. com MNU 3 -08 a MNU 4 -08

Ratio & Proportional Division www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Example : Step 1 : Bill and Ben share a raffle win of £ 400 in the ratio 3: 5. How much does each get ? 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 10 -Nov-20 Created by Mr. Lafferty Maths Dept. Check ! 150 + 250 = 400

Ratio & Proportional Division www. mathsrevision. com MNU 3 -08 a MNU 4 -08

Ratio & Proportional Division www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Example : Step 1 : Ryan and Ross share 24 cakes in the ratio 3: 1. How many cakes does each get ? 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 10 -Nov-20 Created by Mr. Lafferty Maths Dept. Check ! 18 + 6 = 24

Ratio & Proportional Division www. mathsrevision. com MNU 3 -08 a MNU 4 -08

Ratio & Proportional Division www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Now try Exercise 4 Ch 41 (page 161) 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a 10

Starter Questions www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Learning Intention 1 Success Criteria We are learning the term proportion. 1. Understand the idea of proportion. 2. Solve simple proportional problems. 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a If you know the total cost of several items, you can easily find the cost per item. Example : The cost of 5 cakes is £ 4. 00. Find the cost of one. Cost of one is simply : 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Now try Exercise 5 Ch 41 (page 163) 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a 10

Starter Questions www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion www. mathsrevision. com MNU 3 -08 a MNU 4

Ratio & Proportion Direct Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Learning Intention Success Criteria 1. We are learning the term Direct Proportion. 1. Understand the idea of Direct Proportion. 2. Solve simple proportional problems. 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion MNU 3 -08 a MNU 4 -08 a www.

Ratio & Proportion Direct Proportion MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com Two quantities, (for example, number of cakes and total cost) Are weare said to be in DIRECT PROPORTION, if : expecting “. . When you double the number of cakes more or less you double the cost. ” Example : The cost of 6 cakes is £ 4. 20. Easier. Find method the cost of 5 cakes. Cakes Pence Cakes Cost 6 420 6 4. 20 (less) 5 1 4. 20 ÷ 6 = 0. 70 5 10 -Nov-20 Created by Mr. Lafferty Maths Dept. 0. 70 x 5 = £ 3. 50

Ratio & Proportion Direct Proportion MNU 3 -08 a MNU 4 -08 a www.

Ratio & Proportion Direct Proportion MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com Example : Are we expecting more or less On holiday I exchanged £ 30 for $45. How many $ will I get for £ 50. £ $ Easier 30 method 1 £ $ 50 30 45 (more) 50 10 -Nov-20 45 45 ÷ 30 = 1. 5 What name do we give to this Exchange value rate 1. 5 x 50 = $75 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion MNU 3 -08 a MNU 4 -08 a www.

Ratio & Proportion Direct Proportion MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com Sometimes it is easier to find the cost of 10, 100 or 1000 items Are we rather than 1. expecting Example 300 pencils cost £ 6. How much will 200 cost. more or less: Pencils Easier method 300 Pencil Pence 100 300 200 600 (less) 200 10 -Nov-20 Cost £ 6. 00 ÷ 3 = £ 2. 00 x 2 = £ 4. 00 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion www. mathsrevision. com MNU 3 -08 a MNU 4

Ratio & Proportion Direct Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Now try Exercise 6 Ch 41 (page 164) 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a 10

Starter Questions www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion Graphs www. mathsrevision. com MNU 3 -08 a MNU

Ratio & Proportion Direct Proportion Graphs www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a 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. 2. Construct Direct Proportion Graphs. 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion Graphs MNU 3 -08 a MNU 4 -08 a

Ratio & Proportion Direct Proportion Graphs MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com The table below shows the cost of packets of “Biscuits”. We can construct a graph to represent this data. What type of graph do we expect ? 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Notice that the Direct Proportion Graphs points lie on a straight line passing through

Notice that the Direct Proportion Graphs points lie on a straight line passing through the origin This is true for any two quantities which are in Direct Proportion. 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion Graphs www. mathsrevision. com MNU 3 -08 a MNU

Ratio & Proportion Direct Proportion Graphs www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Key. Point Two quantities which are in DIRECT PROPORTION always lie on a straight line passing through the origin. 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion Graphs MNU 3 -08 a MNU 4 -08 a

Ratio & Proportion Direct Proportion Graphs MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com Example : Plot the points in the table below. Are they in direct proportion? X y 1 3 2 6 3 9 4 12 We plot the points (1, 3) , (2, 6) , (3, 19) , (4, 12) 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a 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 10 -Nov-20 Created by Mr. Lafferty Maths Dept. 0 1 2 3 4 x

Ratio & Proportion Direct Proportion www. mathsrevision. com MNU 3 -08 a MNU 4

Ratio & Proportion Direct Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Now try Exercise 7 Ch 41 (page 166) 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a y

Starter Questions www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a y x x xx x x 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Inverse Proportion www. mathsrevision. com MNU 3 -08 a MNU 4

Ratio & Proportion Inverse Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Learning Intention Success Criteria 1. We are learning the term Inverse Proportion. 1. Understand the idea of Inverse Proportion. 2. Solve simple inverse proportion problems. 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Inverse Proportion MNU 3 -08 a MNU 4 -08 a www.

Ratio & Proportion Inverse Proportion MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com Inverse proportion is when one quantity doubles and Are wethe other halves. The two quantities are said expecting to be INVERSELY PROPORTIONAL) to each other. moreor or(INDIRECTLY less 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 (less) 4 1 3 x 8 = 24 hours 4 10 -Nov-20 Created by Mr. Lafferty Maths Dept. 24 ÷ 4 = 6 hours

Ratio & Proportion Inverse Proportion MNU 3 -08 a MNU 4 -08 a www.

Ratio & Proportion Inverse Proportion MNU 3 -08 a MNU 4 -08 a www. mathsrevision. com Example : It takes 10 workers 12 months to build a house. Are we How long should it take 8 men. expecting more or less Men Months 12 Easier 10 method 1 12 x 10 = 120 Workers months 8 120 ÷ 8 = 15 months 10 12 (more) 8 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion www. mathsrevision. com MNU 3 -08 a MNU 4

Ratio & Proportion Direct Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Now try Exercise 8 Ch 41 (page 168) 10 -Nov-20 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a

Ratio & Proportion www. mathsrevision. com MNU 3 -08 a MNU 4 -08 a Mixed Problems Exercise 9 Ch 41 (page 168) 10 -Nov-20 Created by Mr. Lafferty Maths Dept.