# Ratio Proportion www mathsrevision com Simplifying Ratios Ratio

- Slides: 42

Ratio & Proportion www. mathsrevision. com Simplifying Ratios Ratio Calculations Proportional Division Proportion Direct Proportion Graph of Direct Proportion Inverse Proportion 11/24/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Starter Questions 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com What is a ratio ? Learning Intention 1. To understand what a ratio is and explain how we can sometimes simplify them. 11/24/2020 Success Criteria 1. Understand the term ratio. . 2. Calculate and simplify basic ratios. Created by Mr. Lafferty Maths Dept.

Ratio & Proportion What is a ratio ? 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 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Simplifying a ratio ? Simplifying a ratio is like simplifying fractions Fraction : Ratio : 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Simplifying a ratio ? Sometimes we need to multiply to simplify Ratio : 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Simplifying a ratio ? When working with ratios, the two units MUST be the same Ratio : 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Simplifying a ratio ? Now try Exercise 1&2 Ch 41 (page 158) 11/24/2020 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com 9 8 6 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Ratio Calculations Learning Intention 1. To show to do ratio calculations. Success Criteria 1. Use tabulating method to work out ratios. 2. Show appropriate working. 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Ratio Calculations Example : The ratio of boys to girls is 4: 5. If there are 16 boys, how many girls are there. boys girls x 4 11/24/2020 4 5 16 20 x 4 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Ratio Calculations Example : The ratio of cars to buses is 3: 7. If there are 49 buses, how many cars are there. cars buses x 7 11/24/2020 3 7 21 49 x 7 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Ratio Calculations Now try Exercise 3 Ch 41 (page 160) 11/24/2020 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com 9 8 6 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Proportional Division Learning Intention 1. Explain how to work out proportional division by using shares. Success Criteria 1. Work out equal number of shares for a ratio. 2. Solve problems using shares. 3. Show appropriate working. 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Proportional Division 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 Bill gets 5 x 50 = £ 250 11/24/2020 Created by Mr. Lafferty Maths Dept. Check ! 150 + 250 = 400

Ratio & Proportion www. mathsrevision. com Proportional Division 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 11/24/2020 Created by Mr. Lafferty Maths Dept. Check ! 18 + 6 = 24

Ratio & Proportion www. mathsrevision. com Proportional Division Now try Exercise 4 Ch 41 (page 161) 11/24/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Starter Questions 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Proportion Learning Intention 1. To explain the term proportion. Success Criteria 1. Understand the idea of proportion. 2. Solve simple proportional problems. 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Proportion 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 : 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Proportion Now try Exercise 5 Ch 41 (page 163) 11/24/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Starter Questions 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Direct Proportion Learning Intention 1. To explain the term Direct Proportion. Success Criteria 1. Understand the idea of Direct Proportion. 2. Solve simple proportional problems. 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Direct Proportion Two quantities, (for example, number of cakes and total cost) are said to be in DIRECT PROPORTION, if : “. . When you double the number of cakes you double the cost. ” Example : The cost of 6 cakes is £ 4. 20. find the cost of 5 cakes. Cakes Cost 6 4. 20 1 4. 20 ÷ 6 = 0. 70 5 11/24/2020 Created by Mr. Lafferty Maths Dept. 0. 70 x 5 = £ 3. 50

Ratio & Proportion www. mathsrevision. com Direct Proportion Example : On holiday I exchanged £ 30 for $45. How many $ will I get for £ 50. £ 11/24/2020 $ 30 1 50 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 www. mathsrevision. com Direct Proportion 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. Pencils 300 100 200 11/24/2020 Cost £ 6. 00 ÷ 3 = £ 2. 00 x 2 = £ 4. 00 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Direct Proportion Now try Exercise 6 Ch 41 (page 164) 11/24/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Starter Questions 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Direct Proportion Graphs Learning Intention 1. To explain how Direct Proportion Graph is always a straight line. 11/24/2020 Success Criteria 1. Understand that Direct Proportion Graph is a straight line. 2. Construct Direct Proportion Graphs. Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion Graphs 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 ? 11/24/2020 Created by Mr. Lafferty Maths Dept.

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. 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Direct Proportion Graphs Key. Point Two quantities which are in DIRECT PROPORTION always lie on a straight line passing through the origin. 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion Direct Proportion Graphs 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) 11/24/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Ratio & Proportion 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 11/24/2020 Created by Mr. Lafferty Maths Dept. 0 1 2 3 4 x

Ratio & Proportion www. mathsrevision. com Direct Proportion Now try Exercise 7 Ch 41 (page 166) 11/24/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Starter Questions y x x xx x x 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Inverse Proportion Learning Intention 1. To explain the term Inverse Proportion. Success Criteria 1. Understand the idea of Inverse Proportion. 2. Solve simple inverse proportion problems. 11/24/2020 Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Inverse Proportion Inverse proportion is the 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. (Less time !!) Men 3 1 4 11/24/2020 Created by Mr. Lafferty Maths Dept. Hours 8 3 x 8 = 24 hours 24 ÷ 4 = 6 hours

Ratio & Proportion www. mathsrevision. com Inverse Proportion Example : It takes 10 men 12 months to build a house. How long should it take 15 men. Men 10 1 15 11/24/2020 Months 12 12 x 10 = 120 ÷ 15 = 8 months Created by Mr. Lafferty Maths Dept.

Ratio & Proportion www. mathsrevision. com Direct Proportion Now try Exercise 8 Ch 41 (page 168) 11/24/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Ratio & Proportion Mixed Problems Exercise 9 Ch 41 (page 168) 11/24/2020 Created by Mr. Lafferty Maths Dept.