Rate and Proportion www mathsrevision com S 4

Rate and Proportion www. mathsrevision. com S 4 Rates and Finding Rates Direct Proportion graphs Inverse Proportion Saturday, October 31, 2020 Created by Mr. Lafferty @www. mathsrevision. com 1

Starter Questions www. mathsrevision. com S 4 Saturday, October 31, 2020 Created by Mr. Lafferty @www. mathsrevision. com 2

Rates www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To explain the term ‘rate’ is and how to find the rate. Saturday, October 31, 2020 Created by Mr. Lafferty @www. mathsrevision. com 1. To understand the term ‘rate’ and calculate it. 3

Rates www. mathsrevision. com S 4 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) This means that if Sean walked at this speed for one hour he would travel 5 km. Saturday, October 31, 2020 Created by Mr. Lafferty @www. mathsrevision. com 4

Rates www. mathsrevision. com S 4 We are often interested in rates • • • Miles per gallon Goals per game £’s spent per day Calories per day Words per minute Why are we interested in rates? www. mathsrevision. com

Rates www. mathsrevision. com S 4 Example : Sean walks at 5 km per hour (km/hr) How far would he walk in : (a) 4 hours (a) 4 x 5 = 20 km (b) 5 x 0. 5 =2. 5 km Saturday, October 31, 2020 (b) Half an hour Created by Mr. Lafferty @www. mathsrevision. com 6

Finding the Rate S 4 www. mathsrevision. com Example : For 5 hours’ work Jennifer is paid £ 30. Calculate her rate of pay per hour. Answer : 5 hours £ 30 1 hour £ 30 ÷ 5 = £ 6 This means that Jennifer is paid a ‘rate’ of £ 6 per hour Saturday, October 31, 2020 Created by Mr. Lafferty @www. mathsrevision. com 7

Finding the Rate S 4 www. mathsrevision. com Example : 3 litres of paint covers a fence area of 36 m 2 How much will 1 litre cover. Answer : 3 litres 36 1 litre 36 ÷ 3 = 12 m 2 This means that 12 m 2 requires 1 litre of paint. Saturday, October 31, 2020 Created by Mr. Lafferty @www. mathsrevision. com 8

Finding the Rate S 4 www. mathsrevision. com Example : Nicola gets paid £ 48 000 pounds a year. What is her monthly rate of pay. Answer : 12 months £ 48 000 1 month £ 48 000 ÷ 12 = £ 4 000 This means Nicola gets paid £ 4 000 per month Saturday, October 31, 2020 Created by Mr. Lafferty @www. mathsrevision. com 9

Finding the Rate www. mathsrevision. com S 4 Now try Ex 1 Ch 2 (page 26) Saturday, October 31, 2020 Created by Mr. Lafferty @www. mathsrevision. com 10

Starter Questions www. mathsrevision. com S 4 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To explain the term Direct Proportion. 1. Understand the idea of Direct Proportion. 2. Solve simple proportional problems. 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com S 4 Two quantities, (for example, number of cakes and total cost) are said Are we 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. find the cost Easier method of 5 cakes. Cakes Pence Cakes Cost 6 420 6 4. 20 (less) 5 1 4. 20 ÷ 6 = 0. 70 5 31 -Oct-20 Created by Mr. Lafferty Maths Dept. 0. 70 x 5 = £ 3. 50

Direct Proportion S 4 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 31 -Oct-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.

Direct Proportion S 4 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 31 -Oct-20 Cost £ 6. 00 ÷ 3 = £ 2. 00 x 2 = £ 4. 00 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com S 4 Now try Ex 2 Ch 2 (page 28) 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 4 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Proportion Direct Proportion Graphs www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To explain how Direct Proportion Graph is always a straight line. 31 -Oct-20 1. Understand that Direct Proportion Graph is a straight line. 2. Construct Direct Proportion Graphs. Created by Mr. Lafferty Maths Dept.

Proportion Direct Proportion Graphs S 4 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 ? 31 -Oct-20 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. 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Proportion Direct Proportion Graphs www. mathsrevision. com S 4 Key. Point Two quantities which are in DIRECT PROPORTION always lie on a straight line passing through the origin. 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Proportion Direct Proportion Graphs S 4 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) 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Proportion www. mathsrevision. com S 4 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 31 -Oct-20 Created by Mr. Lafferty Maths Dept. 0 1 2 3 4 x

Proportion Direct Proportion www. mathsrevision. com S 4 Now try TJ Extension booklet 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 4 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Proportion Inverse Proportion www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To explain the term Inverse Proportion. 1. Understand the idea of Inverse Proportion. 2. Solve simple inverse proportion problems. 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Proportion Inverse Proportion S 4 www. mathsrevision. com Inverse proportion is when one quantity increases and we the other decreases. The two quantities are said Are expecting to be INVERSELY PROPORTIONAL) to each other. moreor or(INDIRECTLY less Example : If it takes 3 men 8 hours to build a wall. How long will it take 4 men. (Less time !!) Easier method Workers Hours. Men Hours 3 8 (less) 4 1 3 x 8 = 24 hours 4 31 -Oct-20 Created by Mr. Lafferty Maths Dept. 24 ÷ 4 = 6 hours

Proportion Inverse Proportion S 4 www. mathsrevision. com Example : Are we expecting more or less It takes 10 men 12 months to build a house. How long should it take 8 men. Men Months 12 Easier 10 method 1 12 x 10 = 120 Workers months 8 120 ÷ 8 = 15 months 10 12 (more) 8 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Proportion Inverse Proportion www. mathsrevision. com S 4 Now try TJ Extension Booklet 31 -Oct-20 Created by Mr. Lafferty Maths Dept.