2 Objectives Understand how to use ratios to find specific quantities Simplify ratios by identifying common factorsDemonstrate a medium level of understanding of multiplication and division
3 A ratio can be written as 3:2 and is said to be 3 to 2. A ratio is a comparison between two numbers or two quantities of different items.A ratio can be written as 3:2 and is said to be 3 to 2.If you have 2 biscuits and 1 cups of tea, the ratio of biscuits to cups of tea would be 2:1.Ratio is also a way in which quantities can be divided or shared.
4 Simplifying RatiosLike fractions, ratios can be simplified by finding common factors.The factors of a number are those numbers that divide into it exactly.E.g 1 × 12 = 12 2 × 6 = 12 3 × 4 = 12So the factors of 12 are 1, 2, 3, 4, 6 and 12.
5 ExampleThere are 15 males and 12 females in a group. What is the ratio of males to females? Give your example in its simplest form.So the ratio of males to females is 15:12. However, both sides of the ratio can be divided by 3. Dividing 15 and 12 by 3 gives 5:4. 5:4 is the ratio in its simplest form.
6 Simplifying Ratios QUIZ Write 1 to ten in your margin10 seconds for each question
18 Ratios and finding quantities Adrian is building a barbecue and needs 300g of mortar. He needs to mix cement and sand in a ratio of 2:1.How much of each does he need?
19 How do you split 300g in the ratio 2:1? Ask yourself 3 questions:How many parts are there?3 (2 of cement, 1 of sand)How much is 1 share worth?300g ÷ 3 = 100gHow much of each is needed?2 parts cement = 2 x 100g = 200g1 part sand = 1 x 100g = 100g
20 The next jobAdrian runs a job renovating a house. He employs painters, carpenters and brickies.They earn £600 for the day. Adrian decides to pay out his painters, carpenters and brickies in the ratio 1:2:3 (painters get 1, carpenters 2 and brickies 3)How do they split it?
21 How do you split £600 in the ratio 1:2:3? Ask yourself 3 questions:How many shares are there?6 (3 for Brickies, 2 for Carpenters and 1 for Painters)How much is 1 share worth?600 ÷ 6 = £100How much do they get?Brickies get 3 x 100 = £300Carpenters get 2 x 100 = £200Painters get 1 x 100 = £100
22 Sharing in Ratios 10 multiple choice questions to be answered in pairs 20 seconds for each question
23 £20 is shared in the ratio 1:3 How much is 1 share worth?12131089111419201817151675162End43£4£1A)B)£5£3C)D)
24 £30 is shared in the ratio 2:3 How much is 1 share worth?12131089111419201817151675162End43£1£5A)B)£2£6C)D)
25 £18 is shared in the ratio 1:2 How much is 1 share worth?12131089111419201817151675162End43£3£6A)B)£2£18C)D)
26 £45 is shared in the ratio 4:5 How much is 1 share worth?12131089111419201817151675162End34£5£9A)B)£6£4C)D)
27 £20 is shared in the ratio 1:3 How much is 3 shares worth?12131089111419201817151675162End43£16£12A)B)£3£15C)D)
28 £30 is shared in the ratio 2:3 How much is 3 shares worth?12131089111419201817151675162End43£12£18A)B)£20£15C)D)
29 £18 is shared in the ratio 1:2 How much is 2 share worth?12131089111419201817151675162End43£6£12A)B)£3£18C)D)
30 £45 is shared in the ratio 4:5 How much is 5 shares worth?12131089111419201817151675162End43£18£15A)B)£25£20C)D)
31 Tom and Ellie share £15 in the ratio 1:2 1213119781014192018171516651234EndHow much do they get each?Tom- £5Ellie- £10Tom- £10Ellie- £5A)B)Tom- £3Ellie- £6Tom- £1Ellie- £2C)D)
32 Libby and Grant share £42 in the ratio 3:4 1213119781014192018171516651234EndHow much do they each getLibby- £20Grant- £22Libby- £24Grant- £18A)B)Libby- £21Grant- £28Libby- £18Grant- £24C)D)
33 Questions £30 is shared in the ratio 1:2 How many shares are there?How much is one share worth?How much does each person get?2) £40 is shared in the ratio 1:35) £56 is shared in the ratio 1:2:43) £50 is shared in the ratio 2:3
34 QuestionsArchie and Charlie share their Thomas the tank engine toys in the ratio 1:4, how many do they each get if they have:Sue and Linda share some money in the ratio 3:7, how many do they each get if they share:£30 b)£60 c)£9010 toys b) 30 toys c) 45 toysTom and Jerry share sweets in the ratio 2:3, how many do they each get if they share:Mike, Dave and Henry share some little bits of blue tack in the ratio 1:2:3, how many do they each get if they share:20 sweets b) 30 sweets c)55 sweets60 pieces b) 72 pieces c) 300 pieces
35 ExtensionBen and Jerry share some money in the ratio of 3:4, Ben gets £21, how much does Jerry get?Jon and Ade share some socks in the ratio 2:7 Jon gets 18 socks, how many does Ade getNora, Ben and Jon share some Easter eggs in the ratio 2:5:7, Ben gets 60, how many do Jon and Nora get?
36 ExtensionFirstly, do you remember what the angles in a triangle add up to???The angles in this triangle (x, y and z) are in the ratio 5:1:3 - find the size of the angles.zyx