Grade DE Compare quantities using ratio Express a

Grade D/E Compare quantities using ratio Express a multiplicative relationship between two quantities as a ratio or a fraction If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Ratio Parts Common units

How to compare quantities using ratio 1) Luke and Ben shared some money into the ratio 2 : 3. If Ben got £ 24, how much did Luke get? Luke had 2 parts and Ben had 3 parts. Ben had £ 24. If 3 parts is equivalent to £ 24, then 1 part is: 24 ÷ 3 = £ 8 Since Luke got 2 parts = 2 x £ 8 = £ 16 Can we calculate the total money shared?

How to compare quantities using ratio 2) Lucy had maths and science tests. Her scores were in the ratio of 3 : 5. She got 16 marks more in science than maths. What was her score in maths and science? Difference in the parts of ratio: 5 – 3 = 2 16 marks refers to 2 parts, therefore 1 part is 16 ÷ 2 = 8 marks. Maths score is 3 parts, 3 x 8 = 24 marks Science score is 5 parts, 5 x 8 = 40 marks

How to compare quantities using ratio 3) Carrot cake uses carrot, sugar, butter in the ratio 1: 4: 3 a) If you use 200 g of sugar, how much carrot and butter would you need to use. b) What percentage of this mixture is carrot. a) 200 g refers to 4 parts, therefore 1 part is 200 ÷ 4 = 50 g. Carrot is 1 part, 1 x 50 = 50 g Butter is 3 parts, 3 x 50 = 150 g b) Carrot = 50 g Total mixture = 200+50+150 = 400 g 50 x 100 = 12. 5% 400

Compare quantities using ratio – Now you try… 1) In a survey, the ratio of people who prefer to go to the cinema than theatre is 5 : 3. If 45 people said they preferred to go to the cinema, how many people were surveyed? 2) To make icing, Andy mixes butter, icing sugar and vanilla in the ratio 4 : 5 : 1. She needs 200 g of icing. Calculate the quantity of ingredients she will need. 3) Orange drink can be made by mixing squash with water in the ratio 3 : 5. Water is sold in 1 lt bottles and squash 50 cl bottles. If a 2 lt drink is needed, how many bottles of each need to be bought?

Compare quantities using ratio – Now you try… 1) In a survey, the ratio of people who prefer to go to the cinema than theatre is 5 : 3. If 45 people said they preferred to go to the cinema, how many people were surveyed? 1) 72 2) To make icing, Andy mixes butter, icing sugar and vanilla in the ratio 4 : 5 : 1. She needs 200 g of icing. Calculate the quantity of ingredients she will need. 2) 80 g butter, 100 g icing sugar, 20 g vanilla 3) Orange drink can be made by mixing squash with water in the ratio 3 : 5. Water is sold in 1 lt bottles and squash 50 cl bottles. If 2 lt of drink is needed for a party, how many bottles of each need to be bought? 3) 2 bottles each

Problem Solving and Reasoning In a school of 360 pupils, they can study French, German or Spanish. The ratio of pupils who study French to Spanish is 5 : 2. If 215 pupils study French, what is the percentage of students who study German?

Problem Solving and Reasoning In a school of 360 pupil they can study French, German or Spanish. The ratio of pupils who study French to Spanish is 5 : 2. If 215 pupils study French, what is the percentage of students who study German? 215 pupils study French and this is 5 parts. 215 ÷ 5 = 43 pupils one part Spanish is 2 parts, 2 x 43 = 86 pupils study Spanish The rest of the pupils study German. 215 + 86 = 301 360 – 301 = 59 pupils study German = 59 59 x 100 = 16. 4% Total no of pupils = 360

Reason and explain • What is the relationship between ratio and proportion? • What happens to the method of sharing when there are 3 parts in a ratio? • If the ratio of girls to boys is 1: 2, this means half of the people are girls. Is this a true statement? • In a school, 2/5 are girls, the rest are boys. Express this as a ratio girls to boys. • Think about a cube with 1 cm sides. Find the volume. Then double the side length and find the volume. What do you notice?