Functional Skills Mathematics

Transcription

1 Functional Skills Mathematics Level 1 Learning Resource Ratio

2 Contents Ratio and Direct Proportion Pages - 5 Simplifying Ratios Pages 6-7 West Nottinghamshire College 2

3 Information Ratio and Direct Proportion Ratio is a way of comparing amounts or items. A ratio of 4:1 states that the first item or amount is 4 times larger than the second. Ratios can be written in various ways; 4:1 4/1 4 to 1 When increasing or decreasing a ratio, multiplying each part of the ratio by the same number ensures the ratio split is the same, this is called direct proportion. Examples If the ratio of men to women is shown as 2:1, this means that there are 2 men to every 1 woman. If the ratio of people with blue eyes to people with brown eyes is 4:1, this means that there are 4 people with blue eyes to every 1 person with brown eyes. If we directly increased this ratio to 20 people with blue eyes, you would expect there to be 5 people with brown eyes. Both numbers have been multiplied by 5. (4 x 5 = 20; 1 x 5 = 5) 4:1 becomes 20:5 West Nottinghamshire College

4 Exercise 1 Ratio and Direct Proportion 1) A builder uses ratio to mix mortar when building a wall. The ratio of sand to cement is 4:1, that means for every 4 shovels of sand, the builder needs 1 shovel of cement. a) How many shovels of sand need to be added to two shovels of cement? b) How many shovels of sand need to be added to five shovels of cement? 2) Here is a recipe for 10 scones. 225 g self-raising flour pinch of salt 55 g butter 25 g caster sugar 150 ml milk Rewrite the scones recipes for; a) 20 scones b) 60 scones c) How much castor sugar is to be used to make 0 scones? ) Tyrone has decided to clean the carpets in his flat. The instructions on the carpet shampoo state Pour capfuls into a bucket of 6 litres of water. How much floor cleaner should he use for; a) 12 litres of water b) litres of water West Nottinghamshire College 4

5 Exercise 2 Ratio and Direct Proportion In a group of 20 teenagers: 11 are male 9 are female 15 have brown eyes 5 have blue eyes 2 are over 1 8 m tall 18 are less than 1 8 m tall 16 wear trousers 4 wear skirts wear shoes 17 wear boots 10 wear sweatshirts wear sweaters 7 wear shirts 2 are over 18 years old 5 are 17 years old 1 are 16 years old. We can compare these people using ratios. The ratio of male:female is 11:9 because 11 are male and 9 are female. 1) Using the information given, complete the following, remembering to cancel down: a) The ratio of brown eyes:blue eyes is b) The ratio of less than 1 8 m tall:more than 1 8 m tall is.... c) The ratio of skirts:trousers is d) The ratio of boots:shoes is e) The ratio of sweatshirts:sweaters:shirts is.... f) The ratio of over 18 year olds:17 years old:16 years old is West Nottinghamshire College 5

6 Information Simplifying Ratios You can sometimes make the numbers smaller so that they are easier to compare. We call this simplifying. To simplify a ratio, divide each part of the ratio by the same number. Examples Example: The ratio of males:females in a hotel is 150: and 60 both divide by = = 6 The ratio males : females becomes 15:6 15 and 6 both divide by 15 = 5 6 = 12 The ratio of males:females then becomes 5:12. That means that for every 5 males there are 12 females. That is much easier to understand than 150:60. Example: It is always useful to have ratios with 1 in them because it is easier to compare. It is much easier to compare 7:1 than (say) 7:2 If the ratio of rabbits to mice is 7:2 it means that there are 7 rabbits to every 2 mice. You could not simplify this figure any more unless you used fractions or decimals 1 i.e. 7:2 = :1 or.5:1 2 Example: Sometimes the number of each part of the ratio is not given, and you have to firstly find what the missing part/s are. Of the 16 animals at the vet s, 6 were cats. Assuming that the rest were dogs, what is the ratio of dogs:cats? 16 animals 6 cats = 10 dogs. 10 dogs:6 cats giving a ratio of 10:6 this is simplified to 5: (divide by 2). West Nottinghamshire College 6

7 Exercise Simplifying Ratios 1) Simplify these ratios; a) 25:0 (divide by 5) b) 12:2 (divide by 2) c) 100:1000 (divide by 100) d) 50:700 (divide by 50) e) 88:22 (divide by 22) f) 60:24 (divide by 12) 2) On a Health and Social Care course there are 5 learners, 21 of whom are female. What is the ratio of: a) females:males? b) males:females? ) A firm employs 200 staff. 10 earn 25,000 a year 40 earn 15,000 a year the rest earn 12,000 a year. a) How many earn 12,000 a year? b) What is the ratio of the number of people who earn 25,000, people who earn 15,000 and people who earn 12,000? Give your answer in simplified form. 4) Simplify these ratios; a) The ratio of male to female at the disco is 90:120. b) The ratio of cats to dogs at the rescue centre is 45 to 65. c) The ratio of games won, drawn and lost at the local football club is 28:14:21. d) The ratio of Ford, Peugeot, Toyota and Vauxhall cars in the car park is 2:16:20:6 West Nottinghamshire College 7