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Ratio and Proportion • A ratio is a comparison of one number to another. The order that the ratio is written in matters. For example, 1 (apple) to 2 (oranges) is not the same as 2 (apples) to 1 (orange). Note that a fraction is a specific kind of ratio comparing part to a whole. • Ratios can be written in three different ways: With a colon e.g. 5:3 In words e.g. 5 to 3 As a fraction 5 e.g. 3 • Ratios should be simplified to lowest terms (Just like fractions). e.g. 6:3 can be simplified to 3:1 by dividing each number in the ratio by 3. • A proportion is made up of two equal ratios. For example, 2:3 = 4:6 • Proportions can be solved using cross multiplication. Example: 3 7 3 7 45 = = 𝑥 45 𝑥 3x = 45(7) x= 45(7) x= 15(7) 3 [Cross multiply. Remember to keep the equal sign between two sides.] [Divide both sides by 3 to isolate x.] [Reduce here if you can. (45 and 3 can both be divided by 3).] 1 x = 105 Tutoring and Learning Centre, George Brown College 2013 www.georgebrown.ca/tlc Practice Questions: 1. Solve for x. a) b) c) d) e) f) 𝑥 12 3 𝑥 3 𝑥 = = 9 11 2 11 1 5 = 2 5 10 a) 2:3 = x:18 60 b) 5:3 = 10:x c) x:2 = 3:4 30 = 5 = = 2. Solve for x. 𝑥 9 d) 9:12 = x:3 45 e) 18:x = 30:7 𝑥 𝑥 f) 1:2 = x:9 7 Answers: 1 1 1. a) 2 b) 7 2 c) 2 d) 55 2. a) 12 b) 6 c) 1 2 1 1 d) 2 4 Tutoring and Learning Centre, George Brown College 2013 3 4 e) 1 11 f) 1 5 e) 4 5 f) 4 2 1 1 www.georgebrown.ca/tlc