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Ratios and Proportions

This guide explores the concepts of ratios and proportions, essential components of mathematics. Ratios compare two quantities, illustrated through engaging examples like the ratio of boys to girls or marbles of different colors. Learn how to express ratios in various forms and calculate percentages from given ratios. Dive into proportions, which consist of two equal ratios, with practical examples and problems to solve. Whether it’s finding marshmallows in a box or calculating train travel distance, this guide equips you with the skills to master ratios and proportions.

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Ratios and Proportions

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  1. Ratios and Proportions

  2. Ratios • Ratio – a comparison of two quantities or numbers Examples: • The ratio of boys to girls • The ratio of students to teachers • The ratio of red marbles to blue marbles Ratios are written 3 ways: a , a:b , a to b b

  3. Find Percentage if Given the Ratio • If the ratio of boys to girls is 2:3, what percentage of the students are boys? • Jim’s CD collection consists of just rock and country. If the ratio of rock to country is 3:5, what percentage of the CDs are rock? • If the ratio of blue shirts to red shirts is 5:2, what percentage of the shirts are blue?

  4. Proportions Proportions – two ratios that are equal to each other Two ratios are equal if their cross- products are equal Examples: 2 = 124 = 810 = 28 3 18 9 17 15 42

  5. Solve each Proportion 4 = 93 = 72 = x 25 x x 18 5 12

  6. Write and solve a proportion for each problem. • Suzy counted 24 marshmallows in 3 servings of Marshy Morsels. The box contains 12 servings. How many marshmallows are in the box? • A train travels 165 miles in 3 hours. At that rate, how many miles will the train travel in 5 hours? • Kim can text 150 words in 2 minutes. How many words can she text in 5 minutes?

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