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Mastering Ratios and Proportions in Mathematics

Learn about ratios, rates, and proportions in mathematics with detailed explanations, examples, and exercises to enhance your understanding and skills. Explore how to solve ratio and proportion problems effectively.

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Mastering Ratios and Proportions in Mathematics

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  1. Section 1.4 Ratios & Proportions

  2. Ratios • A ratio is a comparison of two numbers that can be written in three different ways • For example, if the student to faculty ratio at a certain college is 40 to 1, the ratio can also be expressed as 40:1 or as . • This means that four every one faculty member, there are 40 students.

  3. Rates • When the quantities being compared in a ratio have different units, the ratio is called a rate. • For example: the rate 30 mpg (miles per gallon) is a comparison of the two quantities 30 miles and 1 gallon. The rate could have been written as .

  4. Exercise 1 A juice drink recipe calls for 3 parts orange juice and 2 parts pineapple juice. Which of the following statements are correct. • For every cup of pineapple juice, you need 1.5 cups of orange juice. • For every two quarts of pineapple juice you need 6 quarts of orange juice. • When the juices are mixed, the mixture is orange juice. • The ratio of pineapple juice to orange juice is 2:3. • If you have 15 oz. of orange juice, you need to add 10 oz. of pineapple juice.

  5. Proportions • When two ratios are equal, they form a proportion. • When two ratios are equal, the quantities being compared are in proportion with each other or just proportional. • For example: 30 mpg

  6. Exercise 2 Complete the following ratios:

  7. Exercise 2 Complete the following ratios: * ½ * 3 * ½ * 3

  8. Exercise 3 If a school has 70 computers in the ratio of 3 desktops for every 4 laptops, how many of the computers are desktops?

  9. Exercise 3 If a school has 70 computers in the ratio of 3 desktops for every 4 laptops, how many of the computers are desktops? 3 desktops : 4 laptops means 3 desktops : 7 computers 3 desktops : 7 computers means 30 desktops : 70 computers

  10. Exercise 4a The racial composition in a Texas town is shown in the table below: A local university has 20250 total students. How many of them would need to be Hispanic so that the Hispanic students have a proportional representation at the University?

  11. Exercise 4a The racial composition in a Texas town is shown in the table below: A local university has 20250 total students. How many of them would need to be Hispanic so that the Hispanic students have a proportional representation at the University?

  12. Exercise 4b The racial composition in a Texas town is shown in the table below: Another local university has 2450 Black students. How many total students are needed so that the Black students have a proportional representation at the University?

  13. Exercise 4b The racial composition in a Texas town is shown in the table below: Another local university has 2450 Black students. How many total students are needed so that the Black students have a proportional representation at the University?

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