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Ratio, Proportion, and Percent: Writing Ratios, Solving Proportions, and Finding Percentages

This chapter covers the concept of ratios, how to write ratios, solve proportions, and find percentages. Examples and applied problems are provided to help with understanding.

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Ratio, Proportion, and Percent: Writing Ratios, Solving Proportions, and Finding Percentages

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  1. Chapter 2 Section 6

  2. Ratio, Proportion, and Percent Write ratios. Solve proportions. Solve applied problems by using proportions. Find percents and percentages. 2.6 2 3 4

  3. Objective 1 Write ratios. Slide 2.6-3

  4. A ratio is a comparison of two quantities using a quotient. Write ratios. Ratio The ratio of the number a to the number b (b ≠ 0) is written or The last way of writing a ratio is most common in algebra. Slide 2.6-4

  5. EXAMPLE 1 Writing Word Phrases as Ratios Write a ratio for each word phrase. 3 days to 2 weeks 12 hr to 4 days Solution: Slide 2.6-5

  6. EXAMPLE 2 Finding Price per Unit The supermarket charges the following prices for pancake syrup. Which size is the best buy? What is the unit cost for that size? Solution: The 36 oz. size is the best buy. The unit price is $0.108 per oz. Slide 2.6-6

  7. Objective 2 Solve proportions. Slide 2.6-7

  8. A ratio is used to compare two numbers or amounts. A proportionsays that two ratios are equal, so it is a special type of equation. For example, is a proportion which says that the ratios and are equal. In the proportion a, b, c, and dare the terms of the proportion. The terms aandd are called the extremes, and the terms bandc are called the means. We read the proportions as “ais to basc is to d.” Solve proportions. Slide 2.6-8

  9. Beginning with this proportion and multiplying each side by the common denominator, bd, gives Solve proportions. (cont’d) We can also find the products ad and bc by multiplying diagonally. For this reason, ad andbcare called cross products. Slide 2.6-9

  10. Cross Products If then the cross products ad and bc are equal—that is, the product of the extremes equals the product of the means. Also, if then If then ad = cb, or ad = bc. This means that the two proportions are equivalent, and the proportion can also be written as Sometimes one form is more convenient to work with than the other. Solve proportions. (cont’d) Slide 2.6-10

  11. EXAMPLE 3 Deciding Whether Proportions Are True Decide whether the proportion is true or false. Solution: False Solution: True Slide 2.6-11

  12. Solve the proportion EXAMPLE 4 Finding an Unknown in a Proportion Solution: The solution set is {5}. The cross-product method cannot be used directly if there is more than one term on either side of the equals symbol. Slide 2.6-12

  13. Solve The solution set is EXAMPLE 5 Solving an Equation by Using Cross Products Solution: When you set cross products equal to each other, you are really multiplying each ratio in the proportion by a common denominator. Slide 2.6-13

  14. Objective 3 Solve applied problems by using proportions. Slide 2.6-14

  15. EXAMPLE 6 Applying Proportions Twelve gallons of diesel fuel costs $37.68. How much would 16.5 gal of the same fuel cost? Solution: Let x = the price of 16.5 gal of fuel. 16.5 gal of diesel fuel costs $51.81. Slide 2.6-15

  16. Objective 4 Find percents and percentages. Slide 2.6-16

  17. A percent is a ratio where the second number is always 100. Since the word percent means “per 100,” one percent means “one per one hundred.” or Write ratios. Slide 2.6-17

  18. EXAMPLE 7 Converting Between Decimals and Percents Convert. 310% to a decimal 8% to a decimal 0.685 to a percent Solution: 3.1 .08 68.5% Slide 2.6-18

  19. EXAMPLE 8 Solving Percent Equations Solve each problem. What is 6% of 80? 16% of what number is 12? What percent of 75 is 90? Solution: Slide 2.6-19

  20. EXAMPLE 9 Solving Applied Percent Problems Mark scored 34 points on a test, which was 85% of the possible points. How many possible points were on the test? Solution: Let x = the number of possible points on the test. There were 40 possible points on the test. Slide 2.6-20

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