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Understanding Percents Lesson: Equivalent Ratios and Percentages

Learn how to find equivalent ratios, convert them to percents, and practice with examples and quick checks in this comprehensive lesson.

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Understanding Percents Lesson: Equivalent Ratios and Percentages

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  1. 2 5 13 50 Understanding Percents LESSON 6-1 • Please take your homework notebooks from the ledge. • I still need to check Activity 5-5a for: • Jason Lee • Sungho • Addison • Hanson • Natalie • Kelly • Bryan • Problem of the Day: Find equivalent ratios for the following • 1) 2) 6-1

  2. 2 5 = = 13 50 26 100 39 150 2 5 13 50 = = 4 10 6 15 Understanding Percents LESSON 6-1 Problem of the Day: Find equivalent ratios for the following 1) 2) Possible Answers: 6-1

  3. There are 4 grid spaces for the chair. Write as a ratio to the total number of grid spaces, 100. 4 100 chair  Then write as a percent. = 4% Understanding Percents LESSON 6-1 Additional Examples In a floor plan of a 10  10 room, a chair takes up 4 spaces. Write the ratio and percent of the chair space to the total floor space. Quick Check 6-1

  4. Shade 82 of the 100 grid spaces. Understanding Percents LESSON 6-1 Additional Examples Model 82% in a 10  10 grid. Quick Check 6-1

  5. 3 5 60 100 = Understanding Percents LESSON 6-1 Additional Examples What percent does the shaded area represent? = 60% Quick Check 6-1

  6. Since 10 • 10 is 100, multiply numerator and denominator by 10. 3 • 10 10 • 10 = 30 100 Simplify. Write as a percent. 30% 3 10 3 10 Since 5 • 20 is 100, multiply numerator and denominator by 20. 4 • 20 5 • 20 = 80 100 Simplify. Write as a percent. 80% Understanding Percents LESSON 6-1 Additional Examples Write each ratio as a percent. a. 4 5 b. 4 5 Quick Check 6-1

  7. 30 100 ; 30% 1 10 Understanding Percents LESSON 6-1 Lesson Quiz 1. Write a ratio and a percent for the shaded figure. Write each ratio as a percent. 2. 3. 11 50 10% 22% 6-1

  8. 30 100 ; 30% 1 10 Understanding Percents LESSON 6-1 Homework 1. Write a ratio and a percent for the shaded figure. Write each ratio as a percent. 2. 3. 11 50 10% 22% 6-1

  9. 11 40 11 40 = 5 ÷ 16 = 0.3125 4 9 = 11 ÷ 40 = 0.275 4 9 = 2 ÷ 15 = 0.133…= 0.13 = 4 ÷ 9 = 0.44…= 0.4 5 16 2 15 5 16 Percents, Fractions, and Decimals LESSON 6-2 Check Skills You’ll Need (For help, go to Lesson 2-6.) 1. Vocabulary Review What is a repeating decimal? Write each fraction as a decimal. 2. 3. 4. 5. Check Skills You’ll Need 6-2

  10. . 0.04 0.343 . Move the decimal point two places to the left. . 0.16 0.064 . Percents, Fractions, and Decimals LESSON 6-2 Additional Examples Write each percent as a decimal. a. 4% b. 34.3% c. 16% d. 6.4% 0 04. 0 34.3 0 16. 0 06.4 Why can you do this shortcut? Because “percent” means “for every 100” or “divided by 100” so 4% = 4 divided by 100 4/100 = 0.04 Quick Check 6-2

  11. . . Move the decimal point two places to the right . . Percents, Fractions, and Decimals LESSON 6-2 Additional Examples Write each decimal as a percent. a. 0.06 b. 0.523 c. 0.5 d. 0.95 0.06 = 6% = 52.3% 0.52 3 0.50 = 50% = 95% 0.95 Notice that this is just the opposite shortcut. Quick Check 6-2

  12. 3 10 Divide the numerator by the denominator. = 0.3 Write as a percent. = 30% Use a calculator. 37 49 0.7551020408 Write as a percent. = 75.5102041% Round to the nearest tenth of a percent. 75.5% Percents, Fractions, and Decimals LESSON 6-2 Additional Examples Write each fraction as a percent. When necessary, round to the nearest tenth of a percent. 3 10 a. 37 49 b. 6-2

  13. Use a calculator. 6 30 0.2 Write as a percent. 20% Use a calculator. 14 65 0.2153846154 Write as a percent. = 21.5384615% Round to the nearest tenth of a percent. 21.5% Percents, Fractions, and Decimals LESSON 6-2 Additional Examples (continued) 6 30 c. 14 65 d. Quick Check 6-2

  14. 18 100 Write 18% as a fraction with a denominator of 100. 18% = 18 ÷ 2 100 ÷ 2 Divide the numerator and the denominator by the GCF, 2. = 9 50 Simplify the fraction. = 12 100 Write 12% as a fraction with a denominator of 100. 12% = 12 ÷ 4 100 ÷ 4 Divide the numerator and the denominator by the GCF, 4. = 3 25 Simplify the fraction. = Percents, Fractions, and Decimals LESSON 6-2 Additional Examples Write each percent as a fraction in simplest form. a. 18% b. 12% 6-2

  15. 45 100 Write 45% as a fraction with a denominator of 100. 45% = 45 ÷ 5 100 ÷ 5 Divide the numerator and the denominator by the GCF, 5. = 9 20 Simplify the fraction. = Percents, Fractions, and Decimals LESSON 6-2 Additional Examples (continued) c. 45% Quick Check 6-2

  16. 3 5 Divide the numerator by the denominator. = 0.6 2 10 = 0.2 Divide the numerator by the denominator. 0.645 This number is already in decimal form. Move the decimal point two places to the left. 13% = 0.13 Percents, Fractions, and Decimals LESSON 6-2 Additional Examples Order from least to greatest. 3 5 2 10 a. , , 0.645, 13% Write all numbers as decimals. Then locate each on a number line. 6-2

  17. Move the decimal point two places to the left. 40% = 0.4 10 20 Divide the numerator by the denominator. = 0.5 Move the decimal point two places to the left. 18% = 0.18 This number is already in decimal form. 0.082 Percents, Fractions, and Decimals LESSON 6-2 Additional Examples (continued) 10 20 b. 40%, , 18%, 0.082 Write all numbers as decimals. Then locate each on a number line. Quick Check 6-2

  18. 7 8 9%, , 0.9 2 5 0.24, 30%, 7 10 1 4 7 10 7%, , 0.77 , 0.35, 40% Percents, Fractions, and Decimals LESSON 6-2 Lesson Quiz Write in order from least to greatest. 1. 30%, 0.24, 2. 0.9, , 9% 3. , 40%, 0.35 4. , 0.77, 7% 2 5 7 8 1 4 6-2

  19. Percents, Fractions, and Decimals LESSON 6-2 Homework: Lesson 6-1, pp. 276-277, #s 4, 8, 16, 18-20, 24, 25, 29, 34 Lesson 6-2, pp. 282-283, #s 4-28 (multiples of 4), 36 Scale Model Project due Friday: Chapter 5 test (bring a metric ruler) 6-2

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