Finding a Percent of a Number LESSON 6-4 Check Skills You’ll Need (For help, go to Lesson 1-9.) 1. Vocabulary Review The Distributive Property combines the operation of ? with addition or subtraction. Find each product using the Distributive Property and mental math. See the example below for how to do this: 80 • 15 = 80(10 + 5) = 80(10) + 80(5) = 800 + 400 = 1,200 2. 75 • 18 = 3. 78 • 0.9 = 4. 27 • 1.1 = Check Skills You’ll Need 6-4
Finding a Percent of a Number LESSON 6-4 Check Skills You’ll Need (For help, go to Lesson 1-9.) 1. Vocabulary Review The Distributive Property combines the operation of multiplication with addition or subtraction. Find each product using the Distributive Property and mental math. See the example below for how to do this: 80 • 15 = 80(10 + 5) = 80(10) + 80(5) = 800 + 400 = 1,200 2. 75 • 18 = 75(10 + 8) = 75(10) + 75(8) = 750 + 600 = 1,350 3. 78 • 0.9 = 78(1 – 0.1) = 78(1) – 78(0.1) = 78 – 7.8 = 70.2 4. 27 • 1.1 = 27(1 + 0.1) = 27(1) + 27(0.1) = 27 + 2.7 = 29.7 6-4
Finding a Percent of a Number LESSON 6-4 Additional Examples “of” means “multiply” so the expression is 15% • 40 Find each answer. How else can you rewrite a percent? a. 15% of 40 Method 1 Write 15% as a fraction and multiply. Write the percent as a fraction in simplest form. 15% = = 15 100 3 20 3 20 • 40 = 6 Multiply. Method 2 Write 15% as a decimal and multiply. Write the percent as a decimal. 15% = 0.15 0.15 • 40 = 6 Multiply. Which method do you prefer? 6-4
Finding a Percent of a Number LESSON 6-4 Additional Examples (continued) b. 80% of 460 Now do this on your own. Method 1 Write 80% as a fraction and multiply. Write the percent as a fraction in simplest form. 80% = = 80 100 4 5 4 5 • 460 = 368 Multiply. Method 2 Write 80% as a decimal and multiply. Write the percent as a decimal. 80% = 0.80 0.80 • 460 = 368 Multiply. Quick Check 6-4
Finding a Percent of a Number LESSON 6-4 Additional Examples Find each answer using mental math. a. 49% of 300 Use the distributive property. What you think 49% is 50% – 1% 50% of 300 is 0.5 • 300, or 150. 1% of 300 is 0.01 • 300, or 3. So 150 – 3 = 147. Why it works 0.49 • 300 Write 49% as a decimal. (0.50 – 0.01) • 300 Substitute 0.50 – 0.01 for 0.49. (0.50 • 300) – (0.01 • 300) Use the Distributive Property. 150 – 3 Multiply. 147 Simplify. 6-4
Finding a Percent of a Number LESSON 6-4 Additional Examples Find the answer using mental math. b. 11% of 720 Now do this on your own. What you think 11% is 10% + 1% 10% of 720 is 0.1 • 720, or 72. 1% of 720 is 0.01 • 720, or 7.2. So 72 + 7.2 = 79.2. Why it works 0.11 • 720 Write 11% as a decimal. (0.10 + 0.01) • 720 Substitute 0.10 + 0.01 for 0.11. (0.10 • 720) + (0.01 • 720) Use the Distributive Property. 72 + 7.2 Multiply. 79.2 Simplify. Quick Check 6-4
Finding a Percent of a Number LESSON 6-4 Additional Examples Estimate each answer. a. 76% of 405 Write an expression. 76% • 405 3 4 • 400 = 300 Use compatible numbers such as and 400. Check for Reasonableness 76% of 405 is 0.76 • 405, or 307.8, which is close to the estimate 300. The answer is reasonable. b. 12% of 5,575 Now do this on your own. 12% • 5,575 Write an expression. • 5,600 = 560 1 10 Use compatible numbers such as and 5,600. Check for Reasonableness 12% of 5,575 is 0.12 • 5,575, or 669, which is close to the estimate 672. The answer is reasonable. 6-4
Finding a Percent of a Number LESSON 6-4 Additional Examples (continued) c. 48% of 925 Write an expression. 48% • 925 1 2 • 900 = 450 Use compatible numbers such as and 900. Check for Reasonableness 48% of 925 is 0.48 • 925, or 444, which is close to the estimate 450. The answer is reasonable. Quick Check 6-4
Finding a Percent of a Number LESSON 6-4 Lesson Quiz Find the percent of each number. 1. 40% of 90 2. 120% of 45 3. 3.5% of 700 4. 90% of 650 36 54 24.5 585 Homework: Prepare for Chapter 5 Quiz Practice 6-4 (handout) Before you leave today, please leave your homework notebook on the ledge, open to the Ch 5 Corrections page. 6-4