6-4 Percent of a Number Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

6-4 Percent of a Number Warm Up Multiply     

6-4 Percent of a Number Problem of the Day In a group of 60 triangular and square tiles, 25% are red, and 75% are blue. The ratio of triangles to squares is 1:2. Seventy percent of the squares are blue. Find the number of each kind of tile (red or blue squares or triangles). 3 red triangles, 17 blue triangles, 12 red squares, 28 blue squares

6-4 Percent of a Number MA.7.A.1.2 Solve percent problems, including problems involving discounts…[and] taxes… Sunshine State Standards

6-4 Percent of a Number The human body is made up mostly of water. In fact, about 67% of a person’s total (100%) body weight is water. If Cameron weighs 90 pounds, about how much of his weight is water? Recall that a percent is a part of 100. Since you want to know the part of Cameron’s body that is water, you can set up and solve a proportion to find the answer. Part 67 = nPart Whole

6-4 Percent of a Number Find the percent of each number. Additional Example 1A: Using Proportions to Find Percents of Numbers 30% of = n · 50 = 100 · n 1,500 = 100n 1, = 100n 15 = n 30% of 50 is 15. Write a proportion. Set the cross products equal. Multiply. Divide each side by 100 to isolate the variable.

6-4 Percent of a Number When solving a problem with a percent greater than 100%, the part will be greater than the whole. Helpful Hint

6-4 Percent of a Number Additional Example 1B: Using Proportions to Find Percents of Numbers Find the percent of each number. 200% of = n · 24 = 100 · n 4,800 = 100n 4, = 100n 48 = n 200% of 24 is 48. Write a proportion. Set the cross products equal. Multiply. Divide each side by 100 to isolate the variable.

6-4 Percent of a Number Use proportional reasoning to find the percent of each number. Check It Out: Example 1A 40% of = n = 100n = 100n 7.2 = n

6-4 Percent of a Number Use proportional reasoning to find the percent of each number. Check It Out: Example 1B 120% of = n = 100n 48, = 100n 480 = n

6-4 Percent of a Number In addition to using proportions, you can find the percent of a number by using decimal equivalents.

6-4 Percent of a Number Find the percent of the number. Check whether your answer is reasonable. Additional Example 2A: Using Decimal Equivalents to Find Percents of Numbers 9% of 80 9% of 80 = 0.09 · 80 = 7.2 Model Since 10% of 80 = 8, a reasonable answer for 9% of 80 is 7.2. Write the percent as a decimal and multiply. 0 20% 40% 60% 80% 100% % 7.2

6-4 Percent of a Number Additional Example 2B: Using Decimal Equivalents to Find Percents of Numbers Find the percent of the number. Estimate to check whether your answer is reasonable. 0.6% of % of 270 = · 270 = 1.62 Write the percent as a decimal and multiply.

6-4 Percent of a Number Use decimal equivalents to find the percent of each number. Check It Out: Example 2 6% of 18 6% of 18 = = % of % of 2000 = · 2000 = 16 A. B.

6-4 Percent of a Number Additional Example 3: Geography Application The estimated world population in 2001 was 6,157 million. About 40% of the people were 19 or younger. What was the approximate number of people 19 or younger, to the nearest million? Find 40% of 6,157 million · 6,157 2,462.8 The number of people 19 or younger was about 2,463 million. Write the percent as a decimal. Multiply.

6-4 Percent of a Number Check It Out: Example 3A The estimated world population in 2001 was 6,157 million. About 60% of the people were above 19 years of age. What was the approximate number of people 19 or older, to the nearest million? 60% of 6,157 million = 0.60 · 6,157 = The number of people 19 or older was about 3,694 million.

6-4 Percent of a Number Check It Out: Example 3B A bookstore finds that 55% of its total income in March came from online orders. The total income for March was $3,150. What was the income from online orders? 55% of 3,150 = 0.55 · 3,150 = 1, The income from online orders was $1,

6-4 Percent of a Number Check It Out: Example 3C There are 43,578 students in the public schools of a city. About 38% of these students are enrolled in middle school. About how many students are enrolled in middle school? 38% of 43,578 = 0.38 · 43,578 = 16, About 16,560 students are enrolled in middle school.

6-4 Percent of a Number Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

6-4 Percent of a Number Lesson Quiz Find the percent of each number % of % of 110 Find the percent of each number. Check whether your answer is reasonable % of % of Whitmer Middle School has 850 students. If 42% of the students bought lunch on Monday, how many students bought lunch on Monday?

6-4 Percent of a Number 1. Identify 75% of 4. A. 1 B. 2 C. 3 D. 4 Lesson Quiz for Student Response Systems

6-4 Percent of a Number 2. Identify 30% of 120. A. 36 B. 38 C. 40 D. 42 Lesson Quiz for Student Response Systems

6-4 Percent of a Number 3. Identify 140% of 85. A. 125 B. 120 C. 119 D. 109 Lesson Quiz for Student Response Systems

6-4 Percent of a Number 4. Identify 0.6% of 130. A B C D Lesson Quiz for Student Response Systems

6-4 Percent of a Number 5. A school has 250 students. If 56% of the students went on a hiking trip, how many students went on a hiking trip? A. 194 students B. 166 students C. 154 students D. 140 students Lesson Quiz for Student Response Systems