Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Write each percent as a fraction and as a decimal. 1. 75% 2. 10% 3. 32% 4. 17% 3 4 , 0.75 , 0.1 10 1 , 0.32 25 8 , 0.17 100 17

Problem of the Day You are biking to the library. When you are 75% of the way there, you realize you forgot a book. So you turn around and head back. When you are of the way back you realize you don’t need the book, so you turn around again and bike 3.2 miles back to the library. How far do you live from the library? 1 3 6.4 miles

Learn to estimate percents.

The table shows common percents and their fraction equivalents The table shows common percents and their fraction equivalents. You can use fractions to estimate the percent of a number by choosing a fraction that is close to a given percent. Fraction Percent 33 % 1 3 66 % 2 3 10% 20% 25% 50% 1 10 1 5 1 4 1 3 1 2 2 3

Additional Example 1: Using Fractions to Estimate Percents Use a fraction to estimate 27% of 63. 1 4 Think: 27% is about 25% and 25% is equivalent to . 27% of 63  · 63 1 4 1 4 Change 63 to a compatible number.  · 60  15 Multiply. 27% of 63 is about 15. Compatible numbers are close to the numbers in the problem and help you use mental math to find a solution. Remember!

Check It Out: Example 1 Use a fraction to estimate 48% of 91. 1 2 Think: 48% is about 50% and 50% is equivalent to . 48% of 91  · 91 1 2 1 2  · 90 Change 91 to a compatible number.  45 Multiply. 48% of 91 is about 45.

Additional Example 2: Consumer Math Application Tara’s T’s is offering 2 T-shirts for $16, while Good-T’s is running their buy one for $9.99, get one for half price sale. Which store offers the better deal? First find the discount price for 2 t-shirts at Good T’s. 1 2 1 2 50% of $9.99 = · $9.99 Think: 50% is equivalent to . 1 2 · $10 Change $9.99 to a compatible number.   $5 Multiply. The second shirt cost approximately $5. Since $10 + $5 = $15, the 2 T-shirts for $15 at Good-T’s is the better deal.

Check It Out: Example 2 Billy’s Office Supply Store is offering 25% off a leather notebook, originally priced at $9.75. K’s Office Supply Store offers the same notebook, not on sale, at $7.00. Which store offers the better deal? First find the discount on the notebook at Billy’s Office Supply. 1 4 25% of $9.75 = · $9.75 1 4 Think: 25% is equivalent to . 1 4 · $10 Change $9.75 to a compatible number.   $2.50 Multiply. The discount is approximately $2.50. Since $10 - $2.50 = $7.50, the notebook from K’s Office Supply Store is the better deal.

Another way to estimate percents is to find 1% or 10% of a number. You can do this by moving the decimal point in the number. 1% of 45 = . 45 . 10% of 45 = 45 . . To find 1% of a number, move the decimal point two places to the left. To find 10% of a number, move the decimal point one place to the left.

Additional Example 3A: Estimating with Simple Percents Use 1% or 10% to estimate the percent of each number. 4% of 18 18 is about 20, so find 4% of 20. 1% of 20 = 20. . 4% of 20 = 4 · 0.2 = 0.8 4% equals 4 · 1%. 4% of 18 is about 0.8.

Additional Example 3B: Estimating with Simple Percents Use 1% or 10% to estimate the percent of each number. 29% of 80 29% is about 30, so find 30% of 80. 10% of 80 = 80. . 30% of 80 = 3 · 8.0 = 24.0 30% equals 3 · 10%. 29% of 80 is about 24.

14 is about 15, so find 5% of 15. 1% of 15 = 15. . Check It Out: Example 3A Use 1% or 10% to estimate the percent of each number. 5% of 14 14 is about 15, so find 5% of 15. 1% of 15 = 15. . 5% of 15 = 5 · 0.15 = 0.75 5% equals 5 · 1%. 5% of 14 is about 0.75.

21% is about 20, so find 20% of 60. 10% of 60 = 60. . Check It Out: Example 3B Use 1% or 10% to estimate the percent of each number. 21% of 60 21% is about 20, so find 20% of 60. 10% of 60 = 60. . 20% of 60 = 2 · 6.0 = 12.0 20% equals 2 · 10%. 21% of 60 is about 12.

Additional Example 4: Consumer Math Application Tim spent $58 on dinner for his family. About how much money should he leave for a 15% tip? Since $58 is about $60, find 15% of $60. 15% = 10% + 5% Think: 15% is 10% + 5%. 10% of $60 = $6 5% is of 10% so divide $6 by 2. 1 2 5% of $60 = $6 ÷ 2 = $3 $6 + $3 = $9 Add the 10% and 5% estimates. Tim should leave about $9 for a 15% tip.

Since $12 is about $10, find 15% of $10. Check It Out: Example 4 Amanda spent $12 on a hair cut. About how much money should she leave for a 15% tip? Since $12 is about $10, find 15% of $10. 15% = 10% + 5% Think: 15% is 10% + 5%. 10% of $10 = $1 5% is of 10% so divide $1 by 2. 1 2 5% of $10 = $1 ÷ 2 = $0.50 $1 + $0.50 = $1.50 Add the 10% and 5% estimates. Amanda should leave about $1.50 for a 15% tip.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz 1. Use a fraction to estimate 48% of 72. 2. A café is offering 10% off the $4.99 lunch. If a diner is offering the same lunch for $4.59, which is offering the better deal? Use 1% or 10% to estimate the percent of each number. 3. 4% of 220 4. 19% of 75 5. Mr. and Mrs. Dargen spend $46.25 on a meal. About how much should they leave for a 15% tip? 36 The café Possible answers: 8.8 15 $7

Lesson Quiz for Student Response Systems 1. Use a fraction to estimate 52% of 84. A. 30 B. 40 C. 50 D. 60

Lesson Quiz for Student Response Systems 2. During the annual sale, Brand A offers 20% off on a $6.55 shirt. Which of the following will make Brand B a better deal? A. Brand B sells the same shirt for $4.89. B. Brand B sells the same shirt for $5.59. C. Brand B sells the same shirt for $5.89. D. Brand B sells the same shirt for $6.29.

Lesson Quiz for Student Response Systems 3. Use 1% or 10% to estimate 6% of 239. A. 2.4 B. 14.4 C. 16.6 D. 24

Lesson Quiz for Student Response Systems 4. Use 1% or 10% to estimate 18% of 88. A. 8.8 B. 14 C. 18 D. 22

Lesson Quiz for Student Response Systems 5. Patricia bought accessories worth $52.75 in an online store. About how much would she spend for a 13% shipping charge? A. $5 B. $7 C. $9 D. $13