text: # Finding the Percent of a Number 4.4 2 ACTIVITY:
  
  ```English
  4.4
  Spanish
  Finding the Percent of a Number
  How can you use mental math to find the
  S
  STATE
  STANDARDS
  percent of a number?
  MA.6.A.5.1
  “I have a secret way for
  finding 21% of 80.”
  1
  “10% is 8 and 1% is 0.8.”
  “So 21% is 8 + 8 + 0.8 = 16.8.”
  EXAMPLE: Finding 10% of a Number
  a. How did Newton know that 10% of 80 is 8?
  Write 10% as a fraction.
  10
  10
  100
  10% = —
  per
  1
  10
  =—
  cent
  Method 1: Using a Model
  0%
  0
  10%
  8
  20%
  30%
  40%
  50%
  60%
  70%
  80%
  90%
  16
  24
  32
  40
  48
  56
  64
  72
  Method 2: Using Multiplication
  1
  10
  1
  10
  80
  10
  10% of 80 = — of 80 = — × 80 = — = 8
  b. How do you move the decimal point to find 10% of a number?
  Move the decimal point one place to the left.
  2
  10% of 80. = 8.0
  ACTIVITY: Finding 1% of a Number
  Work with a partner.
  a. How did Newton know that 1% of 80 is 0.8?
  b. How do you move the decimal point to find 1% of a number?
  168
  Chapter 4
  Fractions, Decimals, and Percents
  100%
  80
  English
  Spanish
  3
  EXAMPLE: Using Mental Math
  Use mental math to find each percent of a number.
  a. 12% of 40
  b. 19% of 50
  Think: 12% = 10% + 1% + 1%
  10% of 40 = 4
  Think: 19% = 10% + 10% − 1%
  1% of 40 = 0.4
  10% of 50 = 5
  4 + 0.4 + 0.4 = 4.8
  4
  1% of 50 = 0.5
  5 + 5 − 0.5 = 9.5
  ACTIVITY: Using Mental Math
  Work with a partner. Use mental math to find each percent of a number.
  a. 20% tip for a \$30 meal
  b. 18% tip for a \$30 meal
  c. 6% sales tax on a \$20 shirt
  d. 9% sales tax on a \$20 shirt
  e. 6% commission on selling a \$200,000 house
  f. 2% property tax on a \$200,000 house
  g. 21% income tax on an income of \$40,000
  h. 38% income tax on an income of \$80,000
  5. IN YOUR OWN WORDS How can you use mental math to find the percent
  of a number?
  6. Describe two real-life examples of finding a percent of a number.
  Use what you learned about finding the percent of a number to
  complete Exercises 3 –10 on page 172.
  Section 4.4
  Finding the Percent of a Number
  169
  English
  Spanish
  Lesson
  4.4
  Lesson Tutorials
  Finding the Percent of a Number
  Words
  Write the percent as a fraction or decimal. Then multiply.
  Numbers
  20% of 60 is 12.
  1
  5
  Model
  0%
  20% 40%
  60% 80% 100%
  0
  12
  36
  — × 60 = 12
  0.2 × 60 = 12
  EXAMPLE
  1
  24
  48
  60
  Finding the Percent of a Number
  Use a fraction to find the percent of the number.
  a. Find 25% of 40.
  b. Find 60% of 150.
  3
  5
  1
  4
  60% of 150 = — × 150
  25% of 40 = — × 40
  30
  10
  1 × 40
  =—
  4
  3 × 150
  =—
  5
  = 10
  = 90
  1
  1
  So, 25% of 40 is 10.
  0%
  0
  So, 60% of 150 is 90.
  25%
  50%
  75%
  100%
  10
  20
  30
  40
  0% 20%
  0
  30
  40%
  60%
  60
  90
  80% 100%
  120
  150
  Use a fraction to find the percent of the number.
  1. 90% of 20
  EXAMPLE
  Summer Vacation
  Did you go on a
  vacation this
  past summer?
  Yes
  No
  48%
  52%
  Note: 200 students surveyed
  2
  2. 75% of 32
  3. 10% of 110
  4. 30% of 75
  Standardized Test Practice
  How many students went on vacation?
  A 48
  ○
  B 96
  ○
  C 100
  ○
  D 104
  ○
  From the survey, you can see that 48% out of 200 students said yes.
  48% of 200 = 0.48 × 200
  = 96
  Write 48% as a decimal.
  Multiply.
  So, 96 students went on vacation. The correct answer is ○
  B.
  170
  Chapter 4
  Fractions, Decimals, and Percents
  English
  Spanish
  Use a decimal to find the percent of the number.
  5. 15% of 40
  Exercises 3–18
  EXAMPLE
  3
  6. 78% of 150
  7. 35% of 16
  8. 4% of 70
  Using Mental Math
  Your friend is bidding online for concert tickets. The current bid is
  shown. The winning bid is 150% of the current bid. How much is the
  winning bid?
  View larger picture
  Current bid:
  US \$120.00
  Time remaining:
  1 hour 45 min
  Method 1: Write 150% as a
  decimal and multiply.
  Method 2: Using mental math,
  think 150% = 100% + 50%.
  150% of 120 = 1.5 × 120
  100% of 120 = 1 × 120 = 120
  1
  2
  50% of 120 = — × 120 = 60
  = 180
  Add: 120 + 60 = 180
  So, the winning bid is \$180.
  9. WHAT IF? In Example 3, the winning bid is 225% of the
  current bid. How much is the winning bid?
  Exercises 23–30
  EXAMPLE
  4
  Real-Life Application
  The width of a rectangular room is 80% of its length. What is the area
  of the room?
  Find 80% of 15 feet.
  4
  5
  80% of 15 = — × 15
  3
  Tim
  e
  4 × 15
  =—
  5
  0%
  0
  20%
  3
  40%
  60%
  80%
  100%
  6
  9
  12
  15
  1
  15
  1
  5 ftt
  = 12
  The width is 12 feet.
  Use the formula for the area A of a rectangle.
  U
  A = 15 × 12 = 180
  So, the area of the room is 180 square feet.
  10. The width of a rectangular stage is 55% of its length. The stage
  is 120 feet long. What is the area?
  Section 4.4
  Finding the Percent of a Number
  171
  English
  Spanish
  Exercises
  4.4
  Help with Homework
  1. DIFFERENT WORDS, SAME QUESTION Which is different? Find “both” answers.
  What is twenty percent of 30?
  What is one-fifth of 30?
  What is 20 multiplied by 30?
  What is 0.2 times 30?
  2. REASONING If 52 is 130% of a number, is the number greater or less than 52?
  Explain.
  6)=3
  9+(- 3)=
  3+(- 9)=
  4+(- =
  1)
  9+(-
  Find the percent of the number.
  1
  2
  3. 20% of 60
  4. 10% of 40
  5. 18% of 70
  7. 8% of 90
  8. 14% of 20
  9. 26% of 50
  10. 3% of 60
  11. 30% of 70
  12. 75% of 48
  13. 45% of 45
  14. 92% of 19
  15. 40% of 60
  16. 38% of 22
  17. 70% of 20
  18. 87% of 55
  19. ERROR ANALYSIS Describe and correct the
  error in finding 40% of 75.
  ✗
  6. 32% of 30
  40% of 75 = 40% × 75 = 3000
  20. MANGROVES Lake Worth, near West Palm Beach, had about 2120 acres of
  mangrove trees 40 years ago. Only about 13% of the mangrove trees remain.
  How many acres of mangrove trees remain?
  21. SPIDER MONKEY The tail of the
  spider monkey is 64% of its length.
  What is the length of its tail?
  55
  22. CABLE A family pays \$45 each month
  for cable television. The cost increases 7%.
  in.
  a. How many dollars is the monthly increase?
  b. What is the new monthly cost?
  Find the percent of the number.
  172
  3 23. 140% of 60
  24. 120% of 33
  25. 175% of 54
  26. 250% of 146
  27. 4.5% of 50
  28. 0.7% of 40
  29. 2.8% of 150
  30. 7.2% of 235
  Chapter 4
  Fractions, Decimals, and Percents
  English
  Spanish
  Copy and complete the statement using <, >, or =.
  31. 80% of 60
  60% of 80
  32. 20% of 30
  30% of 40
  33. 120% of 5
  0.8% of 250
  34. 85% of 40
  25% of 136
  35. TIME How many minutes is 40% of 2 hours?
  36. LENGTH How many inches is 78% of 3 feet?
  37. GEOMETRY The width of the rectangle is 75% of its length.
  a. What is the area of the rectangle?
  b. The length of the rectangle is doubled. What percent
  of the length is the width now? Explain your reasoning.
  24 in.
  back to between 68% and 75% of the starting height. A new ball is
  dropped from 6 feet and bounces back 4 feet 1 inch. Does the ball
  pass inspection? Explain.
  39. REASONING You know that 15% of a number n is
  12. How can you use this to find 30% of n? 45% of
  n? Explain.
  40. SURFBOARD You have a coupon for 10% off the
  sale price of a surfboard.
  a. What is the sale price of the surfboard?
  b. What is the price of the surfboard after using the coupon?
  c. Is taking 40% off the regular price the same as taking
  30% off the regular price and then 10% off the sale
  41.
  On three geography tests, you earned grades of 88%, 94%,
  and 90%. Each test was worth 150 points.
  a. The final exam is worth 250 points. How many points do you need
  on the final exam to earn 93% of the total points on tests?
  b. What percent do you need on the final?
  Multiply. Write the answer in simplest form.
  2
  3
  42. — × 4
  3
  8
  43. — × 4
  SECTION 2.2
  3
  5
  44. 6 × —
  46. MULTIPLE CHOICE What is the quotient of 7.5 and 2.4?
  A 0.0032
  ○
  B 0.03125
  ○
  C 0.32
  ○
  Section 4.4
  5
  6
  45. 12 × —
  SECTION 3.5
  D 3.125
  ○
  Finding the Percent of a Number
  173
  ```
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