MathBored

Virginia SOL Mathematics Textbook

Grade 7 Workbook — Chapter 6: Percent of a Number

SOL 7.CE.2 (d) · Companion to Textbook Chapter 6

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/. Item numbers match the textbook exactly, so one answer key serves both books.

PAGE 1 — Chapter opener

Chapter 6 · Percent of a Number

Standard 7.CE.2 (d)

In this chapter you will:

Words to know: percent · whole (base) · benchmark percentage · estimate · double number line · tip · sales tax · discount · sale price

Chapter 5 built ratio tables and proportions. This chapter uses them, so keep that work nearby.

FIGURE: fig1-benchmark-percent-bar.png (full width)

PAGE 2 — Percent means per hundred

6.1 Benchmark Percentages

FIGURE: fig2-hundred-grid-35.png (half width, right)

Fill in the blanks.

The symbol %\% means ______________________.

35%35\% means ______ out of every ______.

35%=00100=0.0035\% = \dfrac{\phantom{00}}{100} = 0.\phantom{00}

Each small square in a 100-grid is ______% of the whole grid.

A percent by itself is not an amount. You must also know the ______________, which is also called the base.

Write each percent three ways.

Percent Fraction out of 100 Decimal
50%50\%
25%25\%
10%10\%
1%1\%
75%75\%

PAGE 3 — The benchmark toolkit

The Seven Benchmarks

Complete the table.

Benchmark How to find it That percent of 200
100%100\% leave the number alone
50%50\% divide by ______
25%25\% divide by ______
75%75\% 50%+50\% + ______%
10%10\% shift the decimal point ______ place left
5%5\% find 10%10\%, then ____________
1%1\% shift the decimal point ______ places left

FIGURE: fig5-decimal-shift.png (full width)

Guided practice. Show the benchmark you used.

  1. 50%50\% of 86 = ______

  2. 25%25\% of 120 = ______

  3. 10%10\% of 74 = ______

  4. 1%1\% of 74 = ______

  5. 5%5\% of 60 = ______ (First find 10%10\% of 60 = ______, then halve it.)

  6. 75%75\% of 200 = ______ (50%50\% of 200 = ______ plus 25%25\% of 200 = ______)

PAGE 4 — Building percents from benchmarks

Combining Benchmarks

FIGURE: fig4-benchmark-decomposition.png (full width)

Complete each decomposition.

35%=25%+35\% = 25\% + ______%

15%=10%+15\% = 10\% + ______%

20%=10%+20\% = 10\% + ______%

60%=50%+60\% = 50\% + ______%

Percents over 100 and under 1.

200%200\% of a number is ______ times the number.

150%150\% of 48 = 48+48 + ______ = ______

0.5%0.5\% is ______ of 1%1\%, so 0.5%0.5\% of 400 = ______

FIGURE: fig3-percent-double-number-line.png (full width)

Read the double number line. In a class of 60 students:

30%30\% is ______ students. 70%70\% is ______ students. 100%100\% is ______ students.

PAGE 5 — Independent practice 6.1

Practice · Lesson 6.1

  1. a) 50%50\% of 250 = ______ b) 25%25\% of 88 = ______ c) 10%10\% of 4{,}500 = ______ d) 1%1\% of 620 = ______

  2. a) 5%5\% of 140 = ______ b) 75%75\% of 48 = ______ c) 100%100\% of 39 = ______ d) 200%200\% of 45 = ______

  3. 10%10\% of 96 = ______, so 20%20\% of 96 = ______

  4. Which is greater, 25%25\% of 160 or 10%10\% of 380?

    25%25\% of 160 = ______ 10%10\% of 380 = ______ Greater: ______

  5. Explain how to find 10%10\% of 730 without dividing on paper. Answer: ______

  6. Complete the benchmark table for a whole of 600.

    Percent 50%50\% 25%25\% 10%10\% 5%5\% 1%1\% 75%75\%
    Amount of 600

  7. Application. A restaurant bill is $40.

    10%10\% tip: $______ 20%20\% tip: $______

  8. Reasoning. Why is 5%5\% of a number always exactly half of 10%10\% of that number?

PAGE 6 — Exit ticket 6.1

Exit Ticket · Lesson 6.1

Name: ________________________ Date: ____________

  1. 50%50\% of 92 = ______

  2. 10%10\% of 830 = ______

  3. 1%1\% of 830 = ______

  4. Describe two different ways to find 25%25\% of 48. Answer: ______

    Way 1: _______________________________________________

    Way 2: _______________________________________________

PAGE 7 — Estimating with benchmarks

6.2 Estimating a Percent of a Number

Two decisions, every time.

  1. Round the ______________ to a nearby benchmark.
  2. Round the ______________ to a friendly number.

Round each percent to the nearest benchmark.

Percent 48%48\% 26%26\% 9%9\% 73%73\% 52%52\% 11%11\%
Benchmark

The symbol ≈\approx is read ____________________________.

FIGURE: fig6-estimate-then-check.png (full width)

High or low? Circle one for each.

Rounding the percent UP makes the estimate ( higher / lower )

Rounding the percent DOWN makes the estimate ( higher / lower )

Rounding the whole UP makes the estimate ( higher / lower )

Rounding the whole DOWN makes the estimate ( higher / lower )

PAGE 8 — Guided practice 6.2

Estimate It

Guided practice. Use the benchmark named in each problem.

  1. Estimate 52%52\% of 78 by finding 50%50\% of 80. About ______

  2. Estimate 24%24\% of 41 by finding 25%25\% of 40. About ______

  3. Estimate 11%11\% of 89 by finding 10%10\% of 90. About ______

  4. Estimate 76%76\% of 61 by finding 75%75\% of 60. About ______

  5. Estimate 9%9\% of 412 by finding 10%10\% of 400. About ______

  6. Estimate 48%48\% of 305 by finding 50%50\% of 300. About ______

PAGE 9 — Independent practice 6.2

Practice · Lesson 6.2

  1. Estimate using the benchmark and friendly whole in parentheses.

    a) 49%49\% of 62 (50%50\% of 60) → about ______ b) 26%26\% of 79 (25%25\% of 80) → about ______

    c) 9%9\% of 51 (10%10\% of 50) → about ______ d) 74%74\% of 81 (75%75\% of 80) → about ______

  2. Which is closest to 31%31\% of 297? 30 · 60 · 90 · 120 Benchmark used: ______________

  3. Which is closest to 6%6\% of 396? 8 · 16 · 24 · 40 Benchmark used: ______________

  4. Estimate 48%48\% of 398 by finding 50%50\% of 400. About ______

    Higher or lower than exact? ______ Why?

  5. Estimate 35%35\% of 61 by combining two benchmarks of 60.

    25%25\% of 60 = ______ plus 10%10\% of 60 = ______ → about ______

  6. Application. A jacket costs $59. About how many dollars is 20%20\% of that price? Use $60. About $______

  7. Application. A school has 412 students and about 25%25\% ride the bus. Friendly whole: ______ About ______ students

  8. Reasoning. Marisol estimates 9%9\% of 240 as 24. Higher or lower than exact? ______

    Why? _______________________________________________

PAGE 10 — Exit ticket 6.2

Exit Ticket · Lesson 6.2

Name: ________________________ Date: ____________

  1. Estimate 51%51\% of 78 by finding 50%50\% of 80. About ______

  2. Estimate 24%24\% of 121 by finding 25%25\% of 120. About ______

  3. Which is closest to 11%11\% of 508? 5 · 50 · 100 · 250

  4. Why does rounding the whole up, with the percent left alone, make an estimate greater than the exact answer?

PAGE 11 — Four routes to an exact answer

6.3 Finding an Exact Percent

All four methods find 18%18\% of 250. Complete each one.

Method 1 — decimal. 18%=0.00‾18\% = 0.\underline{\phantom{00}}, and 0.18×250=0.18 \times 250 = ______

Method 2 — fraction. 18100×250=950×250=\dfrac{18}{100} \times 250 = \dfrac{9}{50} \times 250 = ______

Method 3 — proportion. x250=18100\dfrac{x}{250} = \dfrac{18}{100}, so 100x=100x = ______ and x=x = ______

Method 4 — benchmarks. 10%=10\% = ______, 5%=5\% = ______, 1%=1\% = ______

18%=10%+5%+1%+1%+1%=18\% = 10\% + 5\% + 1\% + 1\% + 1\% = ______

Write each percent as a decimal.

Percent 45%45\% 8%8\% 120%120\% 0.5%0.5\%
Decimal

Warning. 8%8\% is 0.080.08, not 0.80.8. Writing 0.80.8 makes your answer ten times too big.

PAGE 12 — Guided practice 6.3

Exact Percents

Guided practice.

  1. 20%20\% of 45 = ______

  2. 15%15\% of 60 = ______ (10%10\% of 60 = ______ plus 5%5\% of 60 = ______)

  3. 8%8\% of 250 = ______ (Decimal: ______)

  4. 45%45\% of 80 = ______

  5. 35%35\% of 140 = ______ (25%25\% of 140 = ______ plus 10%10\% of 140 = ______)

  6. 110%110\% of 90 = ______

Check yourself. Is each answer above smaller or larger than its whole? Which item should be larger, and why?

PAGE 13 — Independent practice 6.3

Practice · Lesson 6.3

  1. a) 30%30\% of 70 = ______ b) 12%12\% of 300 = ______ c) 65%65\% of 40 = ______ d) 4%4\% of 225 = ______

  2. a) 55%55\% of 120 = ______ b) 85%85\% of 60 = ______ c) 150%150\% of 48 = ______ d) 2%2\% of 850 = ______

  3. Find 65%65\% of 240 by combining benchmarks.

    50%50\% = ______ 10%10\% = ______ 5%5\% = ______ Total = ______

  4. Find 18%18\% of 950 by multiplying by a decimal. 0.18×950=0.18 \times 950 = ______

  5. Write and solve a proportion for 24%24\% of 175.

    x000=00100\dfrac{x}{\phantom{000}} = \dfrac{\phantom{00}}{100} Cross products: ______ x=x = ______

  6. 0.5%0.5\% of 600 = ______

  7. Application. A store has 640 T-shirts and 45%45\% are blue. Blue T-shirts: ______

  8. Reasoning. Why does finding 25%25\% of 84 give the same result as dividing 84 by 4? Answer: ______

PAGE 14 — Exit ticket 6.3

Exit Ticket · Lesson 6.3

Name: ________________________ Date: ____________

  1. 40%40\% of 65 = ______

  2. 15%15\% of 220 = ______

  3. 130%130\% of 50 = ______

  4. Find 35%35\% of 60 two different ways.

    Way 1: _______________________ = ______

    Way 2: _______________________ = ______

PAGE 15 — Percent in the real world

6.4 Percent in Context

Match each word to its meaning.

Word Meaning
tip an amount subtracted from a price
sales tax a percent of a bill added for service
discount the original price minus the discount
sale price a percent of a price added by law

The five-step procedure.

  1. Name the ______________.
  2. Name the ______________.
  3. ______________ with a benchmark.
  4. Compute ______________.
  5. Answer the question that was ______________.

The benchmark tip.

10%10\% tip on $40: shift the decimal point → $______

20%20\% tip on $40: find 10%10\% and ______________ → $______

15%15\% tip on $40: 10%10\% = $______ plus 5%5\% = $______ → $______

PAGE 16 — Guided practice 6.4

Tips, Tax, and Discounts

Guided practice.

  1. 10%10\% tip on a $36 bill: $______

  2. 20%20\% tip on a $55 bill: $______

  3. 5%5\% sales tax on a $240 furniture order: $______

  4. Shoes cost $64, marked 25%25\% off. Discount: $______

  5. In a group of 250 students, 40%40\% chose soccer. Students: ______

Careful. In item 58, does the problem ask for the discount or the sale price? ______________

PAGE 17 — Independent practice 6.4

Practice · Lesson 6.4

  1. 15%15\% tip on an $80 bill: $______ (10%10\% = $______ plus 5%5\% = $______)

  2. A tablet costs $150 and sales tax is 7%7\%. Tax: $______

  3. A coat costs $120, marked 35%35\% off. Discount: $______ Sale price: $______

  4. A team attempted 40 free throws and made 65%65\%. Made: ______

  5. A plan includes 1{,}250 megabytes and Jordan used 8%8\%. Used: ______ megabytes

  6. Application. A restaurant bill is $48. 18%18\% tip: $______ Total paid: $______

  7. Application. A theater has 350 seats and 22%22\% are in the balcony.

    Estimate using 20%20\% of 350: about ______ Exact: ______ seats

  8. Reasoning. Why does taking 20%20\% off $60 give the same sale price as finding 80%80\% of $60?

    20%20\% of 60 = ______, so 60−60 - ______ = ______ 80%80\% of 60 = ______

PAGE 18 — Exit ticket 6.4

Exit Ticket · Lesson 6.4

Name: ________________________ Date: ____________

  1. 20%20\% tip on a $65 bill: $______

  2. 6%6\% sales tax on a $250 chair: $______

  3. A $140 bike is marked 30%30\% off. Discount: $______

  4. Describe a benchmark strategy for a 15%15\% tip on a $40 bill. Tip: $______

PAGE 19 — Chapter 6 review, part 1

Chapter 6 Review

Part A · Benchmark percentages

  1. 50%50\% of 148 = ______

  2. 25%25\% of 320 = ______

  3. 10%10\% of 76 = ______

  4. 1%1\% of 76 = ______

  5. 5%5\% of 180 = ______

  6. 75%75\% of 88 = ______

Part B · Estimating

  1. Estimate 49%49\% of 122 with 50%50\% of 120. About ______

  2. Estimate 26%26\% of 79 with 25%25\% of 80. About ______

  3. Estimate 9%9\% of 305 with 10%10\% of 300. About ______

  4. Estimate 74%74\% of 41 with 75%75\% of 40. About ______

  5. Closest to 34%34\% of 298? 30 · 60 · 100 · 150 Benchmark: ______________

  6. Is 10%10\% of 480 high or low for 9%9\% of 480? ______

    Estimate: ______ Exact: ______

PAGE 20 — Chapter 6 review, part 2

Chapter 6 Review (continued)

Part C · Exact percents

  1. 30%30\% of 150 = ______

  2. 12%12\% of 425 = ______

  3. 65%65\% of 80 = ______

  4. 4%4\% of 375 = ______

  5. 140%140\% of 60 = ______

  6. 0.5%0.5\% of 800 = ______

Part D · Percent in context

  1. 18%18\% tip on a $60 bill: $______

  2. A $45 backpack with 6%6\% sales tax. Tax: $______ Total: $______

  3. A $95 tent marked 40%40\% off. Discount: $______ Sale price: $______

Part E · Mixed application and reasoning

  1. Find 35%35\% of 260 with benchmarks. 25%25\% = ______ 10%10\% = ______ Total = ______

  2. Estimate 48%48\% of 250, then compute exactly. Estimate: ______ Exact: ______

    Why is the estimate high? _______________________________________________

  3. Why does moving the decimal point give 10%10\% and 1%1\% of a number? Use 640.

    10%10\% of 640 = ______ 1%1\% of 640 = ______

Canva production notes