The People’s Share

GED Math

Percents and Proportion Practice

Percents, decimals and fractions; the three percent questions; tax, tips, discounts and interest; ratios, rates and proportions. 162 problems, with the answer key at the end.

← Math · Family 5

Practice for family 5. Quizzes 17 to 19 explain percents, and Quizzes 23 to 25 explain ratios and proportions; this sheet is for doing them until they are quick. 162 problems in four parts, each section starting with its plainest version.

Part One

What percent means

Percent means “out of 100.” 35% is 35 out of 100: the fraction 35⁄100, or the decimal 0.35.

1.Percent to decimal

Move the point two places to the left.

Example45% = 0.45, 7% = 0.07, and 120% = 1.2.

Write each as a decimal.

  1. 1.Write 0.6% as a decimal
  2. 2.Write 13% as a decimal
  3. 3.Write 16% as a decimal
  4. 4.Write 38% as a decimal
  5. 5.Write 53% as a decimal
  6. 6.Write 54% as a decimal
  7. 7.Write 82% as a decimal
  8. 8.Write 96% as a decimal
  9. 9.Write 172% as a decimal
  10. 10.Write 177% as a decimal

2.Decimal to percent

Move the point two places to the right.

Example0.6 = 60%, and 0.045 = 4.5%.

Write each as a percent.

  1. 11.Write 0.005 as a percent
  2. 12.Write 0.01 as a percent
  3. 13.Write 0.074 as a percent
  4. 14.Write 0.11 as a percent
  5. 15.Write 0.144 as a percent
  6. 16.Write 0.62 as a percent
  7. 17.Write 0.63 as a percent
  8. 18.Write 0.752 as a percent
  9. 19.Write 0.8 as a percent
  10. 20.Write 0.89 as a percent

3.Percent to fraction

Put the percent over 100, then simplify.

Example35% = 35⁄100 = 7⁄20.

Write each as a fraction.

  1. 21.Write 8% as a fraction in simplest form
  2. 22.Write 15% as a fraction in simplest form
  3. 23.Write 20% as a fraction in simplest form
  4. 24.Write 25% as a fraction in simplest form
  5. 25.Write 30% as a fraction in simplest form
  6. 26.Write 50% as a fraction in simplest form
  7. 27.Write 62.5% as a fraction in simplest form
  8. 28.Write 90% as a fraction in simplest form
  9. 29.Write 110% as a fraction in simplest form
  10. 30.Write 125% as a fraction in simplest form

4.Fraction to percent

Divide top by bottom, then move the point two places right.

Example3⁄8 = 3 ÷ 8 = 0.375 = 37.5%.

Write each as a percent.

  1. 31.Write 1⁄2 as a percent
  2. 32.Write 1⁄3 as a percent
  3. 33.Write 1⁄4 as a percent
  4. 34.Write 2⁄5 as a percent
  5. 35.Write 3⁄5 as a percent
  6. 36.Write 1⁄6 as a percent
  7. 37.Write 1⁄8 as a percent
  8. 38.Write 7⁄10 as a percent
  9. 39.Write 1⁄20 as a percent
  10. 40.Write 1⁄25 as a percent

Part Two

The three percent questions

Every percent question gives two of three numbers, the part, the percent and the whole, and asks for the third. Part = percent × whole.

5.Finding the part

Change the percent to a decimal and multiply.

ExampleWhat is 15% of 80? 0.15 × 80 = 12.

Find each part.

  1. 41.What is 10% of 48?
  2. 42.What is 50% of 64?
  3. 43.What is 15% of 80?
  4. 44.What is 80% of 120?
  5. 45.What is 150% of 90?
  6. 46.What is 5% of 200?
  7. 47.What is 75% of 1,200?
  8. 48.What is 12% of 400?
  9. 49.What is 30% of 500?
  10. 50.What is 75% of 640?

6.Finding the percent

Divide the part by the whole, then change the decimal to a percent.

Example12 is what percent of 48? 12 ÷ 48 = 0.25 = 25%.

Find each percent.

  1. 51.5 is what percent of 20?
  2. 52.25 is what percent of 50?
  3. 53.12 is what percent of 60?
  4. 54.32 is what percent of 64?
  5. 55.12 is what percent of 200?
  6. 56.96 is what percent of 240?
  7. 57.18 is what percent of 300?
  8. 58.180 is what percent of 300?
  9. 59.80 is what percent of 400?
  10. 60.250 is what percent of 500?

7.Finding the whole

Divide the part by the percent, written as a decimal.

Example18 is 30% of what number? 18 ÷ 0.30 = 60.

Find each whole.

  1. 61.6 is 5% of what number?
  2. 62.18 is 12% of what number?
  3. 63.8 is 20% of what number?
  4. 64.32 is 8% of what number?
  5. 65.32 is 50% of what number?
  6. 66.135 is 45% of what number?
  7. 67.150 is 50% of what number?
  8. 68.225 is 150% of what number?
  9. 69.250 is 50% of what number?
  10. 70.300 is 60% of what number?

8.Percent change

Find the change, then divide it by the old number, the one you started from.

ExampleFrom 80 to 92: the change is 12, and 12 ÷ 80 = 0.15, a 15% increase.

Find each percent change.

  1. 71.From 60 to 54. Find the percent decrease.
  2. 72.From 80 to 48. Find the percent decrease.
  3. 73.From 60 to 120. Find the percent increase.
  4. 74.From 250 to 275. Find the percent increase.
  5. 75.From 300 to 270. Find the percent decrease.
  6. 76.From 400 to 480. Find the percent increase.
  7. 77.From 500 to 400. Find the percent decrease.
  8. 78.From 500 to 700. Find the percent increase.
  9. 79.From 500 to 800. Find the percent increase.
  10. 80.From 800 to 896. Find the percent increase.

Part Three

Percent in the world

Tax and tips are added on. Discounts are taken off. Simple interest is principal × rate × time.

9.Sales tax

ExampleA $40.00 item with 6% tax: 0.06 × 40 = $2.40 tax, so $42.40 in all.

Find the tax and the total.

  1. 81.A $35.00 item. Sales tax is 9%. Find the tax and the total.
  2. 82.A $39.25 item. Sales tax is 4%. Find the tax and the total.
  3. 83.A $96.25 item. Sales tax is 4%. Find the tax and the total.
  4. 84.A $145.00 item. Sales tax is 8%. Find the tax and the total.
  5. 85.A $147.00 item. Sales tax is 5%. Find the tax and the total.
  6. 86.A $181.00 item. Sales tax is 8%. Find the tax and the total.

10.Tips

ExampleA $30.00 meal with a 20% tip: 0.20 × 30 = $6.00, so $36.00 in all.

Find the tip and the total.

  1. 87.A $59.60 meal. Leave a 10% tip. Find the tip and the total.
  2. 88.A $77.40 meal. Leave a 20% tip. Find the tip and the total.
  3. 89.A $104.80 meal. Leave a 15% tip. Find the tip and the total.
  4. 90.A $106.40 meal. Leave a 25% tip. Find the tip and the total.
  5. 91.A $130.80 meal. Leave a 25% tip. Find the tip and the total.
  6. 92.A $131.00 meal. Leave a 20% tip. Find the tip and the total.

11.Discounts

ExampleA $50.00 coat at 30% off: 0.30 × 50 = $15.00 off, so it costs $35.00.

Find the discount and the sale price.

  1. 93.An item priced at $30.00 is 35% off. Find the discount and the sale price.
  2. 94.An item priced at $50.00 is 15% off. Find the discount and the sale price.
  3. 95.An item priced at $150.00 is 50% off. Find the discount and the sale price.
  4. 96.An item priced at $150.00 is 60% off. Find the discount and the sale price.
  5. 97.An item priced at $199.00 is 20% off. Find the discount and the sale price.
  6. 98.An item priced at $199.00 is 15% off. Find the discount and the sale price.

12.Simple interest

Interest = principal × rate × time. The principal is the amount borrowed or saved. The time is in years.

Example$2,000 at 5% for 3 years: 2,000 × 0.05 × 3 = $300.

Find the interest.

  1. 99.$5,000 at 2.5% simple interest a year, for 5 years. Find the interest.
  2. 100.$2,000 at 5% simple interest a year, for 3 years. Find the interest.
  3. 101.$4,000 at 5% simple interest a year, for 2 years. Find the interest.
  4. 102.$5,000 at 3.5% simple interest a year, for 6 years. Find the interest.
  5. 103.$2,000 at 2% simple interest a year, for 10 years. Find the interest.
  6. 104.$2,500 at 6% simple interest a year, for 3 years. Find the interest.

13.Percent stories

These mix everything above. Decide first which of the three numbers is missing.

Answer each question.

  1. 105.Rent went from $1,200 a month to $1,290 a month. By what percent did it go up?
  2. 106.A worker earns $18.00 an hour and gets a 4% raise. What is the new hourly pay?
  3. 107.A town of 24,000 people grew by 5% one year. How many people live there now?
  4. 108.A shirt is on sale for $21.00, which is 30% off. What was the price before the sale?
  5. 109.A $60.00 pair of shoes is 25% off, and then 8% tax is added to the sale price. What do you pay?
  6. 110.A $200 phone is marked down 20%, and later marked down another 20%. What is the price now? Is that 40% off?
  7. 111.Of the 350 people who took a class, 280 finished it. What percent finished?
  8. 112.A loan of $3,000 at 6% simple interest a year is paid back after 3 years. What is paid back in all?
  9. 113.Gas went from $3.20 a gallon to $2.88 a gallon. By what percent did it go down?
  10. 114.A school raised $4,500, which was 90% of its goal. What was the goal?

Part Four

Ratio and proportion

A ratio compares two amounts. A proportion says two ratios are equal.

14.Simplifying ratios

Divide both numbers by the largest number that goes into both.

Example12 to 18: both divide by 6, so 2 to 3.

Simplify.

  1. 115.Simplify the ratio: 2 minutes to 4 minutes
  2. 116.Simplify the ratio: 27 women to 18 men
  3. 117.Simplify the ratio: 11 minutes to 33 minutes
  4. 118.Simplify the ratio: 40 minutes to 16 minutes
  5. 119.Simplify the ratio: 54 minutes to 24 minutes
  6. 120.Simplify the ratio: 60 wins to 48 losses
  7. 121.Simplify the ratio: 81 cups of flour to 36 cups of water
  8. 122.Simplify the ratio: 50 wins to 90 losses

15.Unit rates

A unit rate is the amount for one: divide by the number of units.

Example$4.80 for 6 cans: 4.80 ÷ 6 = $0.80 per can.

Find each unit rate.

  1. 123.$0.52 for 2 ounces of cheese. Find the price for one ounce.
  2. 124.$2.72 for 4 pounds of rice. Find the price for one pound.
  3. 125.$7.80 for 2 pounds of rice. Find the price for one pound.
  4. 126.$9.68 for 8 pounds of rice. Find the price for one pound.
  5. 127.$24.00 for 12 cans. Find the price for one can.
  6. 128.A car goes 96 miles in 2 hours. Find the speed.
  7. 129.A car goes 210 miles in 6 hours. Find the speed.
  8. 130.A car goes 260 miles in 4 hours. Find the speed.
  9. 131.A car goes 300 miles in 6 hours. Find the speed.
  10. 132.You earn $562.50 for 25 hours of work. Find the pay for one hour.

16.The better buy

Find the price of one ounce for each. The lower price per ounce is the better buy.

Choose, and give the price per ounce for each.

  1. 133.Which is the better buy: 12 ounces for $6.00, or 18 ounces for $8.64?
  2. 134.Which is the better buy: 12 ounces for $2.76, or 18 ounces for $3.06?
  3. 135.Which is the better buy: 20 ounces for $8.80, or 32 ounces for $14.72?
  4. 136.Which is the better buy: 12 ounces for $2.52, or 32 ounces for $8.00?
  5. 137.Which is the better buy: 20 ounces for $4.60, or 32 ounces for $6.40?
  6. 138.Which is the better buy: 20 ounces for $11.60, or 32 ounces for $17.60?

17.Solving proportions

Cross-multiply, then divide.

Examplex⁄12 = 5⁄8: 5 × 12 = 8 × x, so 60 = 8x, and x = 7.5.

Find x.

  1. 139.2⁄10 = 8⁄x
  2. 140.5⁄12 = 15⁄x
  3. 141.5⁄x = 15⁄27
  4. 142.7⁄6 = 35⁄x
  5. 143.2⁄x = 8⁄36
  6. 144.x⁄4 = 40⁄20
  7. 145.x⁄7 = 40⁄35
  8. 146.7⁄5 = 42⁄x
  9. 147.x⁄13 = 20⁄52
  10. 148.11⁄13 = 55⁄x
  11. 149.12⁄x = 60⁄10
  12. 150.11⁄15 = 66⁄x

18.Scale drawings and maps

Set up the scale as a ratio and keep the same units on top.

Example1 inch = 25 miles, and 3.5 inches on the map: 3.5 × 25 = 87.5 miles.

Answer each.

  1. 151.A map scale is 1 inch = 10 miles. Two towns are 3 inches apart on the map. How far apart are they?
  2. 152.A floor plan uses 1 inch for 2 feet. A wall is 24 feet long. How long is it on the plan?
  3. 153.A floor plan uses 1 inch for 8 feet. A wall is 24 feet long. How long is it on the plan?
  4. 154.A floor plan uses 1 inch for 4 feet. A wall is 32 feet long. How long is it on the plan?
  5. 155.A map scale is 1 inch = 40 miles. Two towns are 2 3⁄4 inches apart on the map. How far apart are they?
  6. 156.A floor plan uses 1 inch for 4 feet. A wall is 40 feet long. How long is it on the plan?

19.Proportional or not?

y is proportional to x when y ÷ x is the same number for every pair. Then y = kx, and the graph is a straight line through (0, 0).

Example(2, 6), (3, 9), (5, 15): 6 ÷ 2 = 3, 9 ÷ 3 = 3, 15 ÷ 5 = 3. Yes, y = 3x.

Decide, and give the reason.

  1. 157.Pairs (x, y): (4, 4)   (7, 7)   (8, 8)   (9, 9). Is y proportional to x?
  2. 158.Pairs (x, y): (1, 4)   (5, 20)   (6, 24)   (8, 32). Is y proportional to x?
  3. 159.Pairs (x, y): (2, 12)   (3, 17)   (5, 27)   (7, 37). Is y proportional to x?
  4. 160.Pairs (x, y): (1, 5)   (5, 21)   (7, 29)   (10, 41). Is y proportional to x?
  5. 161.Pairs (x, y): (1, 5)   (6, 30)   (8, 40)   (9, 45). Is y proportional to x?
  6. 162.Pairs (x, y): (1, 7)   (3, 17)   (8, 42)   (10, 52). Is y proportional to x?

Answer Key

Money answers are to the cent. Percents that do not end are written with a fraction, as in 33 1⁄3%.

1.Percent to decimal (1–10)

  1. 1.0.006
  2. 2.0.13
  3. 3.0.16
  4. 4.0.38
  5. 5.0.53
  6. 6.0.54
  7. 7.0.82
  8. 8.0.96
  9. 9.1.72
  10. 10.1.77

2.Decimal to percent (11–20)

  1. 11.0.5%
  2. 12.1%
  3. 13.7.4%
  4. 14.11%
  5. 15.14.4%
  6. 16.62%
  7. 17.63%
  8. 18.75.2%
  9. 19.80%
  10. 20.89%

3.Percent to fraction (21–30)

  1. 21.2⁄25
  2. 22.3⁄20
  3. 23.1⁄5
  4. 24.1⁄4
  5. 25.3⁄10
  6. 26.1⁄2
  7. 27.5⁄8
  8. 28.9⁄10
  9. 29.1 1⁄10
  10. 30.1 1⁄4

4.Fraction to percent (31–40)

  1. 31.50%
  2. 32.33 1⁄3%
  3. 33.25%
  4. 34.40%
  5. 35.60%
  6. 36.16 2⁄3%
  7. 37.12.5%
  8. 38.70%
  9. 39.5%
  10. 40.4%

5.Finding the part (41–50)

  1. 41.4.8
  2. 42.32
  3. 43.12
  4. 44.96
  5. 45.135
  6. 46.10
  7. 47.900
  8. 48.48
  9. 49.150
  10. 50.480

6.Finding the percent (51–60)

  1. 51.25%
  2. 52.50%
  3. 53.20%
  4. 54.50%
  5. 55.6%
  6. 56.40%
  7. 57.6%
  8. 58.60%
  9. 59.20%
  10. 60.50%

7.Finding the whole (61–70)

  1. 61.120
  2. 62.150
  3. 63.40
  4. 64.400
  5. 65.64
  6. 66.300
  7. 67.300
  8. 68.150
  9. 69.500
  10. 70.500

8.Percent change (71–80)

  1. 71.10% decrease
  2. 72.40% decrease
  3. 73.100% increase
  4. 74.10% increase
  5. 75.10% decrease
  6. 76.20% increase
  7. 77.20% decrease
  8. 78.40% increase
  9. 79.60% increase
  10. 80.12% increase

9.Sales tax (81–86)

  1. 81.tax $3.15; total $38.15
  2. 82.tax $1.57; total $40.82
  3. 83.tax $3.85; total $100.10
  4. 84.tax $11.60; total $156.60
  5. 85.tax $7.35; total $154.35
  6. 86.tax $14.48; total $195.48

10.Tips (87–92)

  1. 87.tip $5.96; total $65.56
  2. 88.tip $15.48; total $92.88
  3. 89.tip $15.72; total $120.52
  4. 90.tip $26.60; total $133.00
  5. 91.tip $32.70; total $163.50
  6. 92.tip $26.20; total $157.20

11.Discounts (93–98)

  1. 93.discount $10.50; sale price $19.50
  2. 94.discount $7.50; sale price $42.50
  3. 95.discount $75.00; sale price $75.00
  4. 96.discount $90.00; sale price $60.00
  5. 97.discount $39.80; sale price $159.20
  6. 98.discount $29.85; sale price $169.15

12.Simple interest (99–104)

  1. 99.$625.00
  2. 100.$300.00
  3. 101.$400.00
  4. 102.$1,050.00
  5. 103.$400.00
  6. 104.$450.00

13.Percent stories (105–114)

  1. 105.7.5%
  2. 106.$18.72
  3. 107.25,200
  4. 108.$30.00 (the $21.00 is 70% of it)
  5. 109.$48.60. Not 17% off: the tax is 8% of $45.00, not of $60.00
  6. 110.$128.00. No: it is 36% off, because the second 20% comes off $160, not $200
  7. 111.80%
  8. 112.$3,540.00
  9. 113.10%
  10. 114.$5,000

14.Simplifying ratios (115–122)

  1. 115.1 to 2
  2. 116.3 to 2
  3. 117.1 to 3
  4. 118.5 to 2
  5. 119.9 to 4
  6. 120.5 to 4
  7. 121.9 to 4
  8. 122.5 to 9

15.Unit rates (123–132)

  1. 123.$0.26 per ounce
  2. 124.$0.68 per pound
  3. 125.$3.90 per pound
  4. 126.$1.21 per pound
  5. 127.$2.00 per can
  6. 128.48 miles per hour
  7. 129.35 miles per hour
  8. 130.65 miles per hour
  9. 131.50 miles per hour
  10. 132.$22.50 an hour

16.The better buy (133–138)

  1. 133.18 ounces ($0.48 an ounce, against $0.50)
  2. 134.18 ounces ($0.17 an ounce, against $0.23)
  3. 135.20 ounces ($0.44 an ounce, against $0.46)
  4. 136.12 ounces ($0.21 an ounce, against $0.25)
  5. 137.32 ounces ($0.20 an ounce, against $0.23)
  6. 138.32 ounces ($0.55 an ounce, against $0.58)

17.Solving proportions (139–150)

  1. 139.x = 40
  2. 140.x = 36
  3. 141.x = 9
  4. 142.x = 30
  5. 143.x = 9
  6. 144.x = 8
  7. 145.x = 8
  8. 146.x = 30
  9. 147.x = 5
  10. 148.x = 65
  11. 149.x = 2
  12. 150.x = 90

18.Scale drawings and maps (151–156)

  1. 151.30 miles
  2. 152.12 inches
  3. 153.3 inches
  4. 154.8 inches
  5. 155.110 miles
  6. 156.10 inches

19.Proportional or not? (157–162)

  1. 157.Yes: y is always the same as x, so y = x
  2. 158.Yes: y is always 4 times x, so y = 4x
  3. 159.No: 12 ÷ 2 = 6, but 37 ÷ 7 is not 6
  4. 160.No: 5 ÷ 1 = 5, but 41 ÷ 10 is not 5
  5. 161.Yes: y is always 5 times x, so y = 5x
  6. 162.No: 7 ÷ 1 = 7, but 52 ÷ 10 is not 7