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Math 8

Math 8 · Worksheets

Percents, ratios and rates

Ten questions of mixed difficulty, covering Percents, ratios and rates. Print it, or work through it on screen — the answer key starts on its own page.

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Percents, ratios and rates

Math 8 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. A 500 g bag of trail mix costs $3.50 and a 750 g bag costs $4.80. Which is the better buy, and why?

    1. a) The 750 g bag: it costs 64¢ per 100 g, against 70¢.
    2. b) The 500 g bag: it gives 143 g per dollar, against 156 g.
    3. c) The 750 g bag: bigger packages always cost less per gram.
    4. d) The 500 g bag: it costs $1.30 less than the 750 g bag.

  2. A town's population grew from 800 to 1000. What was the percent increase?

    1. a) 25%
    2. b) 125%
    3. c) 80%
    4. d) 20%

  3. On a map, 2 cm stands for 15 km. Two towns are 7 cm apart on the map. How far apart are they really?

    1. a) 20 km
    2. b) 52.5 km
    3. c) 105 km
    4. d) 30 km

  4. Which of these is a rate?

    1. a) 90 km in 1.5 hours
    2. b) 2 wins for every 3 losses
    3. c) 4 cups of flour to 1 cup of sugar
    4. d) 3 red cars to 5 blue cars

  5. What is 150% of 40?

    1. a) 20
    2. b) 6
    3. c) 60
    4. d) 600

  6. A class has 12 girls and 16 boys. What is the ratio of girls to all the students in the class, in lowest terms?

    1. a) 7:3
    2. b) 3:7
    3. c) 4:7
    4. d) 3:4

  7. Written as a decimal, 0.5% is

    1. a) 5
    2. b) 0.005
    3. c) 0.05
    4. d) 0.5

  8. A $60 jacket is on sale for 25% off. Then 5% GST is added to the sale price. What is the total cost?

    1. a) $47.25
    2. b) $48.00
    3. c) $45.00
    4. d) $42.75

  9. A plant was 12 cm tall. Its height then increased by 150%. How tall is it now?

    1. a) 18 cm
    2. b) 30 cm
    3. c) 13.5 cm
    4. d) 180 cm

  10. Ana cycles 18 km in 45 minutes. At that rate, how far does she cycle in 2 hours?

    1. a) 36 km
    2. b) 80 km
    3. c) 48 km
    4. d) 0.8 km

Answer key · Percents, ratios and rates

Math 8 · maddyhelps.com

  1. a) The 750 g bag: it costs 64¢ per 100 g, against 70¢. — Compare the price of the same amount: $3.50 ÷ 5 = 70¢ per 100 g and $4.80 ÷ 7.5 = 64¢ per 100 g, so the 750 g bag is cheaper for each gram. A lower total price just means a smaller bag, and with grams per dollar, more is better — 156 g beats 143 g. Big packages are often cheaper per gram, but not always, which is why you check.
  2. a) 25% — The increase is 1000 − 800 = 200, and a percent increase compares it with the starting amount: 200 ÷ 800 = 0.25 = 25%. 20% divides by the new population instead, and 125% is the new population as a percent of the old one — it includes the 100% the town started with.
  3. b) 52.5 km — 1 cm stands for 15 ÷ 2 = 7.5 km, so 7 cm stands for 7 × 7.5 = 52.5 km. 105 km multiplies 7 by 15, as if each centimetre stood for 15 km, and 20 km adds 5 to both numbers because 7 is 5 more than 2 — but a scale multiplies, it does not add.
  4. a) 90 km in 1.5 hours — A rate compares two quantities measured in different units — here kilometres and hours — so it can be written as a unit rate, 60 km/h. The others compare things counted or measured in the same unit, cars to cars or cups to cups, which makes them ratios.
  5. c) 60 — 150% is all of the number (100%) plus half of it again (50%): 40 + 20 = 60, or 1.5 × 40. 6 treats 150% as 15%, and 20 is only the 50% part. A percent over 100% gives more than you started with.
  6. b) 3:7 — Girls to all students is part to whole: 12 girls out of 12 + 16 = 28 students, and 12:28 = 3:7 after dividing both terms by 4. 3:4 is girls to boys — part to part — and 4:7 compares the boys, not the girls, with the whole class.
  7. b) 0.005 — Percent means out of 100, so 0.5% = 0.5 ÷ 100 = 0.005 — half of 1%, which is 0.01. 0.5 is 50%, and 0.05 is 5%: the decimal point moved one place instead of two.
  8. a) $47.25 — 25% off $60 is $15, so the sale price is $45. GST is 5% of what you actually pay, 0.05 × $45 = $2.25, for a total of $47.25. $48.00 takes off 25% − 5% = 20% in one step, but the two percents are of different amounts, so they cannot be combined like that.
  9. b) 30 cm — An increase of 150% adds 150% of 12 cm, which is 1.5 × 12 = 18 cm, to the 12 cm it already had: 12 + 18 = 30 cm. 18 cm is the increase, not the new height — increased by 150% means it is now 250% of what it was.
  10. c) 48 km — 45 minutes is ¾ of an hour, so her rate is 18 ÷ ¾ = 24 km/h, and in 2 hours she goes 48 km. 80 km writes 45 minutes as 0.45 h — but an hour has 60 minutes, not 100 — and 36 km treats 45 minutes as a whole hour.