Grade 7 Math Practice Test: Unit Rates with Fractions and Complex Fractions
- Unit Rates with Fractions
- 10 questions
- 15 minutes
This test covers finding unit rates when both quantities are fractions, simplifying complex fractions and comparing rates. Tip: a unit rate "per 1" is the first quantity divided by the second, and dividing by a fraction means multiplying by its reciprocal.
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Question 1
Ella paints 23 of a wall in 12 hour. At this rate, how much of a wall does she paint per hour?
Correct answer: D
Divide the amount by the time: 2/3 ÷ 1/2 = 2/3 × 2 = 4/3 = 1 1/3 walls per hour. 1/3 multiplies the fractions instead of dividing, and 3/4 divides the time by the amount.
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Question 2
A recipe uses 34 cup of sugar for every 13 cup of butter. How many cups of sugar are used per cup of butter?
Correct answer: D
Sugar per cup of butter = 3/4 ÷ 1/3 = 3/4 × 3 = 9/4 = 2 1/4 cups. 4/9 is the butter per cup of sugar, the rate the wrong way around.
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Question 3
Omar walks 112 miles in 56 hour. What is his speed in miles per hour?
Correct answer: B
Speed = distance ÷ time = 3/2 ÷ 5/6 = 3/2 × 6/5 = 18/10 = 1 4/5 miles per hour. 1 1/4 multiplies the distance by the time.
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Question 4
A complex fraction has 25 in its numerator and 415 in its denominator. What is its value in simplest form?
Correct answer: C
A complex fraction means division: 2/5 ÷ 4/15 = 2/5 × 15/4 = 30/20 = 3/2. 8/75 multiplies the two fractions, and 2/3 is the reciprocal of the answer.
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Question 5
A car uses 212 gallons of gas to travel 85 miles. How many miles does it travel per gallon?
Correct answer: B
Miles per gallon = 85 ÷ 2.5 = 34. 42.5 divides by 2 and ignores the half gallon, and 212.5 multiplies instead of dividing.
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Question 6
A 12-ounce box of cereal costs $3.30. A 20-ounce box costs $5.20. Which is the better buy?
Correct answer: C
Unit prices: $3.30 ÷ 12 = $0.275 per ounce and $5.20 ÷ 20 = $0.26 per ounce. The 20-ounce box costs less per ounce, so it is the better buy even though its total price is higher.
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Question 7
Leo mows 38 of a lawn in 14 hour. At this rate, how long does it take him to mow the whole lawn?
Correct answer: A
Time per lawn = 1/4 ÷ 3/8 = 1/4 × 8/3 = 2/3 hour, and 2/3 of 60 minutes is 40 minutes. 1 hour 30 minutes is 3/8 ÷ 1/4 = 1 1/2, which is lawns per hour, not hours per lawn.
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Question 8
A printer uses 15 of an ink cartridge for every 112 packs of paper. How much of a cartridge does it use per pack of paper?
Correct answer: D
Cartridge per pack = 1/5 ÷ 3/2 = 1/5 × 2/3 = 2/15. 7 1/2 is packs per cartridge, the rate the wrong way around.
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Question 9
A faucet fills 234 gallons in 13 minute. How many gallons does it fill per minute?
Correct answer: C
2 3/4 ÷ 1/3 = 11/4 × 3 = 33/4 = 8 1/4 gallons per minute. 11/12 multiplies by 1/3 instead of dividing by it.
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Question 10
Ana jogs 23 mile in 16 hour. Ben jogs 34 mile in 15 hour. Who jogs faster, and at what speed?
Correct answer: A
Ana: 2/3 ÷ 1/6 = 4 miles per hour. Ben: 3/4 ÷ 1/5 = 15/4 = 3 3/4 miles per hour. Ben covers more distance, but he also takes more time, so Ana is faster.
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