Grade 7 · Fractions & ratios

Ratio, rate, and proportion word problems practice

Ratio, rate, and proportion word problems is a grade 7 math skill aligned to Common Core standard 7.RP.A.2: recognize and represent proportional relationships between quantities. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 ratio, rate, and proportion word problems problems our math games drill.

CCSS 7.RP.A.210 questions in the bank
Sample questions

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Question 1easy

A passenger train traveled 348348 miles in 44 hours at a constant speed. What was the train's speed, in miles per hour?

Speed = distance ÷\div time: 3484=87\dfrac{348}{4} = 87 miles per hour.

Question 2easy

At an animal shelter, the ratio of cats to dogs is 55 to 88. If there are 3535 cats at the shelter, how many dogs are there?

Scale the ratio: 3535 cats is 77 groups of 55, so dogs = 7×8=567 \times 8 = 56.

Question 3easy

A cyclist rode 6363 kilometers in 1.51.5 hours at a constant speed. What was the cyclist's speed, in kilometers per hour?

Speed = 631.5=42\dfrac{63}{1.5} = 42 kilometers per hour.

Question 4easy

A paint mixture uses red and blue paint in a ratio of 44 to 77. How many ounces of blue paint are needed to mix with 3232 ounces of red paint?

Scale the ratio: 3232 oz red is 88 groups of 44, so blue paint = 8×7=568 \times 7 = 56 ounces.

Question 5medium

A recipe uses 33 cups of flour to make 1818 muffins. At this rate, how many cups of flour are needed to make 3030 muffins?

Set up a proportion: 318=x30\dfrac{3}{18} = \dfrac{x}{30}, so 18x=9018x = 90 and x=5x = 5 cups.

Question 6medium

A water tank held 12,50012{,}500 gallons of water. After leaking at a constant rate for 2525 minutes, the tank held 11,00011{,}000 gallons. How many gallons of water leaked from the tank each minute?

Water leaked: 12,50011,000=1,50012{,}500 - 11{,}000 = 1{,}500 gallons in 2525 minutes. Rate: 1,50025=60\dfrac{1{,}500}{25} = 60 gallons per minute.

Question 7medium

Five identical printing presses can complete a job in 1212 hours. Working at the same rate, how many hours would it take 88 of these presses to complete the same job?

Total work is fixed. Time with 88 presses: 5×128=608=7.5\dfrac{5 \times 12}{8} = \dfrac{60}{8} = 7.5 hours.

Question 8medium

On a map, 1.51.5 inches represents an actual distance of 3636 miles. At this scale, what is the actual distance, in miles, represented by 44 inches on the map?

Scale: 361.5=24\dfrac{36}{1.5} = 24 miles per inch. For 44 inches: 24×4=9624 \times 4 = 96 miles.

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