Unit Rates with Fractions: Grade 7 Math Test Answer Key – PDF Download

Question 1: Bike trip (2 points)

\(\frac{3}{4}: \frac{1}{8}=\frac{3}{4}\times 8=6\). 6 miles per hour

Scoring: 1 point for dividing the distance by the time; 1 point for the correct answer with units.

Question 2: Water flow (2 points)

\(\frac{5}{6}: \frac{1}{3}=\frac{5}{6}\times 3=\frac{15}{6}=\frac{5}{2}\). \(2\frac{1}{2}\) gallons per minute

Scoring: 1 point for multiplying by the reciprocal; 1 point for the simplified answer.

Question 3: Almond price (2 points)

\(\$6.00: \frac{3}{4}=\$6.00\times \frac{4}{3}=\$8.00\). $8.00 per pound

Scoring: 1 point for the correct setup; 1 point for the correct answer with units.

Question 4: Minutes and hours (2 points)

15 minutes is \(\frac{1}{4}\) hour. \(\frac{3}{4}: \frac{1}{4}=3\). 3 miles per hour

Scoring: 1 point for converting 15 minutes to \(\frac{1}{4}\) hour; 1 point for the correct answer.

Question 5: Poster paint (2 points)

\(\frac{5}{8}: \frac{1}{4}=\frac{5}{8}\times 4=\frac{20}{8}=\frac{5}{2}\). \(2\frac{1}{2}\) square feet per hour

Scoring: 1 point for the division; 1 point for the simplified answer with units.

Question 6: Cyclist comparison (2 points)

A: \(\frac{2}{3}: \frac{1}{6}=4\) mph. B: \(\frac{3}{4}: \frac{1}{5}=\frac{3}{4}\times 5=\frac{15}{4}=3\frac{3}{4}\) mph.

\(4-3\frac{3}{4}=\frac{1}{4}\). Cyclist A is faster, by \(\frac{1}{4}\) mile per hour.

Scoring: 1 point for both correct rates; 1 point for naming the faster cyclist with the correct difference.

Question 7: Find the error (2 points)

Liam multiplied instead of dividing. The correct unit rate is \(\frac{1}{3}: \frac{1}{6}=\frac{1}{3}\times 6=2\). 2 miles per hour

Scoring: 1 point for the correct rate of 2 mph; 1 point for explaining that the distance must be divided by the time.

Question 8: Muffin recipe (2 points)

(a) \(\frac{3}{4}: \frac{1}{2}=\frac{3}{2}\). \(1\frac{1}{2}\) cups per batch

(b) \(\frac{3}{2}\times 3=\frac{9}{2}\). \(4\frac{1}{2}\) cups

Scoring: 1 point for each part.

Question 9: Hiking (2 points)

(a) \(1\frac{1}{2}=\frac{3}{2}\), so \(\frac{3}{2}: \frac{3}{4}=\frac{3}{2}\times \frac{4}{3}=2\). 2 miles per hour

(b) \(2\times 2\frac{1}{2}=5\). 5 miles

Scoring: 1 point for each part.

Question 10: Filling a tank (2 points)

(a) \(\frac{1}{2}: \frac{3}{4}=\frac{1}{2}\times \frac{4}{3}=\frac{2}{3}\). \(\frac{2}{3}\) of the tank per minute

(b) \(1: \frac{2}{3}=\frac{3}{2}\). \(1\frac{1}{2}\) minutes

Scoring: 1 point for each part.

⬇ Download the Grade 7 Unit Rates with Fractions test answer key (PDF, 89 KB)

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