7th Grade Unit Rates with Fractions Test Solutions and Scoring (PDF)

7th Grade math test solutions: Unit Rates with Fractions – Maths PDF

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This grade 7 unit rates test answers for 7th Grade covers unit rates with fractions (Common Core 7.RP.A.1), with a free PDF to print.

Use this answer key and scoring guide to grade the unit rates test. Each solution shows the full work, and the scoring note explains how the points are awarded. Give partial credit for correct steps even when the final answer is wrong.

Grade 7 · Common Core State Standards: 7.RP.A.1

Grade 7 unit rates test answers: worked solutions

Question 1 – Walking rate [2 pts]

$\frac{3}{4}\div\frac{1}{3}=\frac{3}{4}\times 3=\frac{9}{4}=2\frac{1}{4}$

$2\frac{1}{4}$ mph

Scoring: 1 point for setting up the division of miles by hours; 1 point for the correct unit rate with units.

Question 2 – Better price [2 pts]

A: $4.50\div 18=0.25$

B: $7.20\div 30=0.24$

Pack B ($0.24 per pencil)

Scoring: 1 point for both unit prices; 1 point for naming Pack B.

Question 3 – Double number line [2 pts]

Unit rate: $\frac{3}{2}\div\frac{1}{4}=\frac{3}{2}\times 4=6$, so 6 miles per hour.
$6\times 2\frac{1}{2}=15$, so 15 miles.

The speed is 6 miles per hour.

Scoring: 1 point for each part. Allow the table or double number line to be used instead of the multiplication.

Question 4 – Hours per page [2 pts]

$\frac{1}{2}\div\frac{2}{3}=\frac{1}{2}\times\frac{3}{2}=\frac{3}{4}$

$\frac{3}{4}$ hour per chapter

Scoring: 1 point for putting hours on top; 1 point for the correct answer with units.

Question 5 – Complex fraction [2 pts]

$\frac{5}{6}\div\frac{2}{3}=\frac{5}{6}\times\frac{3}{2}=\frac{15}{12}=\frac{5}{4}$

$\frac{5}{4}$; the recipe uses $1\frac{1}{4}$ cups of flour per batch

Scoring: 1 point for the correct quotient; 1 point for the meaning in context.

Question 6 – Complete the table [2 pts]

Unit rate: $6\div\frac{1}{2}=12$ dollars per hour.

For 2 1/2 hours: $12\times 2.5=30$.

Completed table.

$12 and $30

Scoring: 1 point for the unit rate; 1 point for both missing entries.

Question 7 – Compare speeds [2 pts]

Turtle: $\frac{3}{8}\times 4=\frac{3}{2}$ ft/min.

Lizard: $\frac{5}{12}\times 3=\frac{5}{4}$ ft/min.

$\frac{3}{2}-\frac{5}{4}=\frac{1}{4}$

The turtle, by $\frac{1}{4}$ foot per minute

Scoring: 1 point for both unit rates; 1 point for the faster animal and the difference.

Question 8 – Trip average [3 pts]

First part: $6\div\frac{1}{2}=12$ mph. Second part: $\frac{9}{2}\div\frac{3}{4}=\frac{9}{2}\times\frac{4}{3}=6$ mph.
Total distance $6+4\frac{1}{2}=10\frac{1}{2}$ miles; total time $\frac{1}{2}+\frac{3}{4}=1\frac{1}{4}$ hours; $\frac{21}{2}\div\frac{5}{4}=\frac{21}{2}\times\frac{4}{5}=\frac{42}{5}=8.4$ mph.

12 mph, 6 mph; average 8.4 mph

Scoring: 1 point for each part speed; 1 point for the average (total distance over total time). Averaging 12 and 6 to get 9 earns no point for the average.

Question 9 – Faucet [3 pts]

$\frac{1}{3}\div\frac{1}{4}=\frac{4}{3}=1\frac{1}{3}$ gallons per minute.
$\frac{4}{3}\times 6=8$ gallons.
$20\div\frac{4}{3}=20\times\frac{3}{4}=15$ minutes.

The unit rate is 4/3 gallons per minute.

$1\frac{1}{3}$ gal/min; 8 gallons; 15 minutes

Scoring: 1 point for each part. Accept the answer 1.33 gal/min only if the fraction is also shown.

Total score

Total

20 points

Key facts behind this grade 7 unit rates test answers

Key facts

A unit rate has 1 as its second quantity, such as 2 miles per 1 hour.
With fractions, write a complex fraction and divide: $a/b \div c/d = a/b \times d/c$.
Dividing by a fraction means multiplying by its reciprocal.
Compare rates by finding each unit rate: a lower unit price is the better buy, and a higher speed is faster.
Every rate has two unit rates, and they are reciprocals of each other.

How to use this grade 7 unit rates test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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