7th Grade Unit Rates with Fractions Worksheet Solutions (PDF)

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

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This grade 7 unit rates 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 to check your work on the unit rates worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.

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

Grade 7 unit rates answers: exercises 1 to 10

Exercise 1 – Words per minute

Divide words by minutes: $180\div 3=60$

60 words per minute

Exercise 2 – Walking speed

Divide distance by time: $\frac{3}{8} \div \frac{1}{6} = \frac{3}{8} \times 6 = \frac{18}{8} = \frac{9}{4}$.

$2\frac{1}{4}$ miles per hour

One hour matches 2 1/4 miles.

Exercise 3 – Sugar per batch

$6 \div \frac{2}{3} = 6 \times \frac{3}{2} = 9$.

$9 per yard

Exercise 4 – Hourly pay

$27 \div 1\frac{1}{2} = 27 \div \frac{3}{2} = 27 \times \frac{2}{3} = 18$.

$18 per hour

Exercise 5 – Cycling speed

Change the mixed number: $2\frac{1}{2}=\frac{5}{2}$

$\frac{5}{2}\div\frac{1}{4}=\frac{5}{2}\times 4=10$

10 miles per hour

Exercise 6 – Painting rate

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

$\frac{2}{3}$ of a wall per hour

Exercise 7 – Complex fraction

Complex fraction: $(\frac{7}{8} in) / (\frac{1}{4} day)$ means $\frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times 4 = \frac{7}{2}$.

$3\frac{1}{2}$ inches per day

Exercise 8 – Cereal price

$4.20\div 12=0.35$

$0.35 per ounce

Exercise 9 – Garden hose

$3\frac{1}{2}=\frac{7}{2}$ and $1\frac{3}{4}=\frac{7}{4}$

$\frac{7}{2}\div\frac{7}{4}=\frac{7}{2}\times\frac{4}{7}=2$

2 gallons per minute

Exercise 10 – Better buy

Store A: $7.50\div 5=1.50$

Store B: $11.60\div 8=1.45$

Store B, at $1.45 per pound

Store B has the lower unit price.

Exercises 11 and up

Exercise 11 – Distance walked

Distance = rate $\times$ time

$\frac{7}{2}\times\frac{9}{4}=\frac{63}{8}=7\frac{7}{8}$

$7\frac{7}{8}$ miles

Exercise 12 – Snail speed

$\frac{7}{10} \div \frac{1}{5} = \frac{7}{10} \times 5 = \frac{7}{2}$.

$3\frac{1}{2}$ feet per minute

In 1 minute the caterpillar climbs 3 1/2 feet.

Exercise 13 – Flipped unit rate

Hours on top: $\frac{1}{3} \div \frac{4}{5} = \frac{1}{3} \times \frac{5}{4} = \frac{5}{12}$.

$\frac{5}{12}$ hour per panel

Exercise 14 – Complete the table

Unit rate: $3\div\frac{1}{4}=12$ miles per hour.

Time $\frac{1}{2}$: $12\times\frac{1}{2}=6$. Time 1: 12. Time $3\frac{1}{2}$: $12\times 3.5=42$.

Completed table.

6, 12, and 42 miles; unit rate 12 miles per hour

Exercise 15 – Who is faster?

Noah: $\frac{3}{4}\times 12=9$ miles per hour.

Aisha: $\frac{2}{3}\times 10=\frac{20}{3}=6\frac{2}{3}$ miles per hour.

Since $9>6\frac{2}{3}$, Noah is faster.

Noah, 9 mph versus $6\frac{2}{3}$ mph

Exercise 16 – Road trip average

Total distance: $45+60=105$ miles.

Total time: $\frac{3}{4}+1\frac{1}{4}=2$ hours.

$105\div 2=52.5$

52.5 miles per hour

Exercise 17 – Filling a pool

Rate: $\frac{3}{5}\div\frac{1}{2}=\frac{6}{5}$ pool per hour.

Time for 1 pool: $1\div\frac{6}{5}=\frac{5}{6}$ hour.

$\frac{5}{6}\times 60=50$

50 minutes

Exercise 18 – Fence painters

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

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

They paint at the same rate, $\frac{1}{2}$ of a fence per hour

Both rates are equal.

Exercise 19 – Gas mileage

Miles per gallon: $130.5\div 4.5=29$.

Gallons for the trip: $348\div 29=12$.

29 miles per gallon; 12 gallons

Exercise 20 – Juice sizes

$2.08\div 16=0.13$, $2.88\div 24=0.12$, $4.16\div 32=0.13$ dollars per ounce.

Best: 24 ounces at $0.12. Worst: $0.13.

$96\times 0.13=12.48$ and $96\times 0.12=11.52$; $12.48-11.52=0.96$

The 24-ounce size is best; savings $0.96

Key facts behind this grade 7 unit rates 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 answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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