Testinar Grade 7 math

Unit Rates with Fractions

Students will build Grade 7 mastery of unit rates with fractions using models, equations, and test-style reasoning.

CH01-01 Ratios and Proportional Relationships

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A runner covers $\frac{3}{4}$ of a mile in $\frac{1}{6}$ of an hour. What is the runner's speed in miles per hour?
1. $\frac{1}{12}$ mph
2. $\frac{1}{8}$ mph
3. $\frac{3}{4}$ mph
4. $\frac{9}{2}$ mph
A cyclist travels $\frac{1}{2}$ mile in $\frac{1}{8}$ hour. What is the cyclist's speed in miles per hour?
1. 8 mph
2. $\frac{1}{16}$ mph
3. $\frac{3}{8}$ mph
4. 4 mph
A store sells $\frac{3}{5}$ pound of cheese for $6. What is the unit price per pound?
1. $9
2. $3.60
3. $4
4. $10
A painter completes $\frac{2}{3}$ of a room in $\frac{1}{5}$ hour. At this rate, how many rooms will the painter complete in 1 hour?
1. $\frac{2}{15}$ room
2. $\frac{3}{5}$ room
3. 1 room
4. $\frac{10}{3}$ rooms
A train travels $3\frac{1}{2}$ miles in $\frac{1}{4}$ hour. What is the train's speed in miles per hour?
1. $\frac{7}{8}$ mph
2. $\frac{1}{14}$ mph
3. 7 mph
4. 14 mph
The table shows the relationship between pages read and time. Find the unit rate in pages per hour.
1. $\frac{1}{12}$ pages per hour
2. $\frac{1}{3}$ pages per hour
3. 6 pages per hour
4. 3 pages per hour
Runner A covers $\frac{1}{3}$ mile in $\frac{1}{20}$ hour. Runner B covers $\frac{2}{5}$ mile in $\frac{1}{12}$ hour. Which runner is faster?
1. Runner A at $\frac{1}{60}$ mph
2. Runner B at $\frac{24}{5}$ mph
3. They run at the same speed
4. Runner A at $\frac{20}{3}$ mph
Five erasers cost $\frac{3}{4}$ dollar. What is the cost per eraser?
1. $1.25
2. $0.60
3. $3.75
4. $0.15

Teacher and parent reference

Answer key and explanations

D. $\frac{9}{2}$ mph
Unit rate $=\frac{3/4}{1/6}=\frac{3}{4}\times 6=\frac{18}{4}=\frac{9}{2}=4.5$ mph.
D. 4 mph
Unit rate $=\frac{1/2}{1/8}=\frac{1}{2}\times 8=4$ mph.
D. $10
Unit rate $=\frac{6}{3/5}=6\times\frac{5}{3}=10$ dollars per pound.
D. $\frac{10}{3}$ rooms
Unit rate $=\frac{2/3}{1/5}=\frac{2}{3}\times 5=\frac{10}{3}$ rooms per hour.
D. 14 mph
Convert $3\frac{1}{2}=\frac{7}{2}$. Unit rate $=\frac{7/2}{1/4}=\frac{7}{2}\times 4=14$ mph.
D. 3 pages per hour
From the table, $\frac{1}{2}$ page in $\frac{1}{6}$ hour gives unit rate $\frac{1/2}{1/6}=\frac{1}{2}\times 6=3$ pages per hour.
D. Runner A at $\frac{20}{3}$ mph
Runner A: $\frac{1/3}{1/20}=\frac{1}{3}\times 20=\frac{20}{3}$ mph. Runner B: $\frac{2/5}{1/12}=\frac{2}{5}\times 12=\frac{24}{5}=4.8$ mph. Runner A is faster.
D. $0.15
Unit rate $=\frac{3/4}{5}=\frac{3}{4}\times\frac{1}{5}=\frac{3}{20}=0.15$ dollars per eraser.