This grade 7 unit worksheet answer key solves all 20 problems of the unit rates with fractions worksheet step by step.
Every one of the twenty solutions below shows the division, the multiplication by the reciprocal, and the final unit rate with its units. Check each answer by multiplying the unit rate by the second quantity, and compare your steps with the ones shown here.
Grade 7 Unit Worksheet Answer Key: problems 1–5
Problem 1: Basic complex fraction
\(\frac{1}{2}: \frac{1}{4}=\frac{1}{2}\times 4=2\)
Check: \(2\times \frac{1}{4}=\frac{1}{2}\). 2 miles per hour
Problem 2: Snail speed
\(\frac{1}{4}: \frac{1}{2}=\frac{1}{4}\times 2=\frac{2}{4}=\frac{1}{2}\)
Check: \(\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}\). \(\frac{1}{2}\) foot per minute
Problem 3: Chapters per hour
\(\frac{2}{3}: \frac{1}{6}=\frac{2}{3}\times 6=\frac{12}{3}=4\)
Check: \(4\times \frac{1}{6}=\frac{2}{3}\). 4 chapters per hour
Problem 4: Pages per minute
\(\frac{3}{4}: \frac{1}{8}=\frac{3}{4}\times 8=\frac{24}{4}=6\)
Check: \(6\times \frac{1}{8}=\frac{6}{8}=\frac{3}{4}\). 6 pages per minute
Problem 5: Buckets per minute
\(\frac{3}{4}: \frac{1}{2}=\frac{3}{4}\times 2=\frac{6}{4}=\frac{3}{2}\)
\(1\frac{1}{2}\) buckets per minute
Grade 7 Unit Worksheet Answer Key: problems 6–10
Problem 6: Price of grapes
\(\$4.50: \frac{5}{6}=\$4.50\times \frac{6}{5}=\$5.40\)
Check: each sixth of a pound costs \(\$4.50: 5=\$0.90\), and \(6\times \$0.90=\$5.40\). $5.40 per pound
Problem 7: Bike speed
\(\frac{3}{4}: \frac{1}{6}=\frac{3}{4}\times 6=\frac{18}{4}=\frac{9}{2}\)
\(4\frac{1}{2}\) miles per hour
Problem 8: Cups of sugar
\(\frac{5}{6}: \frac{2}{3}=\frac{5}{6}\times \frac{3}{2}=\frac{15}{12}=\frac{5}{4}\)
Check: \(\frac{5}{4}\times \frac{2}{3}=\frac{10}{12}=\frac{5}{6}\). \(1\frac{1}{4}\) cups per batch
Problem 9: Cost per pound
\(\$3.75: \frac{1}{2}=\$3.75\times 2=\$7.50\)
Check: half of $7.50 is $3.75. $7.50 per pound
Problem 10: Sealant coverage
\(\frac{5}{6}: \frac{1}{3}=\frac{5}{6}\times 3=\frac{15}{6}=\frac{5}{2}\)
Check: \(\frac{5}{2}\times \frac{1}{3}=\frac{5}{6}\). \(2\frac{1}{2}\) square yards per gallon
Grade 7 Unit Worksheet Answer Key: problems 11–15
Problem 11: Different units
10 minutes is \(\frac{10}{60}=\frac{1}{6}\) hour.
\(\frac{1}{2}: \frac{1}{6}=\frac{1}{2}\times 6=3\)
3 miles per hour
Problem 12: Walk in minutes
20 minutes is \(\frac{20}{60}=\frac{1}{3}\) hour.
\(\frac{5}{6}: \frac{1}{3}=\frac{5}{6}\times 3=\frac{15}{6}=\frac{5}{2}\)
Check: \(\frac{5}{2}\times \frac{1}{3}=\frac{5}{6}\). \(2\frac{1}{2}\) miles per hour
Problem 13: Painting area
\(\frac{2}{3}: \frac{1}{6}=\frac{2}{3}\times 6=4\)
Check: \(4\times \frac{1}{6}=\frac{2}{3}\). 4 square yards per quart
Problem 14: Better buy
Store A: \(\$8.00: \frac{2}{3}=\$8.00\times \frac{3}{2}=\$12.00\) per pound.
Store B: \(\$8.25: \frac{3}{4}=\$8.25\times \frac{4}{3}=\$11.00\) per pound.
Difference: \(\$12.00-\$11.00=\$1.00\).
Store B is cheaper, by $1.00 per pound.
Problem 15: Faster plant
First plant: \(\frac{3}{8}: \frac{1}{4}=\frac{3}{8}\times 4=\frac{3}{2}\) inches per week.
Second plant: \(\frac{5}{6}: \frac{1}{2}=\frac{5}{6}\times 2=\frac{5}{3}\) inches per week.
Common denominator 6: \(\frac{5}{3}=\frac{10}{6}\) and \(\frac{3}{2}=\frac{9}{6}\), so \(\frac{10}{6}-\frac{9}{6}=\frac{1}{6}\).
The neighbor’s bamboo grows faster, by \(\frac{1}{6}\) inch per week.
Grade 7 Unit Worksheet Answer Key: problems 16–20
Problem 16: Garden hose
(a) \(1\frac{1}{2}=\frac{3}{2}\), so \(\frac{3}{2}: \frac{2}{5}=\frac{3}{2}\times \frac{5}{2}=\frac{15}{4}\). \(3\frac{3}{4}\) gallons per minute
(b) \(\frac{15}{4}\times 8=30\). 30 gallons
Problem 17: Gas mileage
(a) \(7\frac{1}{2}=\frac{15}{2}\), so \(\frac{15}{2}: \frac{1}{4}=\frac{15}{2}\times 4=30\). 30 miles per gallon
(b) \(30\times 12=360\). 360 miles
Problem 18: Book club
(a) \(\frac{3}{4}: \frac{1}{2}=\frac{3}{4}\times 2=\frac{3}{2}\). \(1\frac{1}{2}\) chapters per hour
(b) \(12: \frac{3}{2}=12\times \frac{2}{3}=8\). Check: \(\frac{3}{2}\times 8=12\). 8 hours
Problem 19: Muffin batches
(a) \(\frac{3}{4}: \frac{1}{2}=\frac{3}{4}\times 2=\frac{3}{2}\). \(1\frac{1}{2}\) cups per batch
(b) \(\frac{3}{2}\times 2\frac{1}{2}=\frac{3}{2}\times \frac{5}{2}=\frac{15}{4}\). \(3\frac{3}{4}\) cups of oil
Problem 20: Scooter battery
(a) \(3\frac{3}{4}=\frac{15}{4}\), so \(\frac{15}{4}: \frac{1}{5}=\frac{15}{4}\times 5=\frac{75}{4}\). \(18\frac{3}{4}\) miles
(b) \(\frac{3}{5}\times \frac{75}{4}=\frac{225}{20}=\frac{45}{4}\). Check: three cells of \(3\frac{3}{4}\) miles give \(3\times \frac{15}{4}=\frac{45}{4}\). \(11\frac{1}{4}\) miles
How to use this grade 7 unit worksheet answer key
Read this grade 7 unit worksheet answer key after trying each problem yourself, and redo any problem you missed.
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Grade 7 Unit Rates with Fractions worksheet answer key
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