7th Grade Unit Rates with Fractions Quiz: 10 Questions with Explanations

A \(\frac{4}{15}\) mile per hourB \(\frac{3}{20}\) mile per hourC \(\frac{15}{16}\) mile per hourD \(3\frac{3}{4}\) miles per hour

Divide distance by time: \(\frac{3}{4} \div \frac{1}{5} = \frac{3}{4} \times 5 = \frac{15}{4}\). Dividing time by distance gives the flipped rate.

A \(\frac{3}{4} \div \frac{1}{3}\)B \(\frac{1}{3} \div \frac{3}{4}\)C \(\frac{3}{4} \times \frac{1}{3}\)D \(\frac{3}{4} – \frac{1}{3}\)

Cups go on top and batches on the bottom, so divide \(\frac{3}{4}\) by \(\frac{1}{3}\). The reversed division gives batches per cup.

A 16-ounce bottle at \(\$0.19\) per ounceB 24-ounce bottle at \(\$0.175\) per ounceC 24-ounce bottle at \(\$0.19\) per ounceD Both cost the same per ounce

\(3.04 \div 16 = 0.19\) and \(4.20 \div 24 = 0.175\). A lower unit price is the better buy.

A \(\$0.50\) per poundB \(\$7.50\) per poundC \(\$2\) per poundD \(\$12.50\) per pound

Divide \(5 \div 2\frac{1}{2} = 5 \div \frac{5}{2} = 2\). Multiplying 5 by \(2\frac{1}{2}\) is a common mistake.

A \(\frac{3}{16}\) footB \(1\frac{1}{3}\) feetC \(\frac{7}{8}\) footD \(\frac{3}{4}\) foot

Divide \(\frac{3}{8} \div \frac{1}{2} = \frac{3}{8} \times 2 = \frac{3}{4}\). Multiplying by \(\frac{1}{2}\) instead gives \(\frac{3}{16}\).

A 72 milesB 180 milesC 36 milesD 120 miles

The unit rate is \(24 \div \frac{2}{5} = 60\) miles per hour, and \(60 \times 3 = 180\). Tripling 24 ignores the \(\frac{2}{5}\) hour.

A 60 pages per minuteB \(2\frac{2}{5}\) pages per minuteC \(\frac{5}{12}\) page per minuteD \(\frac{1}{60}\) page per minute

Pages per minute is \(12 \div \frac{1}{5} = 60\). The value \(\frac{1}{60}\) is minutes per page.

A \(\frac{1}{2}\) mile in \(\frac{1}{6}\) hourB 2 miles in \(\frac{1}{2}\) hourC \(\frac{3}{4}\) mile in \(\frac{1}{6}\) hourD 1 mile in \(\frac{1}{4}\) hour

The speeds are 4.5, 3, 4, and 4 miles per hour. Compare unit rates, not distances alone.

A \(2\frac{1}{4}\) cupsB 1 cupC \(1\frac{5}{6}\) cupsD 3 cups

Divide \(\frac{3}{2} \div \frac{2}{3} = \frac{3}{2} \times \frac{3}{2} = \frac{9}{4} = 2\frac{1}{4}\). Multiplying \(\frac{3}{2} \times \frac{2}{3}\) gives 1.

A \(\frac{4}{3}\) minutesB \(\frac{3}{4}\) minuteC \(\frac{1}{3}\) minuteD \(1\frac{1}{3}\) minutes

The rate is \(\frac{2}{3} \div \frac{1}{2} = \frac{4}{3}\) buckets per minute, so one bucket takes the reciprocal, \(\frac{3}{4}\) minute.