5th Grade Dividing Unit Fractions and Whole Numbers Test Solutions and Scoring (PDF)

1. \(\frac{1}{3}\div2=\frac{1}{6}\)
2. \(\frac{1}{5}\div3=\frac{1}{15}\)

Scoring: 1 point for each correct quotient.

1. \(4\div\frac{1}{3}=4\times3=12\)
2. \(7\div\frac{1}{2}=7\times2=14\)

Scoring: 1 point for each correct quotient.

One half is cut into 4 equal pieces, so the whole has \(2\times4=8\) pieces and each piece is \(\frac{1}{8}\).

\(\frac{1}{2}\div4=\frac{1}{8}\)

Scoring: 1 point for the equation \(\frac{1}{2}\div4\), 1 point for the quotient \(\frac{1}{8}\).

\(6\div\frac{1}{4}=6\times4=24\) and \(6\div\frac{1}{3}=6\times3=18\).

\(6\div\frac{1}{4}\) is greater (24 > 18).

Scoring: 1 point for each correct value; the comparison must match the values.

Work backward with multiplication: \(\frac{1}{15}\times3=\frac{3}{15}=\frac{1}{5}\).

Check: \(\frac{1}{5}\div3=\frac{1}{15}\).

\(\frac{1}{5}\)

Scoring: 1 point for the answer, 1 point for a correct check or explanation.

Each jump is \(\frac{1}{2}\). There are 2 jumps in each whole, so \(3\times2=6\) jumps.

\(3\div\frac{1}{2}=6\)

Scoring: 1 point for the equation, 1 point for the quotient 6.

\(\frac{1}{4}\div3=\frac{1}{12}\). Check: \(\frac{1}{12}\times3=\frac{1}{4}\).

\(\frac{1}{12}\) pound

Scoring: 1 point for dividing correctly, 1 point for the answer with the unit.

1. \(5\div\frac{1}{3}=5\times3=15\) servings
2. \(15-6=9\) servings
3. \(9\times\frac{1}{3}=3\) cups

Scoring: 1 point per part. In part (c), accept \(5-6\times\frac{1}{3}=3\) as correct.

1. \(\frac{1}{2}\div4=\frac{1}{8}\) gallon
2. \(2\div\frac{1}{8}=2\times8=16\) bottles
3. In (a) the juice is cut into smaller pieces, so each piece is less than \(\frac{1}{2}\). In (b) each bottle is a small part of a gallon, so many bottles fit and the count is greater than 2.

Scoring: 1 point per part. For part (c), award the point for any explanation that compares piece size with the number of pieces.