4th Grade Multiplying a Fraction by a Whole Number Test Solutions and Scoring (PDF)

(a) Each shaded part is \(\frac{1}{6}\), and there are 5 of them.

(b) Five parts of \(\frac{1}{6}\) added together.

(a) \(5 \times \frac{1}{6}\) (b) \(\frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6}\)

Scoring: 1 point for each part.

(a) \(3 \times 1 = 3\), so \(\frac{3}{8}\).

(b) \(\frac{7}{5}\) = \(1\frac{2}{5}\).

(a) \(\frac{3}{8}\) (b) \(\frac{7}{5}\) = \(1\frac{2}{5}\)

Scoring: 1 point for each part.

\(4 \times 3 = 12\), so \(\frac{12}{5}\).

\(12 \div 5 = 2\) remainder 2.

\(\frac{12}{5}\) = \(2\frac{2}{5}\)

Scoring: 1 point for the fraction; 1 point for the mixed number.

There are 3 jumps and each jump is \(\frac{3}{4}\).

\(3 \times \frac{3}{4} = \frac{9}{4} = 2\frac{1}{4}\).

\(3 \times \frac{3}{4} = \frac{9}{4}\), or \(2\frac{1}{4}\)

Scoring: 1 point for the equation; 1 point for the product.

\(8 \times 5 = 40\), so \(\frac{40}{12}\).

\(40 \div 12 = 3\) remainder 4.

\(3\frac{4}{12}\)

Scoring: 1 point for \(\frac{40}{12}\); 1 point for the mixed number.

(a) \(4 \times \frac{5}{6} = \frac{20}{6}\).

(b) \(20 \div 6 = 3\) remainder 2, so \(3\frac{2}{6}\).

(c) \(3\frac{2}{6}\) is greater than 3.

(a) \(4 \times \frac{5}{6} = \frac{20}{6}\) (b) \(3\frac{2}{6}\) miles (c) yes

Scoring: 1 point for each part.

(a) \(6 \times \frac{3}{4} = \frac{18}{4}\).

(b) \(18 \div 4 = 4\) remainder 2, so \(4\frac{2}{4}\).

(c) \(5 = \frac{20}{4}\) and \(\frac{20}{4} – \frac{18}{4} = \frac{2}{4}\).

(a) \(6 \times \frac{3}{4} = \frac{18}{4}\) (b) \(4\frac{2}{4}\) cups (c) \(\frac{2}{4}\) cup

Scoring: 1 point for each part.

\(\frac{9}{4} = 9 \times \frac{1}{4}\) and \(\frac{9}{4} = 3 \times \frac{3}{4}\).

\(9 \times \frac{1}{4}\) and \(3 \times \frac{3}{4}\)

Scoring: 1 point for each correct product.

Diego multiplied the denominator by 3. The denominator names the size of the pieces, and it does not change. Only the number of pieces changes: \(3 \times 2 = 6\) fifths.

\(3 \times \frac{2}{5} = \frac{6}{5}\)

Scoring: 1 point for the explanation; 1 point for \(\frac{6}{5}\).