5th Grade Fractions as Division Test Solutions and Scoring (PDF)

(a) \(5 \div 8 = \frac{5}{8}\): \(\frac{5}{8}\).

(b) \(3 \div 7\).

Scoring: 1 point for each correct answer. In (b), the numerator must come first.

(a) \(11 \div 4 = \frac{11}{4} = 2\frac{3}{4}\): \(2\frac{3}{4}\).

(b) \(19 \div 6 = \frac{19}{6} = 3\frac{1}{6}\): \(3\frac{1}{6}\).

Scoring: 1 point for each correct mixed number.

(a) \(3 \div 4\).

(b) \(3 \div 4 = \frac{3}{4}\): each friend gets \(\frac{3}{4}\) of a bar.

Scoring: 1 point for the sentence; 1 point for the fraction.

\(9 \div 4 = \frac{9}{4} = 2\frac{1}{4}\). \(14 \div 6 = \frac{14}{6} = 2\frac{2}{6} = 2\frac{1}{3}\).

Since \(\frac{1}{3} > \frac{1}{4}\), \(14 \div 6\) is greater.

Scoring: 1 point for writing both quotients as mixed numbers; 1 point for the correct comparison.

(a) P is 13 fourths from 0: \(\frac{13}{4}\).

(b) \(13 \div 4 = 3 \text{ R } 1\): \(3\frac{1}{4}\).

(c) \(13 \div 4\).

Scoring: 1 point for each part.

(a) \(10 \div 4\).

(b) \(\frac{10}{4} = 2\frac{2}{4} = 2\frac{1}{2}\): each player gets \(2\frac{1}{2}\) oranges.

Scoring: (a) 1 point. (b) 1 point for 2 2/4 (or 10/4), 1 point for simplest form.

(a) \(15 \div 6 = \frac{15}{6} = 2\frac{3}{6} = 2\frac{1}{2}\): \(2\frac{1}{2}\) feet.

(b) Yes. \(2\frac{1}{2}\) is greater than 2, or because \(6 \times 2 = 12\) feet is less than 15 feet.

Scoring: (a) 1 point for 15/6 or 2 3/6, 1 point for simplest form. (b) 1 point for a correct explanation.

(a) \(9 \div 4 = \frac{9}{4} = 2\frac{1}{4}\): \(2\frac{1}{4}\) pounds.

(b) \(2\frac{1}{2} = 2\frac{2}{4}\) is greater than \(2\frac{1}{4}\), so the single bag is heavier.

Scoring: (a) 1 point for 2 1/4 (write the final answer as a mixed number). (b) 1 point for the correct comparison with a reason.

Priya switched the numbers. The number being divided (4) is the numerator and the number divided by (9) is the denominator. \(4 \div 9 = \frac{4}{9}\).

Scoring: 1 point for the correct fraction with a valid explanation.