4th Grade Comparing Fractions Test Solutions and Scoring (PDF)

(a) Same denominator, 5 is more than 3. (b) Same numerator, sixths are smaller than fourths.

(a) \(\frac{5}{8} > \frac{3}{8}\) (b) \(\frac{2}{6} < \frac{2}{4}\)

Scoring: 1 point for each correct symbol.

(a) \(\frac{3}{4} = \frac{9}{12}\) and \(\frac{2}{3} = \frac{8}{12}\). (b) \(\frac{4}{8} = \frac{1}{2}\).

(a) \(\frac{3}{4} > \frac{2}{3}\) (b) \(\frac{1}{2} = \frac{4}{8}\)

Scoring: 1 point for each correct symbol.

(a) Half of 10 is 5, and 4 is less than 5. (b) Half of 6 is 3, and 5 is more than 3.

(a) \(\frac{4}{10} < \frac{1}{2}\) (b) \(\frac{5}{6} > \frac{1}{2}\)

Scoring: 1 point for each correct symbol.

\(\frac{3}{5} = \frac{6}{10}\), and 6 tenths is less than 7 tenths.

\(\frac{3}{5} < \frac{7}{10}\)

Scoring: 1 point for writing \(\frac{3}{5}\) as \(\frac{6}{10}\); 1 point for the correct comparison.

Use sixths: \(\frac{5}{6}\), \(\frac{2}{6}\), \(\frac{3}{6}\), \(\frac{4}{6}\). Order the numerators: 2, 3, 4, 5.

\(\frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{5}{6}\)

Scoring: 2 points for the correct order; 1 point if only two fractions are swapped.

(a) A is at 3 eighths. (b) B is at 6 eighths (the same as \(\frac{3}{4}\)). (c) 3 eighths is less than 6 eighths.

(a) \(\frac{3}{8}\) (b) \(\frac{6}{8}\) (c) \(\frac{3}{8} < \frac{6}{8}\)

Scoring: 1 point for each part.

The numerators are the same. Thirds are smaller pieces than halves, so \(\frac{1}{3}\) is less than \(\frac{1}{2}\).

Ethan is not correct. \(\frac{1}{3} < \frac{1}{2}\)

Scoring: 1 point for saying he is not correct; 1 point for a reason about the size of the pieces.

Use twelfths: \(\frac{5}{6}\) = \(\frac{10}{12}\), \(\frac{3}{4}\) = \(\frac{9}{12}\), \(\frac{2}{3}\) = \(\frac{8}{12}\).

(a) Maya (b) \(\frac{2}{3} < \frac{3}{4} < \frac{5}{6}\)

Scoring: (a) 1 point; (b) 2 points for the correct order, 1 point for one pair in the wrong order.

Use 24: \(\frac{3}{8} = \frac{9}{24}\) and \(\frac{5}{12} = \frac{10}{24}\).

Bottle B has more water, because \(\frac{5}{12} > \frac{3}{8}\)

Scoring: 1 point for common denominator work; 1 point for the correct bottle.