4th Grade Adding and Subtracting Fractions and Mixed Numbers Test Solutions and Scoring (PDF)

(a) \(3 + 6 = 9\). (b) \(11 – 4 = 7\).

(a) \(\frac{9}{10}\) (b) \(\frac{7}{12}\)

Scoring: 1 point for each correct answer; 0 points if the denominator is added.

Split 7 into 3 + 4 and 5 + 2.

\(\frac{7}{8} = \frac{3}{8} + \frac{4}{8}\) and \(\frac{7}{8} = \frac{5}{8} + \frac{2}{8}\) (other correct splits are accepted)

Scoring: 1 point for each correct decomposition.

2 whole strips and 3 fifths: \(2\frac{3}{5}\).

\(2 = \frac{10}{5}\), and \(\frac{10}{5} + \frac{3}{5} = \frac{13}{5}\).

\(2\frac{3}{5}\) = \(\frac{13}{5}\)

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

(a) \(17 \div 6 = 2\) remainder 5, so \(2\frac{5}{6}\).

(b) \(3 = \frac{6}{2}\), and \(\frac{6}{2} + \frac{1}{2} = \frac{7}{2}\).

(a) \(2\frac{5}{6}\) (b) \(\frac{7}{2}\)

Scoring: 1 point for each part.

Wholes: \(2 + 3 = 5\). Fractions: \(\frac{5}{8} + \frac{6}{8} = \frac{11}{8} = 1\frac{3}{8}\).

\(5 + 1\frac{3}{8} = 6\frac{3}{8}\).

\(6\frac{3}{8}\)

Scoring: 1 point for adding the wholes and the fractions; 1 point for regrouping to the correct answer.

\(6\frac{2}{5} = \frac{32}{5}\) and \(3\frac{4}{5} = \frac{19}{5}\).

\(\frac{32}{5} – \frac{19}{5} = \frac{13}{5} = 2\frac{3}{5}\).

\(2\frac{3}{5}\)

Scoring: 1 point for converting correctly; 1 point for the correct answer.

(a) \(5\frac{2}{10} = \frac{52}{10}\) and \(2\frac{7}{10} = \frac{27}{10}\). \(\frac{52}{10} – \frac{27}{10} = \frac{25}{10} = 2\frac{5}{10}\).

(b) \(2\frac{5}{10} = \frac{25}{10}\) and \(1\frac{8}{10} = \frac{18}{10}\). \(\frac{25}{10} – \frac{18}{10} = \frac{7}{10}\).

(a) \(2\frac{5}{10}\) miles (b) \(\frac{7}{10}\) mile

Scoring: (a) 1 point for the method, 1 point for the answer; (b) 1 point.

(a) Wholes \(1 + 2 = 3\), fractions \(\frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1\frac{1}{4}\), so \(4\frac{1}{4}\).

(b) \(4\frac{1}{4} + \frac{3}{4} = 4\frac{4}{4} = 5\).

(c) \(6 – 5 = 1\).

(a) \(4\frac{1}{4}\) lb (b) 5 lb (c) 1 lb

Scoring: 1 point for each part.

Mia added the denominators. The size of the parts (fifths) does not change when you add. Two fifths plus two fifths is four fifths.

\(\frac{2}{5} + \frac{2}{5} = \frac{4}{5}\)

Scoring: 1 point for the explanation; 1 point for the correct sum.