6th Grade Dividing Fractions by Fractions Test Solutions and Scoring (PDF)

\(\frac{5}{6} \div \frac{1}{12} = \frac{5}{6} \times 12 = 10\)

Ten twelfths fill five sixths.

Scoring: 1 point for the method (model or reciprocal); 1 point for 10.

\(4 \div \frac{2}{3} = 4 \times \frac{3}{2} = 6\)

\(6\)

Scoring: 1 point for multiplying by the reciprocal; 1 point for 6.

\(\frac{5}{8} \div \frac{3}{4} = \frac{5}{8} \times \frac{4}{3} = \frac{5}{6}\)

\(\frac{5}{6}\)

Scoring: 1 point for the reciprocal step; 1 point for 5/6.

\(\frac{3}{5} \div 6 = \frac{3}{5} \times \frac{1}{6} = \frac{1}{10}\)

\(\frac{1}{10}\)

Scoring: 1 point for the setup; 1 point for 1/10.

\(1\frac{3}{4} \div \frac{1}{2} = \frac{7}{4} \div \frac{1}{2} = \frac{7}{4} \times 2 = \frac{7}{2} = 3\frac{1}{2}\)

\(\frac{7}{2} = 3\frac{1}{2}\)

Scoring: 1 point for converting to improper fractions; 1 point for 7/2 or 3 1/2.

\(\frac{5}{2} \div \frac{1}{2} = \frac{5}{2} \times 2 = 5\)

She can make 5 loaves.

Scoring: 1 point for the division; 1 point for 5 loaves.

\(\frac{5}{6} \div \frac{5}{3} = \frac{5}{6} \times \frac{3}{5} = \frac{1}{2}\)

The width is 1/2 meter.

Scoring: 1 point for dividing area by length; 1 point for 1/2 m.

Friends: \(\frac{3}{4} \div \frac{1}{8} = \frac{3}{4} \times 8 = 6\).

Equal shares: \(\frac{3}{4} \div 3 = \frac{3}{4} \times \frac{1}{3} = \frac{1}{4}\).

6 friends; each of 3 friends gets 1/4.

Scoring: 1 point for each quotient with a correct method; 1 point for a clear final statement.

Speed: \(\frac{3}{4} \div \frac{1}{4} = 3\) miles per hour.

Time: \(\frac{9}{2} \div 3 = \frac{9}{2} \times \frac{1}{3} = \frac{3}{2} = 1\frac{1}{2}\) hours.

Scoring: 1 point for the speed; 1 point for the time setup; 1 point for 1 1/2 hours.