Dividing Fractions: Grade 6 Math Test Answer Key – PDF Download

Question 1: Dividing by a fraction (2 points)

(a) \(\frac{3}{5} \times 10 = \frac{30}{5} = 6\).

(b) \(4 \times \frac{3}{2} = \frac{12}{2} = 6\).

(a) 6. (b) 6.

Scoring: 1 point for each correct answer.

Question 2: Fraction quotients (2 points)

(a) \(\frac{7}{8} \times \frac{4}{7} = \frac{28}{56} = \frac{1}{2}\).

(b) \(\frac{3}{10} \times \frac{1}{3} = \frac{3}{30} = \frac{1}{10}\).

(a) \(\frac{1}{2}\). (b) \(\frac{1}{10}\).

Scoring: 1 point for each correct answer in simplest form.

Question 3: Mixed number quotients (2 points)

(a) \(\frac{5}{2} \times \frac{6}{5} = \frac{30}{10} = 3\).

(b) \(\frac{7}{4} \times \frac{3}{7} = \frac{21}{28} = \frac{3}{4}\).

(a) 3. (b) \(\frac{3}{4}\).

Scoring: 1 point for each correct answer. Award the point only if mixed numbers were converted correctly.

Question 4: Hair bows (3 points)

Divide the ribbon by the amount per bow: \(3\frac{3}{4} : \frac{5}{8} = \frac{15}{4} \times \frac{8}{5} = \frac{120}{20} = 6\).

Check: \(6 \times \frac{5}{8} = \frac{30}{8} = 3\frac{3}{4}\).

6 bows.

Scoring: 1 point for writing the division, 1 point for a correct multiplication by the reciprocal, 1 point for 6 bows.

Question 5: Juice and lemonade (3 points)

(a) \(\frac{2}{3} : \frac{1}{6} = \frac{2}{3} \times 6 = \frac{12}{3} = 4\) bottles.

(b) \(\frac{1}{2} : 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}\) gallon.

(a) 4 bottles. (b) \(\frac{1}{6}\) gallon in each pitcher.

Scoring: (a) 1 point for the correct setup or reciprocal, 1 point for 4. (b) 1 point for \(\frac{1}{6}\).

Question 6: Running pace (3 points)

(a) Speed = distance \(: \) time: \(1\frac{1}{2} : \frac{3}{4} = \frac{3}{2} \times \frac{4}{3} = \frac{12}{6} = 2\) miles per hour.

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

(a) 2 mph. (b) 5 miles.

Scoring: (a) 1 point for converting and multiplying by the reciprocal, 1 point for 2. (b) 1 point for 5; accept follow-through from part (a).

Question 7: Checking a quotient (3 points)

(a) Liam multiplied by 2 instead of dividing, or flipped the whole number. Dividing by 2 means finding half: \(\frac{1}{3} : 2 = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}\).

(b) Check: \(\frac{1}{6} \times 2 = \frac{2}{6} = \frac{1}{3}\), which matches the start.

(a) The correct quotient is \(\frac{1}{6}\). (b) \(\frac{1}{6} \times 2 = \frac{1}{3}\).

Scoring: (a) 1 point for explaining the mistake, 1 point for \(\frac{1}{6}\). (b) 1 point for a correct multiplication check.

Question 8: Garden length (2 points)

Length = area \(: \) width: \(\frac{3}{4} : \frac{1}{2} = \frac{3}{4} \times 2 = \frac{6}{4} = \frac{3}{2} = 1\frac{1}{2}\).

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

\(1\frac{1}{2}\) yards.

Scoring: 1 point for dividing area by width, 1 point for \(1\frac{1}{2}\) yards.

See every chapter on the Grade 6 math page.