This answer key shows a full worked solution for each of the 10 dividing fractions problems, with the reciprocal step and the simplified result. Compare your work and the bold final answers, and check each quotient by multiplying.
Problem 1: Halves and fourths
Multiply by the reciprocal: \(\frac{1}{2} \times 4 = 2\).
Check: two fourths make one half.
2.
Problem 2: Whole number by a fraction
\(3 : \frac{1}{2} = 3 \times 2 = 6\).
Check: each whole has 2 halves, so 3 wholes have 6 halves.
6.
Problem 3: Fraction by a whole number
Dividing by 2 is multiplying by \(\frac{1}{2}\): \(\frac{4}{5} \times \frac{1}{2} = \frac{4}{10} = \frac{2}{5}\).
\(\frac{2}{5}\).
Problem 4: Fourths and eighths
\(\frac{7}{8} \times 4 = \frac{28}{8} = \frac{7}{2}\).
\(\frac{7}{2} = 3\frac{1}{2}\).
\(3\frac{1}{2}\).
Problem 5: Dividing two fractions
\(\frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4}\).
\(\frac{5}{4} = 1\frac{1}{4}\).
\(1\frac{1}{4}\).
Problem 6: Mixed number by a fraction
Change \(1\frac{1}{2}\) to \(\frac{3}{2}\).
\(\frac{3}{2} \times \frac{4}{3} = \frac{12}{6} = 2\).
2.
Problem 7: Two mixed numbers
Change both: \(2\frac{1}{4} = \frac{9}{4}\) and \(1\frac{1}{2} = \frac{3}{2}\).
\(\frac{9}{4} \times \frac{2}{3} = \frac{18}{12} = \frac{3}{2}\).
\(\frac{3}{2} = 1\frac{1}{2}\).
\(1\frac{1}{2}\).
Problem 8: Ribbon bows
Divide the ribbon by the length of one bow: \(4\frac{1}{2} : \frac{3}{4} = \frac{9}{2} \times \frac{4}{3} = \frac{36}{6} = 6\).
6 bows.
Problem 9: Sharing pizza
Divide the pizza by 4: \(\frac{2}{3} : 4 = \frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6}\).
\(\frac{1}{6}\) of the pizza.
Problem 10: Walking rate
(a) Speed = distance \(: \) time: \(3\frac{1}{2} : 1\frac{1}{4} = \frac{7}{2} \times \frac{4}{5} = \frac{28}{10} = \frac{14}{5} = 2\frac{4}{5}\) miles per hour.
(b) Time = distance \(: \) speed: \(7 : \frac{14}{5} = 7 \times \frac{5}{14} = \frac{35}{14} = \frac{5}{2} = 2\frac{1}{2}\) hours.
(a) \(2\frac{4}{5}\) mph. (b) \(2\frac{1}{2}\) hours.
See every chapter on the Grade 6 math page.