Fractions: division and multi-step stories

Advanced Math 6 · Unit 2 · fraction-operations-6 · Teacher edition

fraction-operations-6

Name ______________________________Date ______________

1.
$\dfrac{1}{2} \div \dfrac{1}{8} = \ ?$
1. (A)
  $\dfrac{1}{16}$
2. (B)
  $\dfrac{1}{4}$
3. (C)
  $4$
4. (D)
  $16$
2.
Compute $3\dfrac{1}{2} \div \dfrac{3}{4}$ . Give your answer as a fraction or mixed number.
Answer: ______________
3.
A jug holds $6$ cups of juice. How many $\dfrac{3}{4}$ -cup servings can be poured from it?
Answer: ______________
4.
Compute $2\dfrac{2}{3} \times 1\dfrac{1}{2}$ .
Answer: ______________
5.
Mia spent $\dfrac{2}{5}$ of her money on a book, then $\dfrac{1}{3}$ of the remainder on lunch. She had $24 left. How much money did she start with, in dollars?
Answer: ______________

Answer key — Fractions: division and multi-step stories

1.
(C)
$4$
fraction-operations-6-01
$\frac{1}{2} = \frac{4}{8}$ , and there are $4$ eighths in four-eighths. By the rule: $\frac{1}{2} \times \frac{8}{1} = \mathbf{4}$ . ( $\frac{1}{16}$ comes from multiplying instead of dividing.)
2.
14/3fraction-operations-6-02
$3\frac{1}{2} = \frac{7}{2}$ . Then $\frac{7}{2} \div \frac{3}{4} = \frac{7}{2} \times \frac{4}{3} = \frac{28}{6} = \frac{14}{3} = \mathbf{4\tfrac{2}{3}}$ . Sentence check: four three-quarters make $3$ , and two-thirds of another three-quarter makes the extra half. ✓
3.
8fraction-operations-6-03
$6 \div \frac{3}{4} = 6 \times \frac{4}{3} = \frac{24}{3} = \mathbf{8}$ servings. Check: $8 \times \frac{3}{4} = 6$ . ✓
4.
4fraction-operations-6-04
$\frac{8}{3} \times \frac{3}{2} = \frac{24}{6} = \mathbf{4}$ . (Multiplying parts separately, $2 \times 1 + \frac{2}{3} \times \frac{1}{2} = 2\frac{1}{3}$ , is the classic error.)
5.
60fraction-operations-6-05
After the book, $\frac{3}{5}$ remains. Lunch uses $\frac{1}{3} \times \frac{3}{5} = \frac{1}{5}$ of the original, leaving $\frac{3}{5} - \frac{1}{5} = \frac{2}{5}$ . That $\frac{2}{5}$ is $24, so $\frac{1}{5}$ is $12 and the whole is $5 \times 12 = \mathbf{60}$ dollars.