Dividing Fractions - Pre Algebra

1. What is $\frac{2}{3} \div \frac{4}{9}$?

   $\frac{3}{2}$. Compute $\frac{2}{3} \cdot \frac{9}{4} = \frac{18}{12} = \frac{3}{2}$.

2. What is $6 \div \frac{2}{3}$?

   $9$. Compute $6 \cdot \frac{3}{2} = 9$.

3. How many $\frac{1}{4}$-cup servings are in $3$ cups?

   $12$. Compute $3 \div \frac{1}{4} = 3 \cdot 4$.

4. A ribbon $\frac{9}{10}$ meter long is cut into pieces $\frac{3}{10}$ meter long. How many pieces are there?

   $3$. Compute $\frac{9}{10} \div \frac{3}{10} = \frac{9}{10} \cdot \frac{10}{3} = 3$.

5. When a positive number is divided by a fraction between $0$ and $1$, how does the quotient compare with the number?

   The quotient is greater than the number, because more than one copy of the small divisor fits into it.

6. What is $1\frac{1}{2} \div \frac{3}{4}$?

   $2$. Compute $\frac{3}{2} \cdot \frac{4}{3} = 2$.

7. What is the reciprocal of $\frac{5}{7}$?

   $\frac{7}{5}$. A number times its reciprocal is $1$.

8. What is $\frac{3}{4} \div \frac{1}{2}$?

   $\frac{3}{2}$ (or $1\frac{1}{2}$). Compute $\frac{3}{4} \cdot \frac{2}{1} = \frac{6}{4}$.

9. What is the rule for dividing by a fraction?

   Multiply by the reciprocal of the divisor: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$.

10. What is $\frac{5}{8} \div 5$?

    $\frac{1}{8}$. Compute $\frac{5}{8} \cdot \frac{1}{5}$.

11. What question does $\frac{3}{4} \div \frac{1}{8}$ answer?

    How many eighths are in $\frac{3}{4}$? The answer is $6$, since $\frac{3}{4} = \frac{6}{8}$.

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