Multiplying Fractions - Pre Algebra

1. What is the area of a rectangle $\frac{3}{4}$ foot long and $\frac{2}{3}$ foot wide?

   $\frac{1}{2}$ square foot. Compute $\frac{3}{4} \cdot \frac{2}{3} = \frac{6}{12}$.

2. What is $\frac{3}{4} \times \frac{2}{9}$ in simplest form?

   $\frac{1}{6}$. The product $\frac{6}{36}$ simplifies to $\frac{1}{6}$.

3. In a fraction word problem, what operation does the word "of" usually signal, as in $\frac{1}{3}$ of $15$?

   Multiplication. $\frac{1}{3}$ of $15$ means $\frac{1}{3} \times 15 = 5$.

4. In a class of $30$ students, $\frac{2}{5}$ walk to school. How many students walk?

   $12$. Compute $\frac{2}{5} \cdot 30$.

5. What is $\frac{1}{2}$ of $\frac{3}{5}$?

   $\frac{3}{10}$. The word "of" means multiply: $\frac{1}{2} \cdot \frac{3}{5}$.

6. When a positive number is multiplied by a fraction between $0$ and $1$, how does the product compare with the number?

   The product is less than the number, because you are taking only part of it.

7. What is $1\frac{1}{2} \times \frac{2}{3}$?

   $1$. Compute $\frac{3}{2} \cdot \frac{2}{3} = 1$.

8. Before multiplying $\frac{5}{8} \times \frac{4}{15}$, which common factors can be canceled, and what is the product?

   Cancel $5$ with $15$ (leaving $1$ and $3$) and $4$ with $8$ (leaving $1$ and $2$). The product is $\frac{1}{6}$.

9. What is $2\frac{1}{2} \times 2\frac{1}{2}$?

   $6\frac{1}{4}$. Compute $\frac{5}{2} \cdot \frac{5}{2} = \frac{25}{4}$.

10. What is the rule for multiplying two fractions?

    Multiply the numerators and multiply the denominators: $\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}$.

11. What is $\frac{2}{3} \times 12$?

    $8$. One third of $12$ is $4$, and two thirds is $8$.

12. What is $\frac{2}{3} \times \frac{4}{5}$?

    $\frac{8}{15}$. Multiply the numerators and the denominators.

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