Fractions as Division - Pre Algebra

1. A rope $5$ yards long is cut into $8$ equal pieces. How long is each piece?

   $\frac{5}{8}$ yard, since $5 \div 8 = \frac{5}{8}$.

2. What division does the fraction $\frac{a}{b}$ represent?

   $a \div b$. The numerator is divided by the denominator.

3. Between which two consecutive whole numbers does $\frac{23}{4}$ lie?

   $5$ and $6$. Dividing $23$ by $4$ gives $5$ with remainder $3$, so $\frac{23}{4} = 5\frac{3}{4}$.

4. Three pizzas are shared equally among $4$ people. How much pizza does each person get?

   $\frac{3}{4}$ of a pizza, since $3 \div 4 = \frac{3}{4}$.

5. Twelve cups of soup are poured equally into $5$ bowls. How many cups go in each bowl?

   $2\frac{2}{5}$ cups, since $12 \div 5 = \frac{12}{5}$.

6. Why is a fraction with a denominator of $0$ undefined?

   It would mean dividing by $0$, and no number times $0$ gives a nonzero dividend, so there is no answer.

7. What is $7 \div 9$ written as a fraction?

   $\frac{7}{9}$. The dividend becomes the numerator and the divisor the denominator.

8. Two sandwiches are shared equally among $3$ people. How much does each person get?

   $\frac{2}{3}$ of a sandwich, since $2 \div 3 = \frac{2}{3}$.

9. Ten liters of water are poured equally into $4$ bottles. How many liters go in each bottle?

   $2\frac{1}{2}$ liters, since $\frac{10}{4} = 2\frac{2}{4}$.

10. Using division, what is $\frac{17}{5}$ as a mixed number?

    $3\frac{2}{5}$. Dividing $17$ by $5$ gives $3$ with remainder $2$.

11. When a quantity is shared equally into groups, which number becomes the numerator of the fraction for one share?

    The total amount being shared. The number of groups becomes the denominator.

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