Divide Fractions and Mixed Numbers

**Divide Fractions and Mixed Numbers**

To divide fractions, invert the divisor and multiply.

**Reciprocals** are used to rewrite division problems as related multiplication problems. This is mathematically legal because the product of a fraction and its reciprocal equals one. To find that reciprocal, invert the fraction. That means you flip the numerator and denominator. For instance, the reciprocal of is .

To find the reciprocal of a whole number, first write the whole number as a fraction with a denominator of 1; then find the reciprocal of the fraction.

**Example: **

Find the reciprocal of 3.

Think 3 = . The reciprocal of is .

**Example**

Find .

We got back to the first number in the problem, 12. Therefore, **30** is the correct answer.

**Dividing Mixed Numbers**

When one or more of the numbers in a quotient is a mixed number, write the mixed number as an improper fraction before dividing.

**Example**