Divide Fractions and Mixed Numbers

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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 .

Rewrite the division as a a multiplication by the reciprocal.  Then simplify where needed

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

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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