Dividing Fractions

Objective Learn the procedure for dividing one fraction by another.

There is a main difference between the division of whole numbers and the division of fractions. In fact, when one whole number is divided by another, there may be a remainder since one whole number cannot always be divided evenly into another whole number. However, there is never a remainder when two fractions are divided; the result is always another fraction or a whole number.

When dividing by a fraction we need to invert the fraction and change the division symbol to multiplication. Then we complete the multiplication using the skills.

Example 1

What is the value of ?

Solution

Change from dividing by to multiplying by its reciprocal, . Then multiply.

Example 2

Find .

Solution

		Change to multiplication by the reciprocal.
		Write the improper fraction as a mixed number.

The same procedure works when dividing one fraction by another fraction.

Key Idea

To divide one fraction (the dividend) by another (the divisor), multiply the dividend by the reciprocal of the divisor. In symbols, .

Example 3

What is the value of ?

Solution

		Multiply by the reciprocal of the divisor.
		Multiply numerators and denominators separately.
		Write the improper fraction as a mixed number.

Example 4

Find .

Solution

		Multiply by the reciprocal of the divisor.
		Multiply numerators and denominators separately.