LESSON: Dividing Fractions

READ: Divide Fractions and Mixed Numbers

Divide Fractions and Mixed Numbers

By now you have a pretty solid understanding of how fractions work. You can add, subtract and multiply fractions. Of course, it will also be extremely helpful to learn to divide fractions. There are plenty of real-world situations in which you can use your expertise at dividing fractions.

Dividing fractions is a lot like multiplying fractions. In fact, it’s exactly like multiplying fractions! Remember that when you divide two numbers, one number is the dividend and the other number is the divisor. For example, in the division problem $a \div b, a$ is the dividend and $b$ is the divisor. To divide two fractions, you simply multiply the dividend by the inverted divisor. How do you invert the divisor? Just flip the fraction over! $\frac{1}{2}$ inverted becomes $\frac{2}{1}, \frac{3}{4}$ inverted becomes $\frac{4}{3}$ . This inverted fraction is also called a reciprocal.

Example

$\frac{6}{8} \div \frac{1}{2}$

In this example, one-half is the divisor. We need to flip the divisor so that we multiply by the reciprocal. Here is a rhyme to help you remember

When dividing fractions, never wonder why

Flip the second and multiply

Now we rewrite the problem as a multiplication problem.

$\frac{6}{8} \cdot \frac{2}{1}$

Next, we multiply across.

$\frac{12}{8}=1 \frac{4}{8}$

Our last step is to simplify the fraction part of the mixed number.

Our answer is $1 \frac{1}{2}$ .

How do we divide mixed numbers?

Just like with multiplying fractions, if you are dividing mixed numbers, you have to first convert the mixed number to an improper fraction. Remember how multiplying by fractions usually gave us a product that was smaller than one of the factors? Well, with dividing you usually get an answer that is larger than the divisor or the dividend. But either way, the rhyme is still going to apply here too. Let’s look at some examples.

Example

$4 \frac{1}{3} \div 2 \frac{1}{6}$

First, we convert both of these mixed numbers to improper fractions. Let’s rewrite the problem with these numbers.

$\frac{13}{3} \div \frac{13}{6}$

Now we change this to a multiplication problem by multiplying by the reciprocal.

$\frac{13}{3} \cdot \frac{6}{13}$

Next, we can simplify on the diagonals.

$\xcancel{\frac{13}{3} \cdot \frac{6}{13}} = \frac{1}{1} \cdot \frac{2}{1} = 2$

Our answer is 2.