Multiplying and Dividing Fractions

In short: To multiply fractions, multiply the tops and multiply the bottoms. To divide, keep the first fraction, change $÷$ to $\times$ and flip the second one, so $\frac{1}{2}÷\frac{1}{4}=\frac{1}{2}\times \frac{4}{1}=2$.

Before you start

• Simplifying fractions by dividing top and bottom by a common factor.
• Changing mixed numbers to improper fractions: $2\frac{1}{3}=\frac{7}{3}$.
• A whole number can be written as a fraction over 1: $5=\frac{5}{1}$.

Multiplying fractions

You do not need a common denominator to multiply. That is only for adding and subtracting.

Cancel first

Before multiplying, divide any top number and any bottom number by a common factor. This keeps the numbers small.

Mixed numbers: change them first

Dividing fractions

Dividing asks "how many of these fit into that?". There is a neat rule.

The flipped fraction is called the reciprocal. The reciprocal of $\frac{9}{8}$ is $\frac{8}{9}$, and the reciprocal of 6 is $\frac{1}{6}$.

How many parts in a mixed number?

"How many thirds are in $3\frac{2}{3}$?" Change to an improper fraction: $\frac{11}{3}$. There are 11 thirds.

This is the same as $3\frac{2}{3}÷\frac{1}{3}=11$.

Quick summary

• Multiply fractions: top times top, bottom times bottom.
• Cancel common factors between any top and any bottom first.
• Change mixed numbers to improper fractions before multiplying or dividing.
• Divide: keep the first, change $÷$ to $\times$, flip the second.
• "How many thirds in $3\frac{2}{3}$?" means change it to an improper fraction and read the top.

Quiz