Multiply Fractions (basic)

Multiplying fractions is probably the easiest fraction operation to do: you simply multiply the numerator times the numerator and the denominator times the denominator.

Why multiply both?  Remember that multiply means "of" in math. So, when you multiply fractions you are finding the fraction of another fraction.  If you find half of a half, you get a quarter. Anytime you multiply a fraction that is less than one by another fraction that is less than one, you get a smaller fraction. The way to make fractions smaller is to make the denominators bigger! So, unlike adding and subtracting fractions, in which you are adding or taking away units of the same size (thus you keep the denominator), when you multiply fractions you are actually making your fraction smaller, by another fraction, so you multiply the numerator and the denominator.

Example: 

Unlike adding and subtraction fractions, when you multiply fractions, it's easiest if you write the problem out horizontally:

$\displaystyle{\frac{1}{2}\times\frac{1}{2}=\frac{1 \times 1}{2 \times 2}=\frac{1}{4}}$

One half of one half is one fourth -- and multiplying the numerators times the numerators and the denominators times denominators gives you one fourth.

The multiplication process also works when you have more difficult numbers!

Example: 

Unlike adding and subtraction fractions, when you multiply fractions, it's easiest if you write the problem out horizontally:

$\dfrac{1}{8}\times\dfrac{5}{9}=\dfrac{1 \times 5}{8 \times 9}=\dfrac{5}{72}$

This one is almost impossible to visualize, but 1/8 is a very small fraction and 5/9 is about one half.  When you find a very small part of one half, you get an even smaller portion: 5/72.

Multiplying fractions is easy!  There are just a couple of things to look out for:

• When you multiply fractions the numerators and denominators can get big, fast, which leads to a lot of simplifying (see lesson Simplifying Fractions).  Cross-cancelling can really cut down on simplifying and is good for students to learn as soon as they master simple multiplication of fractions (see lesson Multiply Fractions (advanced)).
• When working with mixed numbers (whole numbers and fractions), students must convert mixed numbers to improper fractions BEFORE they multiply. See lesson Multiply Fractions - with Mixed Numbers.