# Multiplying Fractions

*Multiply the tops, multiply the bottoms.*

### There are 3 simple steps to multiply fractions

1. Multiply the top numbers (the *numerators*).

2. Multiply the bottom numbers (the *denominators*).

3. Simplify the fraction if needed.

### Example:
\frac{1}{2} × \frac{2}{5}

**Step 1**. Multiply the top numbers:

\frac{1}{2} × \frac{2}{5} = \frac{1 × 2}{ } = \frac{2}{ }

**Step 2**. Multiply the bottom numbers:

\frac{1}{2} × \frac{2}{5} = \frac{1 × 2}{2 × 5} = \frac{2}{10}

**Step 3**. Simplify the fraction:

\frac{2}{10} = \frac{1}{5}

### With Pizza

Here you can see it with pizza ...

Do you see that half of two-fifths is two-tenths?

Do you also see that two-tenths is simpler as one-fifth?

### With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

### Another Example:
\frac{1}{3} × \frac{9}{16}

**Step 1**. Multiply the top numbers:

\frac{1}{3} × \frac{9}{16} = \frac{1 × 9}{ } = \frac{9}{ }

**Step 2**. Multiply the bottom numbers:

\frac{1}{3} × \frac{9}{16} = \frac{1 × 9}{3 × 16} = \frac{9}{48}

**Step 3**. Simplify the fraction:

\frac{9}{48} = \frac{3}{16}

(This time we simplified by dividing both top and bottom by 3)

## The Rhyme

*♫ "Multiplying fractions: no big problem,
Top times top over bottom times bottom.*

"And don't forget to simplify,

Before it's time to say goodbye" ♫

"And don't forget to simplify,

Before it's time to say goodbye" ♫

## Fractions and Whole Numbers

What about multiplying fractions **and** whole numbers?

**Make the whole number a fraction, by putting it over 1.**

Example: 5 is also \frac{5}{1}

Then continue as before.

### Example:
\frac{2}{3} × 5

Make 5 into \frac{5}{1} :

\frac{2}{3} × \frac{5}{1}

Now just go ahead as normal.

Multiply tops and bottoms:

\frac{2}{3} × \frac{5}{1} = \frac{2 × 5}{3 × 1} = \frac{10}{3}

The fraction is already as simple as it can be.

Answer = \frac{10}{3}

Or you can just think of the whole number as being a "top" number:

### Example:
3 × \frac{2}{9}

Multiply tops and bottoms:

\frac{3}{ } × \frac{2}{9} = \frac{3 × 2}{9} = \frac{6}{9}

Simplify:

\frac{6}{9} = \frac{2}{3}

## Mixed Fractions

You can also read how to multiply mixed fractions