# 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:

1 | × | 2 |

2 | 5 |

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

1 | × | 2 | = | 1 × 2 | = | 2 |

2 | 5 |

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

1 | × | 2 | = | 1 × 2 | = | 2 |

2 | 5 | 2 × 5 | 10 |

**Step 3**. Simplify the fraction:

2 | = | 1 |

10 | 5 |

### With Pizza

Here you can see it with pizza ...

... and do you see how 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

1 | × | 9 |

3 | 16 |

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

1 | × | 9 | = | 1 × 9 | = | 9 |

3 | 16 |

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

1 | × | 9 | = | 1 × 9 | = | 9 |

3 | 16 | 3 × 16 | 48 |

**Step 3**. Simplify the fraction:

9 | = | 3 |

48 | 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 | 5 |

1 |

Then continue as before.

### Example:

2 | × | 5 |

3 |

Make 5 into ^{5}/_{1} :

2 | × | 5 |

3 | 1 |

Now just go ahead as normal.

Multiply tops and bottoms:

2 | × | 5 | = | 2 × 5 | = | 10 |

3 | 1 | 3 × 1 | 3 |

The fraction is already as simple as it can be.

Answer = | 10 |

3 |

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

### Example:

3 | × | 2 |

9 |

Multiply tops and bottoms:

3 | × | 2 | = | 3 × 2 | = | 6 |

9 | 9 | 9 |

Simplify:

6 | = | 2 |

9 | 3 |

## Mixed Fractions

You can also read how to multiply mixed fractions