## Dividing Integers

Contents

Division is the inverse operation of multiplication. So, \(15÷3=5\) because \(5·3=15\) In words, this expression says that \(\mathbf{\text{15}}\) can be divided into \(\mathbf{\text{3}}\) groups of \(\mathbf{\text{5}}\) each because adding five three times gives \(\mathbf{\text{15}}.\) If we look at some examples of **multiplying integers**, we might figure out the rules for **dividing integers**.

Division of signed numbers follows the same rules as multiplication. When the signs are the same, the **quotient** is positive, and when the signs are different, the quotient is negative.

### Division of Signed Numbers

The sign of the quotient of two numbers depends on their signs.

Same signs | Quotient |
---|---|

•Two positives •Two negatives | Positive Positive |

Different signs | Quotient |
---|---|

•Positive & negative •Negative & positive | Negative Negative |

Remember, you can always check the answer to a division problem by multiplying.

### Optional Video: Division of Integers – The Basics

## Example

Divide each of the following:

- \(−27÷3\)
- \(\phantom{\rule{0.2em}{0ex}}-100÷\left(-4\right)\)

### Solution

\(–27÷3\) | |

Divide, noting that the signs are different and so the quotient is negative. | \(–9\) |

\(–100÷\left(–4\right)\) | |

Divide, noting that the signs are the same and so the quotient is positive. | \(25\) |

Just as we saw with multiplication, when we divide a number by \(1,\) the result is the same number. What happens when we divide a number by \(-1?\) Let’s divide a positive number and then a negative number by \(-1\) to see what we get.

When we divide a number by, \(-1\) we get its opposite.

### Division by -1

Dividing a number by \(-1\) gives its opposite.

## Example

Divide each of the following:

- \(\phantom{\rule{0.2em}{0ex}}16÷\left(-1\right)\phantom{\rule{1em}{0ex}}\)
- \(\phantom{\rule{0.2em}{0ex}}-20÷\left(-1\right)\)

### Solution

\(16÷\left(–1\right)\) | |

The dividend, 16, is being divided by –1. | \(–16\) |

Dividing a number by –1 gives its opposite. | |

Notice that the signs were different, so the result was negative. |

\(–20÷\left(–1\right)\) | |

The dividend, –20, is being divided by –1. | \(20\) |

Dividing a number by –1 gives its opposite. |

Notice that the signs were the same, so the quotient was positive.

### Optional Video: Dividing Integers

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