## Multiplying and Dividing Integers

Read this text. Pay special attention to the sections Multiplication of Signed Numbers and Division of Signed Numbers. These sections give summaries of the rules for multiplying and dividing positive and negative integers. Complete the practice questions and check your answers.

### Multiplying and Dividing Integers

#### Multiply Integers

Since multiplication is mathematical shorthand for repeated addition, our counter model can easily be applied to show multiplication of integers. Let's look at this concrete model to see what patterns we notice. We will use the same examples that we used for addition and subtraction.

We remember that means add , times. Here, we are using the model shown in Figure 3.19 just to help us discover the pattern.

Figure 3.19

Now consider what it means to multiply 5 by −3. It means subtract times. Looking at subtraction as taking away, it means to take away times. But there is nothing to take away, so we start by adding neutral pairs as shown in Figure 3.20.

Figure 3.20

In both cases, we started with 15 neutral pairs. In the case on the left, we took away times and the result was −15. To multiply , we took away times and the result was 15. So we found that

Notice that for multiplication of two signed numbers, when the signs are the same, the product is positive, and when the signs are different, the product is negative.

##### Multiplication of Signed Numbers

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

Same signs | Product |
---|---|

•Two positives •Two negatives |
Positive Positive |

Different signs | Product |
---|---|

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

##### Multiplication by −1

#### Divide Integers

##### Division of Signed Numbers

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.

##### Division by −1

Dividing a number by −1 gives its opposite.

Source: Rice University, https://openstax.org/books/prealgebra/pages/3-4-multiply-and-divide-integers

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