 WME@Kimpton Middle

## Multiplying Integers Multiplication is a shorthand for repeated addition. For example, 3 times 7 means add seven 3's together.

3 × 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3

Observe that

3 × 7 = 7 × 3 = 7 + 7 + 7

as can be easily seen from the photo of soldiers in formation. When multiplying two numbers, you can always switch them around (commutate them) and get the same answer. We say multiplication is commutative for this reason.

Look at the following grid, and you'll see why.

The grid can be viewed either as 3 rows of 5 or 5 columns of 3. Do you see?

The first operand can be negative, for example

− 4 × 3 = (− 4) + (− 4) + (− 4)

With this understanding, perform the following multiplications:

```7 × 5 =

-6 × 3 =
```

Now consider the meaning of multiplication when the 2nd operand is negative.

• The notation 4 × − 2, for example, means take away two 4's or remove two 4's. Hence,

4 × − 2 = − (4 × 2).

• The notation − 6 × − 3, means take away three (− 6)'s which really means add three 6's. Hence,

− 6 × − 3 = 6 × 3.

Thus, we have the following easy to remember rules to help you do multiplication.

1. Multiplying numbers with the same sign--the answer is always positive

2. Multiplying numbers with different signs--the answer is always negative

Now do the following problems to test youreslf.

```8 × 4 =

7 × -3 =

-7 × -4 =

-9 × 2 =
```