4.1 Multiplication
When we work with multiplicatoin of natural numbers, fractions and decimals, we use something called ”repeated addition” to start with, and this is what it looks like:
**Positive number · Positive number **
3 **·** 2 =
2 + 2 + 2 =
(+2) + (+2) + (+2) =
(+2) and (+2) and (+2)
On the number line, it would look like this:
The result is then 6.
**Positive number · Negative number**
You can do this the same way for multiplication of a positive number with a negative number:
3 **·** (-2) =
(-2) + (-2) + (-2) =
(-2) and (-2) and (-2)
This is how it looks on the number line:
The result become -6.
Another way to understand multiplication with negative numbers is to look at how the product changes when you change on of the factors. Study this example:
3 **·** 5 = 15
2 ** ·** 5 = 10
1 ** ·** 5 = 5
0 ** ·** 5 = 0
(-1) ** ·** 5 = -5
(-2) ** ·** 5 = -10
(-3) ** ·** 5 = -15
and so on
**Negative number · Negative number **
Even this can be show in several different way in order to better understand. We begin by continuing the number series from the last example, but now decrease by a factor instead.
We assume now you know how to multiply a positive number with a negative number:
(-3) ** ·** 5 = -15
(-3) ** ·** 4 = -12
(-3) ** ·** 3 = -9
(-3) ** ·** 2 = -6
(-3) ** ·** 1 = -3
(-3) ** ·** 0 = 0
(-3) ** ·** (-1) =
(-3) ** ·** (-2) =
(-3) ** ·** (-3) =
and so on |