Recall that 6 + 6 + 6 = 6 × 3
Instead of adding 6 three times, you can multiply 6 by 3 and get 18, the same answer.
Similarly,
6 + 6 + 6 + 6 + 6 + 6 + 6 = 6 × 7 = 42
Still by the same token,
2 + 2 + 2 + 2 = 2 × 4
In algebra, 2 × 4 can be written as (2)(4)
You can think of this as four groups of 2
In general,when multiplying integers, remember the followings:
Positive × Positive = Positive
For example,
7 × 6 = 42
2 × 5 = 10
3 × 10 = 30
8 × 2 = 16
Now, try adding -3 to -3
- 3 + -3 = -3 × 2
The reasoning is the same; Instead of adding -3 two times, you can just multiply -3 by 2.
To model this on the number line, just start at 0 and put 2 groups of -3 of the number line. You end up at -6 and -6 is negative.
In general,when multiplying integers
Positive × Negative = Negative
For example:
8 × -5 = - 40
2 × -10 = -20
3 × - 6 = - 18
5 × -5 = - 25
The last case we need to cover is:
Negative × Negative = ?
In general,when multiplying integers,
Negative × Negative = Positive
For example:
-9 × -5 = 45
-4 × -2 = 8
-1 × -1 = 1
-2 × - 6 = 12
Source: tes.com
