Why does multiplying or dividing two negative numbers produce a positive?
In: Mathematics
The Khan Academy and others explain it using distributive property of maths, which is therefore a pre-requisite. We did this at age 11 in UK. I’ll show it quickly here:
What is -5 x (3 – 3) ? Ans. 0, since 3 – 3 is 0 and anything multiplied by 0 is 0.
Using distributive property of multiplication: -5 x (3 – 3) = -15 + (-5 x -3) = 0
So it must be true that -5 x -3 = +15.
The other intuition is looking at a pattern such as:
3 x -5 = -15
2 x -5 = -10
1 x -5 = -5
0 x -5 = 0
-1 x -5 = +5
-2 x -5 = +10
And hopefully feel that this makes sense, everything is consistent.
(Ughh, not formatting as it appears on iPad sorry)
Latest Answers