As we start to develop the numbers of operations we can perform, there starts to be pairs of operations that are opposites of each other. These are called inverse relations.
Question
What is the inverse relation to addition? Multiplication?Answer
The inverse relation to addition is subtraction. The inverse relation to multiplication is division.Analysis
When we have two operations that operate in opposite ways, we call those operations inverse relations.
For instance, when we start with a number, say like 4, and we add 3, we have a sum of 7. If we then subtract 3, we have a difference of 4 - it's the same number again. So we can say:
4 + 3 - 3 = 4
In fact, if we start with any given number, and we can call that x, and we add and then subtract (or subtract and then add) another number, say n, we'll end up with a result of x again:
x + n - n = x
x - n + n = x
Addition and subtraction are inverse relations.
We can do the same with multiplication and division:
(Please keep in mind that there is an important exception - we can't do this with fractions if we divide by 0! Dividing by 0 will cause weird things to happen.)
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When you mention multiplication and division, I think that you should also mention an important exception, i.e. multiplication and division by zero.
ReplyDeleteSo if you have n = 0, then you can't have
x * n / n = x
Also, here's a nice resource I came across. Not sure if you'd want to use it here because it describes inverse operations and functions, so more complex stuff, but it's worth keeping around for future use.