How is division the inverse of multiplication?

Answer 1

well, when you divide one number by another, you are really multiplying by the second number's inverse (otherwise known as its reciprocal). For instance:
9/2 is the same as 9 x 1/2, or 9 x 0.5
this gets really handy when you start dividing by fractions, such as:
(1/2)/(15/32) is the same as (1/2) x (32/15), which is much simpler; (32 x 1)/(2 x 15) = 32/30 = 16/15
That's why it's called the inverse.

Answer 2

In math, the division is the inverse of multiplication.
For example:

4/2=2 (since, 2*2=4)
simlarly in the reverse order (4/2=2 implies 4=2*2{multiply both sides with 2)


In this way dividion is inverse of multiplication.

Answer 3

In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication.

Specifically, if c times b equals a, written:

c x b = a

where b is not zero, then a divided by b equals c, written:

a
---- = c
b
For instance,

6 / 3 = 2

since

2 x 3 = 6

Answer 4

The answers about exponents and cumulative subtraction are wrong. The others are pretty much spot-on.

If you do Operation M and the do Operation D, and the result is net no change -- and if that's also true if you do them in the opposite order -- the Operations M and D are inverses of each other.

Answer 5

If you multiply by 5 and then divide by 5 you are back where you started. So to solve an equation like 5x = 10, divide both sides by 5:

5x/5 = 10/5
1x = 2
x = 2.

Answer 6

to briefly answer your question, i suggest that you study the law of exponents.
this is available on all basic algebra textbooks.

you see, 1/x is equal to x^-1

why? because of the laws of exponents

if we multiply x to x we have the equation:
x (x) = x^2

you may notice that the two exponent (1) are added

by the way : x alone automatically means x^1 only simplified
so, x^1 (x^1) = x^2

look at this

x^-1 (x) = 1

this is the same with

x
---= 1
x


do you get it?

Answer 7

Here's how 3X4=12 12/4=3.

Answer 8

If you start with a number

x

multiply and divide it by the same number you end up with x again

x * y = xy
xy/y = x

Answer 9

Multiplication is nothing but cumulative addition.Division is nothing but cumulative subtraction!