why is multiplying by 2 same as dividing by half?

Question

hi
I never understood the logic behind this.
lets say
2 multiplied by x is the same as 2 divded by 1/x, why?

Thanks,

P.S.
I am not stupid , ive been taking things for granted never realize why things work that way, for the last 5 years, and now i am reventing my logic.

Answer 1

Because multiplying a number by x is the same as dividing that number by 1/x (its reciprocal). Or:
x = 1/(1/x).

Let's derive this formula:
1. 1 = 1
2. x * (1/x) = 1
3. x = 1/(1/x).

It's how the math works out.

Answer 2

The problem is with fractional number, when you divide by a fraction you are actually multiplying. Take the opposite example:
(2 * 1/x) is the same as (2 / x)
where is the trick? It's that when you multiply with a fraction you are dividing. And viceversa.
Hope it's clear... I'm getting a little confused now! ;)
Good question anyway! I like logic so much!

Answer 3

well, i mean, its kinda logical. because half means 2 parts of a hwole, so if oyu divide 2 by 1/2 that would be 4 parts of a whole. and when oyu multiply 2 times 2, you will get 4 as well.

Answer 4

Here you go:

Number X 2

Number / (1/2) = number x (2/1) = number x 2

When you divide by a fraction the numerator and demoninator flip.

Answer 5

Not the same. are the opposite. When you multiply by 2, you are duplicating. Wehn you divide by half, you're dividing by 2, thus returning to the original number.

Answer 6

Yes

You are essentially multiplying by the reciprical when dividing by a fraction.
(2)(2) = 4

This should be clearer:
x/2 = 2

x=4

There are 4 halves in 2.

Answer 7

you flip the 1 and the two that make up one half
because thats what you do to the active operation also

Answer 8

Because if you cut something in half you have two equal pieces.