Question

How do you solve `\frac { c } { 12} = - 8`?

Answer 1

`c=-96`

Explanation:

We need to ' eliminate' the fraction to proceed.

When we perform an operation on an equation, we must do so to both sides to retain the ' balance' of the equation.

The method is to multiply by the denominator of the fraction, in this case 12.

multiply both sides by 12

`cancel(12)^1xxc/cancel(12)^1=(12xx-8)`

`rArrc=-96" is the solution"`

Answer 2

Expansion on Jim G's answer

Explanation:

To move a multiply or divide to the other side of the equals sign you change it to 1. As 1 times something does not change a value.

To move an add or subtract to the other side of the equals you change it to 0. As +0 or -0 does not change a value.
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In this question we have `c/12` which is `c-:12`

So we need to change the `1/12` to 1.

What we do to one side of the equals we do to the other side to maintain the truth of the equation.

So to change `1/12xx c=-8` such that the `1/12` becomes 1 we multiply both sides by 12

`12xxc/12" "=" "12xx(-8)" "larr`as in Jim's solution

`12/12xxc" "=" "-96`

...........................................................................................................
but `12/12` is the same as 1 which is why people cancel them out.

`12/12xx"something" -> (12-:12)/(12-:12)xx"something"`

`= 1/1xx"something" = 1xx"something" = "something"`
............................................................................................................

`1xxc" "=" "-96`

but `1xxc=c`

`c=" "=" "-96" "larr` as per Jim's answer