Question

How do you multiply and simplify `\frac { 12} { 5x } \times \frac { x ^ { 3} } { 12x }`?

Answer 1

`x/5`

Explanation:

Multiply the top and bottom together, so

`12/(5x)xxx^3/(12x) = (12xxx^3)/(5x xx 12x) = (12x^3)/(60x^2)`

Now we have effectively two fractions, one with numbers and one with `x`'s:

`(12x^3)/(60x^2) = 12/60 xx x^3/x^2`

The `12/60` fraction simplifies to `1/5` because

`12/60 = (12*1)/(12*5) = (cancel(12)*1)/(cancel(12)*5) = 1/5`

and the `x^3/x^2` fraction, by rules of indices, subtracts the powers, so

`x^3/x^2=x^(3-2)=x^1=x`

The whole thing, then, becomes

`x * 1/5 = x/5`