Question

How do you evaluate `\frac{(4x)/{4}}{(3x)/2}`?

Answer 1

`((4x)/4)/((3x)/2)=2/3`

Explanation:

`((4x)/4)/((3x)/2)=(4x)/4xx2/(3x)`
`(4x)/4xx2/(3x)=(8x)/(12x)`
`(8x)/(12x)=2/3`

Answer 2

`((4x)/4)/((3x)/2)` simplifies to `2/3`.

Explanation:

Simplify:

`((4x)/4)/((3x)/2)`

This is a fraction divided by a fraction.

`(4x)/4-:(3x)/2`

Cancel `4`.

`(color(red)cancel(color(black)(4))^1x)/color(red)cancel(color(black)(4))^1-:(3x)/2`

Simplify. Any single number or variable is understood to be `n/1`.

`x/1-:(3x)/2`

When dividing by a fraction, multiply by its reciprocal.

`x/1xx2/(3x)`

Multiply the numerators and denominators.

`(x xx2)/(1xx3x)`

Simplify.

`(2x)/(3x)`

Cancel `x`.

`(2color(red)cancel(color(black)(x)))^1/(3color(red)cancel(color(black)(x)))^1`

Simplify.

`2/3`