Question

What is the value of `((2/3-5/6)/(3/4))`?

Answer 1

`((2/3-5/6)/(3/4))=-2/9`

Explanation:

`((2/3-5/6)/(3/4))`

The fractions in the numerator must have a common denominator. Determine the least common denominator (LCD) by determining the lowest multiple that each have in common.

`3:` `3,color(red)6,9`
`6:` `color(red)6,12,18`

The LCD is `6`. Multiply `2/3` by an equivalent fraction to obtain a denominator of `6`.

`((2/3xxcolor(red)(2/2))-(5/6))/(3/4)`

Simplify.

`((4/6-5/6))/(3/4)=`

`(-1/6)/(3/4)=`

`-(1/6)/(3/4)`

When dividing by a fraction, invert and multiply.

`-1/6xx4/3`

Simplify.

`-4/18`

Simplify.

`-2/9`