Question

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

Answer 1

See a solution process below:

Explanation:

First, we want to subtract the numbers within the parenthesis. However, to do this we must put each number over a common denominator. We can do his by multiplying `6` by the appropriate for of `1`:

`2/3(6 - 5/6) =>`

`2/3([6/6 xx 6] - 5/6) =>`

`2/3(36/6 - 5/6) =>`

`2/3(31/6)`

Next, we can multiply the two fractions to complete the evaluation of the expression:

`2/3(31/6) =>`

`2/3 xx 31/6 =>`

`(2 xx 31)/(3 xx 6) =>`

`62/18`

Now, we can factor the numerator and denominator so we can cancel common terms. This will give the simplest form of the fraction:

`(2 xx 31)/(2 xx 9) =>`

`(color(red)(cancel(color(black)(2))) xx 31)/(color(red)(cancel(color(black)(2))) xx 9) =>`

`31/9`