Question

How do you simplify `2 1/2+7(6/7-1/7)`?

Answer 1

`15/2` or `7 1/2`

Explanation:

Step 1) Combine the terms within parenthesis:

`2 1/2 + 7*5/7`

`2 1/2 + cancel(7)*5/cancel(7)`

`2 1/2 + 5`

Next we need to convert the mixed fraction to an improper fractions by multiplying the integer by the appropriate for of `1` and adding it to the fraction:

`((2/2 * 2) + 1/2) + 5`

`(4/2 + 1/2) + 5)`

`5/2 + 5`

Finally, we need to get the integer over a common denominator so we can add the terms by multiplying the integer by the appropriate form of `1`:

`5/2 + (2/2 * 5)`

`5/2 + 10/2`

`(5 + 10)/2`

`15/2`

or converting to a mixed fraction:

`(14 + 1)/2`

`14/2 + 1/2`

`7 + 1/2`

`7 1/2`