Question

How do you evaluate `5\frac { 9} { 7} - 5\frac { 5} { 6} + 3\frac { 7} { 14}`?

Answer 1

See a solution process below:

Explanation:

First, convert each mixed number to an improper fraction:

`5 9/7 - 5 5/6 + 3 7/14 =>`

`5 9/7 - 5 5/6 + 3 1/2 =>`

`(5 + 9/7) - (5 + 5/6) + (3 + 1/2) =>`

`((7/7 xx 5) + 9/7) - ((6/6 xx 5) + 5/6) + ((2/2 xx 3) + 1/2) =>`

`(35/7 + 9/7) - (30/6 + 5/6) + (6/2 + 1/2) =>`

`44/7 - 35/6 + 7/2`

Next, we can put each fraction over a common denominator in order to be able to add and subtract the fractions. In this problem the common denominator is `42`. We need to multiply each fraction by the appropriate form of `1` to achieve this result:

`(6/6 xx 44/7) - (7/7 xx 35/6) + (21/21 xx 7/2) =>`

`264/42 - 245/42 + 147/42 =>`

`(264 - 245 + 147)/42 =>`

`(19 + 147)/42 =>`

`166/42`

We can now convert this back into a mixed number:

`166/42 => (126 + 40)/42 => 126/42 + 40/42 => 3 + 40/42 =>`

`3 40/42 => 3 20/21`