Question

How do you evaluate `\frac { 1} { 6+ \frac { 1} { 8} }`?

Answer 1

`8/49`

Explanation:

`color(blue)"Note "6+1/8=6 1/8" as a mixed number"`

`1/(6 1/8)" means " 1-:6 1/8`

To divide by `6 1/8` convert it into an #color(blue)"improper fraction"# ,

`color(blue)" change divide to multiply"` and `color(blue)"invert"` (turn upside down the improper fraction.)

`rArr6 1/8=49/8" as an improper fraction"`

`rArr1-:49/8=1xx8/49=8/49`

Answer 2

`8/49`

Explanation:

`1/(6+1/8)`

`:.=1/(6 1/8)`

`:.=1/(49/8)`

`:.=1/1 xx 8/49`

`:.=8/49`

check:

`1/8=0.125+6=6.125`

`1-:6.125=0.163265306`

`8/49=0.163265306`