Question

How do you simplify `5/6+8/9`?

Answer 1

See the entire simplification process below:

Explanation:

First, we need to get each fraction over a common denominator in order to be able to add the fractions. In this case the lowest common denominator is `18`. To get each fraction over this common denominator we must multiply it by the appropriate form of `1`:

`(5/6 xx 3/3) + (8/9 xx 2/2) -> 15/18 + 16/18`

We can now add the two fractions:

`15/18 + 16/18 -> (15 + 16)/18 -> 31/18`

Answer 2

`color(green)(31/18)` or `color(green)(1 13/18)`

Explanation:

If we note that the LCM (Least Common Multiple) of the denominators `6` and `9`
is `18`,
Then `5/6=5/6 xx 3/3 = 15/18`

and `8/9=8/9 xx 2/2 =16/18`

So `5/6+8/9` is the same as `15/18+16/18`

`15` eighteenths `+ 16`eighteenths `=31` eighteenths
`color(white)("XXX")`(`15` of anything plus `16` of the same thing
`color(white)("XXXX")`equals `31` of that thing)

We would normally write `31` eighteenths as
`color(white)("XXX")31/18`
or
we could write it as a mixed fraction:
`color(white)("XXX")1 13/18`