How do you simplify `6 2/9 + 7 2/5 + 5/9`?

Mixed fraction is of the form:-

`x y/z`

Mixed fraction can be simplified by this method:-

1. Multiply `z xx x`.
2. Add the result of step 1 to `y`.
3. Retain the value of `z` as the denominator.

So,

`6 2/9` = `9*6 + 2` = `56/9`

And,

`7 2/5` = `5 * 7 + 2` = `37/5`

The question can now be re-written as:-

`56/9 + 37/5 + 5/9`

The LCM of the denominators turns out to be `45`.
So, make all the denominators equal:-

`56/9 * 5/5` = `280/45`

`37/5 * 9/9` = `333/45`

`5/9 * 5/5` = `25/45`

Adding like terms together:-

`280/45 + 333/45 + 25/45` = `638/45`

and `638/45` = `14 8/45`

`color(blue)(6) 2/9 +color(blue)(7) 2/5+ 5/9" "larr` add the whole numbers

`= color(blue)(13)" " color(white)(xxxxxxxxxx)/45" "larr` find the LCD

`= 13 (10+18+25)/45" "larr` make equivalent fractions (see below)

`=13 53/45" "larr` change improper fraction to mixed number

`= 13 + 1 8/45`

`= 14 8/45`

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To find an equivalent fraction, multiply the top and bottom by the same number:

`2/9 xx 5/5 = 10/45`

`2/5 xx 9/9 = 18/45`

`5/9 xx5/5 =25/45`