Question

What is `-5/9+ 1 1/3`?

Answer 1

7/9

Explanation:

Basically, you find the LCM of the denominators. That of 3 and 9 being 9, you multiply the numerator of the fraction with the smaller denominator with whatever multiple of the denominator the LCM is.
#-5/9+1 1/3 =4/3-5/9 =(12-5)/9 =7/9#

Perhaps a simpler visualisation would be thus:

`-5/9 + 4/3*3/3 = -5/9+12/9 = (12-5)/9 = 7/9`

Answer 2

`7/9`

Explanation:

`1`. Start by converting `1` `1/3` into an improper fraction.

`color(darkorange)1` `color(teal)1/color(violet)3`

`=(color(violet)3color(darkorange)(xx1)color(white)(i)color(teal)(+1))/color(violet)3`

`=4/3`

`2`. Find the L.C.M. (lowest common multiple) between the denominators of the two fractions.

`|ul(9color(white)(X)3)`

`color(darkorange)3|ul(9color(white)(X)3)`
`color(white)(Xx)color(teal)3color(white)(X)color(violet)1`

L.C.M.`=color(darkorange)3xxcolor(teal)3xxcolor(violet)1=9`

`3`. Write out the problem with improper fractions. If the denominator of any of the fractions is not the L.C.M., `9`, multiply the numerator and denominator of the fraction by a number such that the denominator becomes the L.C.M., `9`. In your case, multiply the numerator and denominator of `4/3` by `3`.

`-5/9+4/3`

`=-5/9+(4color(red)(xx3))/(3color(red)(xx3))`

`=-5/9+12/9`

`4`. Now that both fractions have the same denominator, you can add them the numerators of the two fractions together.

`=(-5+12)/9`

`=color(green)(|bar(ul(color(white)(a/a)7/9color(white)(a/a)|)))`