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

2 Answers
Feb 10, 2017

Answer:

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#

Feb 10, 2017

Answer:

#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#