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

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Answer 1 · 2017-05-30T06:32:09

The question involves the knowledge of fractions, mixed fractions.

#14 8/45#

Mixed fraction is of the form:-

# x y/z #

Mixed fraction can be simplified by this method:-

Multiply #z xx x#.

Add the result of step 1 to #y#.

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#

Answer 2 · 2017-05-30T06:44:34

Add the whole numbers, then the fractions.

#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#