#9 1/6 - 3 2/9=# How do I do this math problem?

2 Answers
Sean
Apr 11, 2018

#55/6-29/9=5##17/18#

Explanation:

.

#9##1/6=((9)(6)+1)/6=(54+1)/6=55/6#

#3##2/9=((3)(9)+2)/9=(27+2)/9=29/9#

#9##1/6-3##2/9=55/6-29/9#

Now, we need to find the Least Common Denominator (LCD) between #6 and 9#:

#6=(2)(3)#

#9=(3)(3)=(3)^2#

They both have #3#. We need to takethe highest power of the piece they have in common; and multiply it by the pieces they do not have in common, i.e. #(2)# to get our LCD.

This way, LCD is divisible by each denominator.

#LCD=(3)^2(2)=(9)(2)=18#

#55/6=55/6*3/3=165/18#

#29/9=29/9*2/2=58/18#

#55/6-29/9=165/18-58/18=(165-58)/18=107/18#

We can now divide #107# by #18#. We will get #5#. #(5)(18)=90#. We subtract #90# from #107# and get #17#.

#107/18=5##17/18#

Therefore,

#55/6-29/9=5##17/18#

EZ as pi
Apr 11, 2018

#5 17/18#

Explanation:

#color(blue)(9) 1/6-color(blue)(3) 2/9" "larr# subtract the whole numbers first.

#=color(blue)(6)" "1/6-2/9" "larr# common denominator is #18#

#=6 (3-4)/18" "larr# make equivalent fractions

Convert #1# to #18/18#

#= 5cancel6 (18+3-4)/18#

#= 5 17/18#

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