What is the sum of #2/2+2/3+2/4+2/5+2/6+2/7+2/8# ?

1 Answer
EZ as pi
Apr 24, 2018

#1443/420 =3 61/140#

Explanation:

#2/2+2/3+2/4+2/5+2/6+2/7+2/8#

Simplify where possible first.

#1+2/3+1/2+2/5+1/3+2/7+1/4#

You need a common denominator. This is easier to find than it seems.

You do not need to consider #2# at all because:
#2# is a factor of #4#

Find the denominator using the prime factors..

#1+2/3+1/2+2/5+1/3+2/7+1/(2xx2)#

#= (color(white)(xxxx))/(2xx2xx3xx5xx7) = (color(white)(xxxx))/420#

Now find equivalent fractions

#= (420+280+210+168+140+120+105)/(2xx2xx2xx3xx5xx7)#

#=1443/420#

#=3 61/140#

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