How do you simplify #\frac{1}{4} + \frac{3}{10} - \frac{2}{5}#?

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Answer 1 · 2016-10-03T06:12:36

#1/4+3/10-2/5=3/20#

This is addition and subtraction together of three fractions whose denominators are #4#, #10# and #5#.

To solve any such question what we need is Least Common Multiple of denominators.

For this let us list out denominators as product of their rime factors.

#4=2xx2#
#10=2xx5#
#5=5#

As #2# occurs maximum two times and #5# occurs maximum once only, LCM is #2xx2xx5=20#. We now write fractions with common denominator as #20#.

Now #1/4+3/10-2/5#

= #(1xx5)/(4xx5)+(3xx2)/(10xx2)-(2xx4)/(5xx4)#

= #5/20+6/20-8/20#

= #(5+6-8)/20#

= #3/20#