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Simplifying fractions quickly!

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Junior | Next Rank: 30 Posts
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by nhyder » Fri Nov 11, 2016 10:28 am
Hey guys,

Can anyone help me simply this fraction in a quick method? I'm using traditional simplifying techniques and am wondering if there is a easier way around this?

1/2 + 1/3 + 1/4

1/2 (multiply top and bottom by 3) + 1/3 (multiply too and bottom by 2) = 3/6+2/6= 5/6+1/4

5/6(multiply top and bottom by 4) + 1/4 (multiply top and bottom by 6) = 26/24

I individually devised each by 2 in long division to get 13/12.

Is there an easier way to do this?

Thanks!

Nadine
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by GMATGuruNY » Fri Nov 11, 2016 10:33 am
nhyder wrote:Hey guys,

Can anyone help me simply this fraction in a quick method? I'm using traditional simplifying techniques and am wondering if there is a easier way around this?

1/2 + 1/3 + 1/4
Multiply and divide by the LCM of the three denominators.
The LCM of 2, 3 and 4 is 12.
Multiplying and dividing by 12, we get:
12(1/2 + 1/3 + 1/4) / 12
(6 + 4 + 3)/12
13/12.
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by Matt@VeritasPrep » Fri Nov 11, 2016 2:00 pm
Here's what I'd do:

1/2 + 1/3 + 1/4 = x

Multiply both sides by 2*3*4:

3*4 + 2*4 + 2*3 = 2*3*4*x

26 = 24x

26/24 = x

13/12 = x

IMHO finding the LCM first for some sets of numbers is more time consuming than reducing the fraction at the end, but YMMV.
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