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Q&A #7499

Teachers' Lounge Discussion: Curious about fractions

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From: MathFreak <saltof_theearth@yahoo.co.in>
To: Teacher2Teacher Public Discussion
Date: 2004091203:05:00
Subject: Why it works

WHY IT WORKS-
I think it works because the product of two numbers is also the
product of the L.C.M and H.C.F. of the two numbers.
Say 1/28+ 1/42

LCM of 28 and 42:

28=2^2*3^0* 7^1
42=2^1*3^1*7^1

LCM= 2^2*3^1*7^1=4*3*7=84

HCF=2^1*3^0*7^1=2*1*7=14

HCF*LCM=2^2*2^1*3^1*3^0*7^1*7^1=28*42

Therefore,1/28+1/42= 1/84 *(3+2)=5/84
as also 1/LCM*HCF times  (3*HCF+2*HCF)= 1/28*42 times(42+28)
Since 3HCF+2HCF=5HCF=5*14=42+28=70.
Hope this helps!
Mathfreak

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