Solution:
Step 1
Find the least common multiple (LCM)
LCM for 4,3 and 12 is 12, thus
Multiples of 4
4,8,12,16,20,24,28,32,36,40,44,48
Multiples of 3
3,6,9,12,15,18,21,24,27,30,33,36
Multiples of 12
Multiples of 12 are numbers 12 can divide without a remainder (Simply the multiplication of 12 ). If you don't know the recitation of the multiples, simply add 12 to the preceding numbers to get the subsequent numbers starting from 12.
12,12+12=24,24+12=36,36+12=48, 48+12=60,60+12=72,72+12=84, 84+12=96,96+12=108,108+12=
120,120+12=132,132+12=144,...
⇒12,24,36,48,60,72,84,96,108,120,132,144,...
From the above you can see that the least number which appeared in all the above multiples is 12, hence the LCM for 3,4 and 12 is 12
Step 2
Divide by the LCM and find out how many times the denominator goes into the LCM and multiply that by the numerator and maintain the signs
Thus for 3∕4, the numerator is 3 and the denominator is 4 and 4 (denominator) goes into 12(the LCM), 3 times, hence 3×3 (numerator)
Thus for −1∕3, the numerator is 1 and the denominator is 3 and 3 (denominator) goes into 12(the LCM), 4 times, hence 4×1 (numerator) and maintain the negative sign.
Thus for +1∕12, the numerator is 1 and the denominator is 12 and 12(denominator) goes into 12(the LCM), 1 time, hence 1×1 (numerator) and maintain the positive sign.
Now simplify the numerator first and afterward simplify the new fraction
As shown below
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