2/3 x 3/4 = 2 x 3/3 x 4 = 6/12 = 1/2.
NOTE : The cancellation of common numbers (or factors) between the numerator and denominator could have taken place early on in the process. The multiplication would then have become :-
2/3 x 3/4 = 2/4 = 1/2.
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It is: 1/4 times 6/8 = 3/16 in its lowest terms
2 goes into 12 six times, so the answer is 1/6
The product of 1/3 times 3/8 is 3/24 or 1/8 in its lowest terms
3/10 times 4/100 = 3/250 in its lowest terms