I'm reviewing my arithmetic and right now I'm at fractions, I'm just having a little bit of problem "visualizing" why cancellation works in multiplying fractions, I know how it works, it's just the why. Take for example.
$$\frac{2}{3}\cdot\frac{3}{4}=\frac{1}{3}\cdot\frac{3}{2}=\frac{1\cdot1}{1\cdot2}=\frac{1}{2}.$$
Through cancellation we know this ends in 1/2 because the common factor of the numerator "2" and denomaninator "4" is 2, so we divide both by "2" and end with new numbers in place, we also know that the common factor of numerator "3" and denominator "3" is "3" which equals "1" in both places, so it makes the work of "reducing to lowest terms" non-existent since this method is already a shortcut to that.
But I just can't seem to visualize how it works, can you guys give me a visual model to help me make sense of this? thank you.
Best Answer
Just write $$\frac{2}{3}:\frac{3}{4}=\frac{2}{3}\cdot\frac{4}{3}=\frac{2\cdot4}{3\cdot3}=\frac{8}{9}.$$