hello! I’m taking basic algebra in college right now and I never learned how to simplify fractions in grade school or high school because I never really tried to learn but now I want to so I can make sure I’m doing it right. I’m having a hard time with it and everything I’ve googled just doesn’t make sense to me. Please help.
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Any whole number can be written as the product of several prime numbers, ie 8 =2*2*2, 39 = 13*3.
So if we have 16/12, we can write that as (2*2*2*2)/(2*2*3), we can cancel 2 of those 2s and were left with (2*2)/3, or 4/3.
Now we don’t need to take it quite that far, only as far as the greatest common factor of both numbers. The greatest common factor of 12 and 16 is 4, so if we just take a 4 out of 12 and 16, we get 4*4/4*3, 4s cancel and we get 4/3.
We also can just take it one step at a time. If we have 48/30, both are divisible by 2, so let’s factor that out. 24*2/15*2, the 2s cancel and we get 24/15. Both are divisible by 3, so we have 8*3/5*3, 3s cancel and we get 8/5 and we’re done.
You know you’re done when the greatest common factor of both numbers is 1, that means they’re coprime and you can’t simplify it any further.
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