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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Imagine a pie that you’ve cut into two pieces, like [this picture](https://etc.usf.edu/clipart/40500/40523/pie_01-02c_40523_lg.gif) we’d call one of those pieces 1/2, right? Now imagine that you’ve cut that same pie into 6 pieces, like [this picture](https://etc.usf.edu/clipart/40500/40557/pie_01-06a_40557_lg.gif). Each piece is 1/6, right? Now, imagine that we have 3 of those slices, or 3/6ths of the pie.
See how 1/2 pie is equal to 3/6ths of the pie? That’s because those two numbers, 1/2 and 3/6ths, both represent the exact same number. And any time that two figures represent the same number, we can simplify them. In this case, we can look at 3/6ths and say that both the 3 and the 6 share a factor – 3. So we’d divide both parts of the fraction by 3, then put them back together.
3 ÷ 3 = 1
6 ÷ 3 = 2
Put the fraction back and we’ll get 1/2. So long as you use the same number to divide the top and bottom of the fraction, you’ll always get the same result.
So let’s make up another example – 12/32. The biggest number that goes into both of those is 4. So let’s simplify by dividing by 4:
12 ÷ 4 = 3
32 ÷ 4 = 8
So that fraction simplifies down into 3/8’s, which means that it’s equal to 3/8ths. Divide a pie into 8 chunks and take 3, you’ll have the same amount of pie as if you divided it into 32 equal chunks (which seems tough to do) and took 12 of them. The only thing you need to make sure of is that you find a number that factors into both the top and bottom of the fraction, and you’re set.
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