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.
In: 0
Given a fraction, you can divide both sides by any number (except 0) without changing the result. 20/40 is the same as 2/4, which is the same as 1/2. A simplified fraction is one where you can’t divide both sides by an integer greater than 1 and still end up with all integers.
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.
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.
to simplify fractions,both numbers on top and bottom must be divivded by a common denominator i.e a whole number.
example, 4/8 can be divided by 2 to give 2/4 and further divided by 2 again to give 1/2. since 1 cannot be divided by 2 to give a whole number, 1/2 is the simplified fraction.
same example but divided by 4 to give 1/2 and can no longer be divided further.
another example, 20/50 can be divided by 5 to give 4/10,then divided by 2 to give 2/5. if it was divided by 10,then it’s 2/5 and can no longer be divided.
the rule here is both numerator and denominator must be divided by the same whole number to give a whole number until it cannot be divided anymore. This is what simplified fractions or simplification is all about.
You and John have 40 marbles and you split it into 2 equal parts. You now have 20 of 40 marbles. An easier way to say that is you have half the marbles, or 1/2. Thats simplifiying factions.
Or say you have 24 cookies and split it with 2 other friends. Thus you have 8/24 cookies, easier way to say that is you have 1/3 of the cookies.
Latest Answers