To divide fractions, we flip the second fraction and then we just multiply. Change it to a multiplication problem. Just follow multiplication rules.
And then we reduce it. Find the quotient. The quotient is the answer when we divide.
So we have two thirds. We're going to change it to a multiplication problem and flip the second fraction. It's the reciprocal is the more technical term for it. Then we're going to do just like we did on multiplication.
We're going to look for ways we can reduce this fraction. Not seeing any. Then we're going to multiply straight across.
2 times 8 is 16. 5 times 3 is 15. This is an improper fraction. The numerator is bigger than the denominator. They teach you to reduce those in like elementary school.
But in college we just... usually leave them just like they are. They're easier to work with that way. Number two, same idea. Keep the first fraction, change it to a multiplication problem, and flip the second one.
This time we have signs to think about. We've got a negative and a positive. Our answer will be negative because those are different signs.
8 times 8 is 64, and 3 times 7 is 21. That will not reduce, so we'll just leave it like that. Number three, I'm going to think of this as three-fifths divided by negative two over one. That'll help me when I flip it.
So this is three-fifths times, I'm going to call it negative one over two. And again, that negative can go on top, it can go on the bottom, it can go out front. it's still a negative fraction, so it really doesn't matter. Okay, I flipped it. I made it a multiplication problem.
I'm going to look and see if I can reduce anything. I don't see anything I can divide the numerator and the denominators by, so I'm just going to multiply straight across. 3 times negative 1 is 3. The signs are different, so my sign here is negative. 5 times 2 is 10. It won't reduce.
So we're done with that one. Last one, the idea is the same except we have negative 3 over 1 to start with. Divide it by 12 fifths. We're going to flip the second fraction. It's always the second fraction.
Make it a multiplication problem. This will reduce. 3 and 12, I'm not going to worry about the sign. We're just going to keep that negative hanging out there in the front.
3 divided by 3 is 1. 12 divided by 3 is 4. Multiply straight across. Negative 1 times 5 is negative 5. I just multiplied. 1 times 5 is 5. The signs are different, so I got a negative.
On the bottom, I have 1 times 4 is 4. And again, it's improper. We just leave it like that.