In this lesson we're going to learn why keep change flip works when we're dividing fractions. So here we're going to start off with our example of two sevenths divided by five sixths. Now in order for us to show why keep change flip works, we're first going to solve this problem the long way. Remember, fractions represent division and vice versa. Any division problem can be set up as a fraction. So here we have a fraction divided by another fraction but we can represent this as just one great big fraction as two sevenths as the numerator divided by 5/6 in the denominator. I know it looks kind of weird - we have fractions within a fraction. But remember, it's really just saying two sevenths divided by five sixths and setting it up this way is going to help us to see how this long way, this longer strategy works. The next thing that we're going to do is multiply that denominator of 5/6 by its reciprocal. Now remember, the reciprocal is just the flip of the fraction. So 5/6 multiplied by its reciprocal of 6/5. Now if we remember whenever we multiply any number by its reciprocal it's going to equal one. So that denominator, once we multiply it by the six fifths will just become a one. Of course we can't just multiply the denominator by 6/5. Whatever we do to one part of a fraction we have to do the same thing to the other part of the fraction. So we also have to multiply the numerator by 6/5. And then that part we can just multiply across like we normally do with multiplication. The two times six will give us twelve as the numerator, seven times five will give us 35. So that part just becomes twelve over 35. And we still have a fraction within a fraction. But remember, whenever we have a one as the denominator of a fraction the fraction will just simplify to whatever the numerator is. So this fraction just becomes the twelve over 35. So that's our final answer, 12/35. So that's the long way of dividing fractions without using keep change flip. Now we're going to see how that same problem is solved the short way with keep change flip and see if we get the same answer. So remember, keep the first fraction the same then we're going to change the division signs of multiplication and flip or take the reciprocal of the second fraction so it'll look like this. And of course now it's just a multiplication problem. We multiply across and we still get twelve over 35. Same answer but much, much faster. So why does keep change flip work? First we saw the long way of dividing fractions where we multiply the denominator by its reciprocal so that we end up with a one as the denominator. And then of course whenever the denominator is one the fraction is just equal to the numerator. That helped us to get to our final answer. And of course, the short way is just doing keep change, flip. It got us the same result as the long way, but much, much faster.