In mathematics we use the acronym KFC for the short cut method of dividing a fraction by a fraction. In the below expression we have a fraction divided by a fraction.

We apply KFC by keeping the first fraction the same, flipping the second fraction (its reciprocal), and changing division to multiplication. This allows us to rewrite it as the expression below.

Now it’s just a matter of multiplying numerators and denominators to get the below solution.

But why does it work? How do we know for sure that this is really the right solution. It doesn’t appear hard or logical and it just requires that we trust a shortcut. So here is the background for why this shortcut works.

First we begin by turning the expression into an equation. The “x” stands for the unknown solution.

Now we know that to undo an operation we do the inverse. In this case we are dividing by four fifths, so now we will multiply by four fifths to undo it. Remembering the golden rule of equations, whatever we do to one side we do to the other. So we multiply the right side by four fifths as well.

This reduces the left side to two thirds and the right multiplies to 4x over 5.

Now we have two fractions equal to each other. The shortcut here would be to cross multiply, but we’ll do this the long way, too (just for funzies!)

We multiply both sides by one of the denominators to cancel it out.

Then, we multiply both sides by the other denominator to cancel it out.

Now we undo the multiplication of 12 times “x” by dividing both sides by 12 and then that gives us our solution.

Now we see that the shortcut KFC does indeed gives us the same solution but without all the extra steps!

If you have any other math questions or want other explanations, please feel free to comment below!