Let’s look at some examples on how we divide fractions and mixed numbers. So here’s an example: five-sixths divided by five-twelfths. How would we go about solving this? And here’s the trick: dividing a fraction by a fraction is the same thing as multiplying by the reciprocal. So look at how I’ve changed the problem. I’ve changed the division symbol to multiplication. So we’re not gonna divide anymore; we’re gonna multiply. And then I’ve taken the reciprocal of five-twelfths. I’ve flipped it and turned it into twelve-fifths. Now we can reduce the two fractions; five over five would just be one, and twelve over six would be two for a final answer of two over one or just two.
Our next example: nine-tenths divided by seven and one-fifth.
Before we deal with the division, here we wanna deal with our mixed number first. We wanna turn this mixed number into an improper fraction. So here I’ve created thirty-six fifths as the improper fraction for seven and one-fifths. Then we just copy the problem exactly how it was written.
For the next step, we wanna turn the division into multiplication and take the reciprocal of thirty-six fifths. It looks like this. Before we multiply, we can simplify; so here I’ve simplified five over ten to one-half, and here nine over thirty-six to one-fourth. Our final answer here comes out to one-eighth.
Okay here’s the next example: one-half divided by two. Even though this one looks very simple, we’re still gonna follow the same procedure: we’re going to multiply by the reciprocal for a final answer of one-fourth.
Let’s look at this question one other way as well. We start here with one-half, and we want to divide what we have, our one-half, into two pieces. This is another way to represent one-fourth. So half of our half is one-fourth.
Ten divided by one-half. I’m gonna let you think about this one for a minute. Pause the video if you need to. Did you think ten divided by one-half equals five? That’s not the case! Ten divided by one-half equals twenty, and here’s why. This problem has a division by a fraction. And when we see that, we always change it to multiplication and we flip our fraction; We use its reciprocal. This is what it would look like here. Once you change it to multiplication, the answer becomes really clear.
But maybe you’re still not understanding how ten divided by one-half could equal twenty. Let’s think about it like this. You have ten cupcakes. What would happen if you cut them all in half? Well it’s true that there would still be ten cupcakes, but you would now have twenty pieces. This is what was happening when we said ten divided by one-half equals twenty. Here’s one way that you can remember the process for dividing fractions; it goes like this: Dividing fractions is easy as pie. Flip the second and multiply.
And now it’s your turn to try.