Dividing fractions

Hello, and welcome to Myriora Maths! What is three divided by one half? It isn't one and a half! There's a famous rule: flip the second fraction, and multiply. But why does it work? Let's find out.

Dividing asks: how many fit in? Three divided by one half means: how many halves fit into three? Each whole has two halves. So three wholes have six halves!

What about two divided by one quarter? Each whole has four quarters, so two wholes have eight quarters. Dividing by one quarter is the same as times four!

Now two divided by two thirds. How many two thirds fit into two? Two wholes have six thirds. Put them in groups of two thirds: that's three groups. So two divided by two thirds is three.

Look at what we did. We multiplied by three, to count the thirds. Then we divided by two, to make the groups. That's the same as times three halves: the second fraction, flipped! So keep the first, flip the second, and multiply.

Let's try one together. What is one half divided by one quarter? Say it out loud!

How many quarters fit into a half? Two! Flip and multiply: one half times four is two.

Here's a question that catches lots of people. What is three quarters divided by one half? Some people flip the first fraction instead of the second. But you keep the first fraction, and flip the one you're dividing by. Three quarters times two is six quarters: one and a half!

Your turn! What is two thirds divided by one sixth? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Keep two thirds, flip one sixth, and multiply. Two thirds times six is twelve thirds, which is four. And that makes sense: two thirds is four sixths!

Quick review. Dividing asks how many fit in. Dividing by one half is the same as times two. To divide by a fraction, keep the first, flip the second, and multiply. It works because you count the pieces, then make the groups. See you next time!