Multiplying fractions

Hello, and welcome to Myriora Maths! What is one half times one third? Multiplying fractions sounds hard, but a square makes it easy. And the answer might surprise you: it's smaller than both! Let's see.

Times means of. So one half times one third means one half of one third. Here's a square. Colour one third of it. Now take half of that third. That's one small piece out of six: one sixth!

Let's try two thirds times three quarters. Split the square into three columns, and colour two of them. Then split it into four rows, and colour three of them. There are twelve small boxes altogether, and six are coloured twice. That's six twelfths, which is one half!

So here's the rule. Multiply the tops, and multiply the bottoms. The bottoms make the number of small boxes. The tops make the boxes coloured twice. Two times three is six, and three times four is twelve.

Notice that one sixth is smaller than one half, and smaller than one third. When you take a part of a part, you get less. So multiplying by a fraction smaller than one makes things smaller!

Let's try one together. What is one half times three quarters? Say it out loud!

Multiply the tops: one times three is three. Multiply the bottoms: two times four is eight. Three eighths!

Here's a question that catches lots of people. Is one half times one third bigger than one half? Some people say yes, because multiplying makes things bigger. But half of a third is only one sixth! Multiplying by a fraction smaller than one makes things smaller.

Your turn! What is two fifths times one third? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Multiply the tops: two times one is two. Multiply the bottoms: five times three is fifteen. Two fifteenths!

Quick review. Times means of: one half times one third is half of a third. Multiply the tops, and multiply the bottoms. A square split into rows and columns shows why. And multiplying by a fraction smaller than one makes things smaller. See you next time!