Equivalent fractions

Hello, and welcome to Myriora Maths! One half, two quarters, three sixths. They look different, but they're all the same amount! Fractions that are worth the same are called equivalent fractions. Let's see why.

Here's a bar with one half coloured in. Below it, a bar cut into quarters, with two quarters coloured. And a bar cut into sixths, with three sixths coloured. The coloured part is exactly the same length every time!

Why does this work? Start with one half. Now cut every piece into two. There are twice as many pieces, and twice as many coloured pieces. So one half becomes two quarters: the top and the bottom were both doubled!

So here's the rule. Multiply the top and the bottom by the same number. Three quarters, times two on the top and the bottom, is six eighths. Times three on the top and the bottom, it's nine twelfths. They're all the same amount!

Let's try one together. One third is the same as how many sixths? Say it out loud!

Two sixths! The bottom went from three to six: that's times two. So the top goes times two as well, and one times two is two.

Here's a question that catches lots of people. Is one half the same as two thirds? Some people add one to the top and the bottom, and think so. But adding changes the amount! You have to multiply, not add.

Your turn! Two thirds is the same as how many twelfths? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Three times four is twelve, so the bottom was multiplied by four. Do the same to the top: two times four is eight. So two thirds is eight twelfths!

Quick review. Equivalent fractions are worth the same amount. Cutting every piece again makes more pieces, but the same amount. To find one, multiply the top and the bottom by the same number. And never just add the same number! See you next time!