Myriora Games
English

Myriora Maths › Maths foundations › Chapter 9: Fractions

Comparing fractions

Ages 7–9Chapter 9 · Lesson 5

In this lesson

Your turn

Which is bigger: three fifths, or two thirds?

Show the answer

Both can be made into fifteenths. Three fifths is nine fifteenths. Two thirds is ten fifteenths. So two thirds is bigger!

The common mistake

Here's a question that catches lots of people. Which is bigger: three eighths, or two thirds? Some people say three eighths, because its numbers are bigger. But eighths are small pieces! Three eighths is nine twenty-fourths, and two thirds is sixteen twenty-fourths.

Try it at home

Pick two fractions, like 2/3 and 3/5. Draw two bars the same length to check which is bigger, then check by working it out.

Read the whole lesson

Hello, and welcome to Myriora Maths! Which is bigger: two thirds, or three quarters? It's hard to tell, because the pieces are different sizes. The trick is to make the pieces the same size first. Let's see how!

When the bottom numbers are the same, it's easy. Three sevenths and five sevenths have the same size pieces. Five pieces are more than three pieces, so five sevenths is bigger.

When the top numbers are the same, look at the bottoms. Three quarters and three eighths both have three pieces. But eighths are smaller pieces! So three quarters is bigger.

Now two thirds and three quarters. The pieces are different sizes. So let's cut both bars into twelfths, because twelve is in the three times table and the four times table. Two thirds is eight twelfths. Three quarters is nine twelfths. Nine is more than eight, so three quarters is bigger!

So here's the method. First, find a bottom number that both bottoms go into. Then change both fractions, multiplying the top and the bottom. Now just compare the tops!

Let's try one together. Which is bigger: one half, or three fifths? Say it out loud!

Both can be made into tenths. One half is five tenths. Three fifths is six tenths. So three fifths is bigger!

Here's a question that catches lots of people. Which is bigger: three eighths, or two thirds? Some people say three eighths, because its numbers are bigger. But eighths are small pieces! Three eighths is nine twenty-fourths, and two thirds is sixteen twenty-fourths.

Your turn! Which is bigger: three fifths, or two thirds? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Both can be made into fifteenths. Three fifths is nine fifteenths. Two thirds is ten fifteenths. So two thirds is bigger!

Quick review. When the bottom numbers are the same, compare the tops. When the tops are the same, the smaller bottom wins, because its pieces are bigger. When they're different, make the bottoms the same first. And bigger numbers don't always mean a bigger fraction! See you next time!