Which fraction is bigger?
for 2nd grade

2nd grade : Compare fractions - which fraction is bigger?

Knowing which fraction is bigger or smaller is not always obvious. If we compare fractions that have the same number on the bottom (the denominator) like ⅖, ⅗ and ⅘, then the bigger the number on the top (the numerator) the bigger the fraction is.

If we compare ⅘ to ⅖, we can see that these two fractions have the same denominator of 5. The numerators are 4 and 2. So we can say that ⅘ is the bigger of these two fractions. This makes sense because if I have ⅘ of a pie, that is more of the pie than if I have only got ⅖ of the pie.

There is another type of fraction that we need to talk about, unit fractions.
A unit fraction is the name for a fraction where the number on the top is a 1.

So ½ is a unit fraction and so are ⅐ and ⅛ but ⅖ is not because it's numerator is not 1, it is 2.

Comparing unit fractions to find the biggest is not as easy as our first example. If we think about the two most common unit fractions, ¼ and ½, we will see why. Which is bigger, ¼ of a cake or ½ a cake? The answer is that ½ a cake is a bigger share of the cake than ¼ of a cake even though the denominator of ½, which is 2, is smaller than the denominator of ¼, which is 4.

In the same way, if we compare ¼ with ⅛ to decide which is bigger, we will find that a ¼ share of that nice cake is a bigger share of the cake than a ⅛ share. So ¼ is a bigger fraction than ⅛.

So now we can compare some fractions with the same denominator, and we can compare some unit fractions, and we can decide which is the biggest and which is the smallest.