Comparing fractions with the same denominator | Math | 3rd grade | Khan Academy

Let's compare ( \frac{2}{4} ) and ( \frac{3}{4} ). First, let's think about what these fractions mean. ( \frac{2}{4} ) means we have some whole and we've split it into four equal size pieces, and we get two of those pieces. Maybe we could think about pizza as an example. We split a pizza into four equal size pieces, and we ate two of them.

( \frac{3}{4} ) means that same whole, that same pizza, was again split into four equal size pieces, but this time what's different is we got three of the pieces. So maybe from that description, we can start to think about which one is larger. But let's also draw them to be sure that we can decide which one is larger.

So for ( \frac{2}{4} ), we're going to have a fraction that represents maybe a pizza. It's going to be divided and split into four equal size pieces. These may not be perfect lines, but they should represent four equal size pieces, and we get two of those pieces. So this represents ( \frac{2}{4} ).

For ( \frac{3}{4} ), again, we will have the same four equal size pieces, but this time we get three of the four. So one, two, three of the four pieces, and this will represent ( \frac{3}{4} ).

Now we can look at it visually and see very clearly that ( \frac{3}{4} ) is greater or takes up more space. Or we can say that ( \frac{2}{4} ) is less than ( \frac{3}{4} ). Remember, this is the less than symbol because we always want this open bigger side facing our larger number, and in this case, it's facing the second number. So we'll say ( \frac{2}{4} ) is less than ( \frac{3}{4} ). Each of these fourths is the same size, so two of them is less than three of the fourths.

Here we can try one more, but this time let's not draw the picture. Let's just think about what they mean and see if we can figure it out. So for ( \frac{5}{8} ), we have a whole and it's been divided into eight equal pieces. For ( \frac{3}{8} ), the same thing, eight equal pieces. But here in ( \frac{5}{8} ), we get five of those pieces, and in ( \frac{3}{8} ), we get three of the pieces.

So the pieces are the same size; they're eighths on both sides. These are eighths, and these are eighths. But here we have five of the eighths, and here we have three. So if the pieces are the same size, five pieces is greater than three pieces, or ( \frac{5}{8} ) is greater than ( \frac{3}{8} ).

Here, our open end, our bigger side, is still facing our bigger number, but our bigger number is first this time. So this is the greater than symbol: ( \frac{5}{8} ) is greater than ( \frac{3}{8} ).