Comparing fractions

A tape diagram is a long bar that shows a whole. We cut the bar into equal parts to show fractions.

Sometimes two fractions have the same number on top. That means they use the same number of pieces, but the pieces can be different sizes.

The bottom number tells you how many equal pieces make the whole. More pieces means smaller pieces.

Try 2/3 and 2/5. Both use 2 pieces.

Cut one bar into 3 equal parts and shade 2 of them. Cut another bar the same length into 5 equal parts and shade 2 of them.

The thirds are big pieces. The fifths are small pieces. Two big pieces take up more space than two small pieces.

So 2/3 is bigger than 2/5.

Remember: when the top numbers match, the smaller bottom number wins, because its pieces are bigger.

Comparing fractions means figuring out which one is bigger.

Step 1: Look at the bottom numbers. Are they the same? The bottom number is called the denominator.

Step 2: If the bottom numbers are the same, the pieces match. Now just look at the top numbers. The bigger top number wins. So 5/7 is bigger than 2/7 because 5 is more than 2.

Step 3: If both fractions have 1 on top, like 1/3 and 1/6, it flips. Each one is a single piece, so the smaller bottom number wins. 1/3 is bigger than 1/6 because thirds are bigger pieces than sixths.

Step 4: Say why. Big bottom number means tiny pieces. Small bottom number means big pieces.

You can also draw two same-size bars or circles and shade them. Seeing the pieces helps your brain believe the answer.

Some fractions have the same top number, or top numbers that are close. These are easy to compare.

Let us compare 3/5 and 3/8.

Both have 3 on top. Both take 3 pieces of a whole.

But the pieces are not the same size. Fifths are bigger pieces than eighths. Cutting a whole into 5 parts makes each part bigger than cutting it into 8 parts.

So 3/5 is bigger than 3/8.

Try it with a drawing. Draw two rectangles the same size. Split one into 5 parts and shade 3. Split the other into 8 parts and shade 3. The first shading covers more of its rectangle.

The rule to remember: when the top numbers are the same, look at the bottom numbers. The smaller bottom number makes the bigger fraction.

A fraction tells us about parts of a whole. In a fraction like 3/4, the whole is cut into 4 equal parts and we take 3 of them.

You can show fractions in many ways. Shade part of a rectangle. Mark a spot on a number line. Circle part of a group of things.

You can also compare two fractions to see which is bigger.

When the bottom numbers are the same, the pieces match. Then the fraction with the bigger top number is bigger. 5/6 is more than 2/6 because both are sixths and 5 is more than 2.

You can check with a picture. Shade 5 parts out of 6, then shade 2 parts out of 6 in another same-size shape. The first one has more shaded.

Fractions are friendly once you remember: the bottom number sizes the pieces, and the top number counts them.