Comparing Fractions with the Same Numerator (3rd Grade)

What is it?

When two fractions have the same top number, compare the size of the parts. Many children think 1/8 is bigger than 1/3 because 8 is bigger than 3. The lesson cuts two bars of the same size, one into 3 equal parts and one into 8, shades 1 part of each, and slides the shaded parts side by side. The third is clearly longer: the more parts you cut a whole into, the smaller each part is.

Step by step: 1/3 and 1/8

1. Start with 2 bars that are the same size.
2. Cut the top bar into 3 equal parts and the bottom bar into 8 equal parts.
3. Shade 1 part of each bar.
4. Slide the shaded parts out and compare. The third is longer.
5. So 1/3 is more than 1/8. Same top number? Fewer parts means bigger parts.

Common mistakes

• Picking the fraction with the bigger bottom number. 8 is bigger than 3, but eighths are smaller parts.
• Comparing bars that are not the same size. Fractions of different wholes cannot be compared this way.
• Using this rule when the top numbers are different. It only works when the numerators match.

Your turn

The lesson ends with a problem to try. Pause and let your child work it out before you check.

Which is more: 3/4 or 3/8?

Answer: 3/4. Both have 3 parts, and fourths are bigger than eighths, so 3 fourths is more than 3 eighths.

Practice at home

Cut two paper strips of the same length. Fold one into 2 parts and the other into 4, or one into 3 and the other into 6, and compare one part of each. Ask your child to predict which piece is bigger before they lay them side by side.