Comparing unlike fractions

What is this skill?

Comparing fractions means deciding which of two fractions is larger, or whether they are equal, when the denominators are different. Is 5/8 more or less than 2/3? Fourth graders write each comparison with >, < or = and must be able to explain why.

There are two main strategies. The first is to rewrite both fractions with a common denominator. 5/8 and 2/3 both become twenty-fourths (15/24 and 16/24), and then it is easy to see that 5/8 is a little smaller. The second is to compare each fraction with a benchmark such as 1/2 or 1. 7/8 is more than 1/2 because 4/8 is one half and 7/8 is more than 4/8. Children use number lines, bars and circles to see that fractions are numbers with a size, not two separate whole numbers.

Why it matters

Comparing is how children come to see fractions as real quantities. Being able to say which is bigger, 3/4 of a pizza or 2/3 of it, makes fractions meaningful in everyday life, from recipes to sharing to measuring.

The common-denominator move is exactly the one needed to add and subtract fractions with unlike denominators in fifth grade. A child who practices it now will find that later work feels familiar. Benchmarks also build estimation, which helps a child notice when an answer cannot be right, such as a claim that 1/5 is bigger than 1/2.

Common mistakes

• Comparing the numerators or the denominators alone. 1/6 is not bigger than 1/4 just because 6 is bigger than 4.
• Comparing across different-sized wholes, as when the pictures are not drawn to the same size.
• Finding a common denominator but changing only the bottom number. The top has to be multiplied by the same amount.
• Missing that two fractions can be equal even when they look very different, like 2/4 and 4/8.
• Choosing the wrong symbol because the arrow points the wrong way. A small habit helps: the open end faces the bigger number.

How to help at home

• Compare real portions: “Would you rather have 3/8 or 1/2 of the cake?” and have your child give a reason.
• Use a measuring cup set. Pouring 1/3 cup and 1/4 cup into a larger cup shows which is more.
• Practice the half benchmark. For any fraction ask, “Is it more or less than one half?”
• Mark fractions on a number line from 0 to 1 and see how they fall in order.
• Ask for the reason, not just the symbol: “How do you know?” is the question that builds the skill.

Worked examples

These are real questions from the Tutorsaurus comparing unlike fractions practice, with the answers worked out.

1. Example 1

   3/6 ? 5/12

   Choices: >, <, =

   Answer: >. Use a common denominator of 12: 3/6 = 6/12. So 3/6 > 5/12.

2. Example 2

   7/8 ? 1/2

   Choices: >, <, =

   Answer: >. Use a common denominator of 8: 1/2 = 4/8. So 7/8 > 1/2.

3. Example 3

   2/6 ? 11/12

   Choices: >, <, =

   Answer: <. Use a common denominator of 12: 2/6 = 4/12. So 2/6 < 11/12.