4th Grade Comparing Fractions Lesson: Notes and Examples (Free PDF)

Q: How do you compare fractions with different denominators?

Rewrite both fractions with the same denominator, then compare the numerators. For 2/3 and 3/4, use twelfths: 8/12 is less than 9/12.

Q: Which is greater, 1/3 or 1/5?

1/3 is greater. When the numerators are the same, the fraction with the smaller denominator has bigger pieces. A third of a pizza is bigger than a fifth.

Q: What is a benchmark fraction?

A benchmark fraction is an easy fraction, like 1/2, that helps you judge other fractions. 3/8 is less than 1/2 and 5/8 is more than 1/2, so 3/8 is less than 5/8.

Q: Why must the wholes be the same size?

Half of a small pizza can be less than a quarter of a huge pizza. Comparisons only make sense when both fractions describe parts of the same whole.

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This 4th grade comparing fractions lesson covers comparing fractions (Common Core 4.NF.A.2), with a free PDF to print.

Key takeaway: This lesson helps fourth grade students decide which of two fractions is greater, using pictures, benchmarks, and common denominators.

Topic: Comparing Fractions (4th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 4.NF.A.2
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

To compare fractions, make the pieces easy to match. With the same denominator, the greater numerator is greater. With the same numerator, the smaller denominator is greater. Otherwise use a common denominator or compare to 1/2, then write the answer with the symbols >, < or =.

This lesson helps fourth grade students decide which of two fractions is greater, using pictures, benchmarks, and common denominators. It also teaches the symbols for greater than, less than, and equal to, and why two fractions are comparable only when they describe the same whole.

The lesson shows four ways to compare: same denominator, same numerator, a benchmark such as one half, and a common denominator. Also, number lines and fraction strips support each method. Then, plan about 20 minutes. Also, after reading, try each method on a pair you choose yourself, and see whether all four methods agree on the answer.

Grade 4 · Common Core State Standards: 4.NF.A.2

Key facts in this 4th grade comparing fractions lesson

Key facts

Compare fractions only when they are parts of the same whole.
Same denominator: compare numerators. Same numerator: compare denominators and the smaller denominator is greater.
A common denominator turns a hard comparison into a numerator comparison, such as 8/12 < 9/12.
Benchmark 1/2: a fraction is less than 1/2 when its numerator is less than half the denominator.
Record a comparison with >, < or = and check it on a number line.

How do you compare fractions?

To compare two fractions, decide which is greater, which is less, or whether they are equal. Fractions can only be compared when they are parts of the same whole. Use the symbols $>$ (greater than), $<$ (less than) and $=$ (equal to).

Four ways to compare

Same denominator: the larger numerator is greater.
Same numerator: the smaller denominator is greater, because the pieces are bigger.
Different numerators and denominators: rewrite both with a common denominator.
Use a benchmark such as $\frac{1}{2}$ to decide quickly.

What if the denominators are the same?

The pieces are the same size, so count the pieces. $\frac{5}{8} > \frac{3}{8}$ because 5 pieces are more than 3 pieces.

Same size pieces: 5 eighths is longer than 3 eighths.

What if the numerators are the same?

Now the number of pieces is the same, but the pieces differ. A fourth is bigger than an eighth, so $\frac{3}{4} > \frac{3}{8}$.

Three bigger pieces beat three smaller pieces.

How do you compare with a common denominator?

Example: Compare $\frac{2}{3}$ and $\frac{3}{4}$.

Find a common denominator. Both 3 and 4 go into 12.
Rewrite: $\frac{2}{3} = \frac{8}{12}$ and $\frac{3}{4} = \frac{9}{12}$.
Compare the numerators: 8 is less than 9.
Write the result: $\frac{2}{3} < \frac{3}{4}$.

In twelfths, 8 pieces is less than 9 pieces.

How does the benchmark $\frac{1}{2}$ help?

Check whether each fraction is less than, equal to, or more than one half. A fraction is less than $\frac{1}{2}$ when the numerator is less than half the denominator. For example, $\frac{3}{8}$ is less than $\frac{1}{2}$ because $\frac{4}{8}$ is one half. And $\frac{5}{8}$ is more than one half. So $\frac{3}{8} < \frac{5}{8}$.

The point $\frac{1}{2}$ splits the line into smaller and greater fractions.

Always check that the comparison makes sense on the number line: fractions to the right are greater.

What mistakes should you avoid?

Comparing only the denominators. A bigger denominator means smaller pieces, so $\frac{1}{8} < \frac{1}{4}$.
Comparing only the numerators when the denominators are different. Rewrite the fractions first.
Comparing different wholes. Half of a small pizza is not always less than a third of a large pizza.

When you finish, read the comparison out loud. For example, two thirds is less than three fourths. If it sounds wrong, check the common denominator again.

4th grade comparing fractions lesson: questions and answers

How do you compare fractions with different denominators?

Rewrite both fractions with the same denominator, then compare the numerators. For 2/3 and 3/4, use twelfths: 8/12 is less than 9/12.

Which is greater, 1/3 or 1/5?

1/3 is greater. When the numerators are the same, the fraction with the smaller denominator has bigger pieces. A third of a pizza is bigger than a fifth.

What is a benchmark fraction?

A benchmark fraction is an easy fraction, like 1/2, that helps you judge other fractions. 3/8 is less than 1/2 and 5/8 is more than 1/2, so 3/8 is less than 5/8.

Why must the wholes be the same size?

Half of a small pizza can be less than a quarter of a huge pizza. Comparisons only make sense when both fractions describe parts of the same whole.

How do you read the symbols > and

The open side faces the greater number, and the point faces the smaller number. So 3/4 > 3/8 reads three fourths is greater than three eighths.

Common mistakes with this 4th grade comparing fractions lesson

Students pick the fraction with the larger bottom number as the larger fraction. With the same numerator, more pieces means smaller pieces, so one eighth is less than one fourth.
Students compare numerators when the denominators differ. Three tenths is not greater than two thirds just because 3 is more than 2. Use a benchmark or a common denominator first.
Students write the symbol backward. The open side of the symbol faces the larger number, so read it as a hungry mouth that eats the bigger fraction.

How to study this chapter

Keep one half in your head as the main benchmark. Also, deciding whether each fraction is above or below one half settles many comparisons quickly.
When a common denominator is needed, choose the easiest one, often the larger denominator or a multiple of both. Fewer steps means fewer mistakes.
Parents can use a ruler or measuring cups. Showing three fourths of a cup next to five eighths makes the comparison concrete.

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