4.NF.2: Compare Two Fractions
Also written as 4.NF.A.2 and CCSS.MATH.CONTENT.4.NF.A.2 · Cluster: Extend understanding of fraction equivalence and ordering.
The Official Wording
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Common Core State Standards, Grade 4, Number & Operations: Fractions · Read it at the source · Checked October 14, 2026
What 4.NF.2 Means in Plain English
Fourth graders compare fractions like 5/8 and 3/5, where neither the tops nor the bottoms match. They rewrite both as fortieths (25/40 and 24/40), match the numerators, or hold each up against 1/2, then write 5/8 > 3/5 and back it with a model.
A comparison only counts when both fractions describe the same whole: 1/2 of a small pizza can be less than 1/3 of a large one. Equivalent fractions (4.NF.1) do most of the work, and in 5th grade the same benchmark sense checks fraction sums (5.NF.2).
4.NF.2 I Can Statements
- I can compare two fractions by finding a common denominator.
- I can compare a fraction to 1/2 to decide which is bigger.
- I can record a comparison with >, = or < and explain it.
4.NF.2 Worked Example
Two runners on the same track, so the whole is the same mile, and three different ways to settle who ran farther.
On the same track, Ana ran 3/4 of a mile and Ben ran 5/6 of a mile. Who ran farther? Then compare Ben’s 5/6 mile with Cara’s 2/5 mile.
- Both distances are parts of the same mile on the same track, so comparing them makes sense.same whole: 1 mile
- Neither the tops nor the bottoms match. Find a denominator that both 4 and 6 go into: 12.3/4 = 9/12, 5/6 = 10/12
- Now the pieces are the same size, so count them. Ten twelfths is more than nine twelfths.10/12 > 9/12, so 5/6 > 3/4
- Check another way: each runner is one piece short of a full mile. Ana is 1/4 short, Ben only 1/6 short, and a sixth is the smaller piece.1 − 3/4 = 1/4, 1 − 5/6 = 1/6, and 1/6 < 1/4
- Cara ran 2/5 of a mile. No common denominator needed: 2/5 is less than half, and 5/6 is more than half.2/5 < 1/2 < 5/6, so 2/5 < 5/6
Check it: On a fraction chart, the 5/6 bar ends past the 3/4 bar, and the 2/5 bar stops short of the 1/2 line.
Common Mistakes with 4.NF.2
Reading eighths as bigger than sixths
1/8 > 1/6, “because 8 is more than 6”
Try this: Shade 1/6 and 1/8 on bars of the same length. Eighths are the smaller pieces, because the whole is shared among more parts.
Comparing only the numerators
3/8 > 2/3, “because 3 is more than 2”
Try this: Check each fraction against 1/2 first: 3/8 is less than half and 2/3 is more, so 2/3 is bigger.
Forgetting to ask “of what?”
“Jo ate 1/4 of a large pizza and Sam ate 1/3 of a small one, so Sam ate more.”
Try this: Draw the two wholes at their real sizes before comparing. The symbols >, = and < only work when both fractions share one whole.
Where 4.NF.2 Fits
Practice 4.NF.2
Quick Check
- Compare 4/5 and 5/8 with >, = or <.
- Which is greater, 3/10 or 4/7? Use 1/2.
- Compare 2/3 and 6/9.