3.NF.3: Equivalent Fractions and Comparing Fractions
Also written as 3.NF.A.3 and CCSS.MATH.CONTENT.3.NF.A.3 · Cluster: Develop understanding of fractions as numbers.
The Official Wording
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Common Core State Standards, Grade 3, Number & Operations: Fractions · Read it at the source · Checked October 14, 2026
What 3.NF.3 Means in Plain English
Third graders see that 1/2 and 2/4 are the same size, so they are the same number, and prove it with a fraction bar or number line. They write 3 as 3/1 and spot that 4/4 is 1. They compare: 3/8 is less than 3/4 because eighths are smaller.
Comparisons only work when both fractions name parts of the same whole: half a cookie is not half a cake. This year the numerators or the denominators match. In 4th grade students compare any two fractions (4.NF.2) and make equivalents by multiplying top and bottom (4.NF.1).
3.NF.3 I Can Statements
- I can show that 1/2 and 2/4 are the same number.
- I can write a whole number as a fraction, like 3 = 3/1.
- I can compare two fractions with the same top or bottom number.
3.NF.3 Worked Example
Three sandwiches the same size, three eaters, and both halves of the standard in one lunch: are two of the amounts equal, and which of two is more?
Leo ate 2/3 of his sandwich and Priya ate 4/6 of hers. Her brother ate 4/8 of his. All three sandwiches were the same size. Did Leo and Priya eat the same amount? Who ate more, Priya or her brother?
- Draw two bars the same length, because the sandwiches were the same size. Cut one into 3 equal parts and shade 2. Cut the other into 6 equal parts and shade 4.2/3 shaded on bar A, 4/6 shaded on bar B
- Line the bars up. The shaded parts end at exactly the same place. Same size means same number.2/3 = 4/6
- Why? Each third was cut in half to make sixths, so 2 thirds became 4 sixths. The pieces are smaller, but there are twice as many.each 1/3 is 2/6, so 2/3 is 4/6
- Now her brother: 4/8. Both fractions count 4 pieces, so compare the pieces. A sandwich cut into 8 has smaller pieces than one cut into 6.4 pieces each, and sixths are bigger than eighths
- Record it with the symbol and say it: four sixths is greater than four eighths because sixths are bigger pieces.4/6 > 4/8
Check it: On a number line from 0 to 1, 2/3 and 4/6 land on the same point, and 4/8 lands to their left, at the same point as 1/2.
Common Mistakes with 3.NF.3
Comparing fractions of different wholes
“My 1/2 of the small pizza is the same as your 1/2 of the large one.”
Try this: Ask “half of what?” before comparing. Draw both wholes the same size first, or say the comparison cannot be made.
Bigger denominator, bigger fraction
3/8 > 3/4 because 8 is more than 4
Try this: Cut two same-size strips, one into fourths and one into eighths. Three of the bigger pieces is more, so 3/4 is greater.
Different numbers, so different fractions
“1/2 and 2/4 can’t be equal, the numbers are different.”
Try this: Place both on one number line from 0 to 1. They land on the same point, and one point is one number.
Where 3.NF.3 Fits
Practice 3.NF.3
Quick Check
- Write 5 as a fraction.
- Compare 5/6 and 5/8 with <, > or =.
- Is 6/8 equivalent to 3/4? Explain with a model.