4.NF.1: Explain and Make Equivalent Fractions
Also written as 4.NF.A.1 and CCSS.MATH.CONTENT.4.NF.A.1 · Cluster: Extend understanding of fraction equivalence and ordering.
The Official Wording
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Common Core State Standards, Grade 4, Number & Operations: Fractions · Read it at the source · Checked October 14, 2026
What 4.NF.1 Means in Plain English
Fourth graders show why 2/3 equals 8/12: cut each third of a fraction bar into 4 equal pieces, and the 2 shaded thirds become 8 shaded twelfths. There are four times as many pieces, each a quarter the size, and the shaded amount never moves.
From that picture comes the rule: multiply the top and bottom by the same number, so 3/5 = 6/10 = 9/15. Equivalent fractions drive comparing (4.NF.2) and tenths as hundredths (4.NF.5), and in 5th grade they make unlike denominators addable (5.NF.1).
4.NF.1 I Can Statements
- I can show with a fraction bar that 2/3 and 8/12 match.
- I can explain why the pieces change but the amount does not.
- I can make equivalent fractions by multiplying top and bottom by one number.
4.NF.1 Worked Example
One fraction bar, cut again, so the name of the fraction changes while the shaded part stays exactly where it was.
Maya shaded 2/3 of a fraction bar. Her partner says the same shading shows 8/12. Is he right? Prove it with the bar, then find two more fractions equal to 2/3.
- Draw a bar, cut it into 3 equal parts and shade 2 of them.2 of 3 parts shaded: 2/3
- Cut every third into 4 equal pieces. The whole bar now has 3 × 4 pieces.3 × 4 = 12 pieces in the whole
- Each shaded third became 4 shaded pieces. Nothing new was shaded, the old shading was only cut up.2 × 4 = 8 shaded pieces, so 8/12
- There are 4 times as many pieces, and each one is 4 times smaller, so the amount is the same. That is the rule: multiply top and bottom by the same number.2/3 = (4 × 2)/(4 × 3) = 8/12
- Cut each third in 2 or in 5 instead and you get two more names for the same amount.2/3 = 4/6 = 10/15
Check it: On a number line from 0 to 1 marked in twelfths, count 8 twelfths: you land on the same point as the second mark of a line marked in thirds.
Common Mistakes with 4.NF.1
Adding the same number to top and bottom
2/3 = 3/4, “because I added 1 to both”
Try this: Shade both on bars of the same length: 3/4 reaches past 2/3. Cutting pieces multiplies the count of parts, it never adds to it.
Multiplying only the denominator
2/3 = 2/12
Try this: Ask how many pieces each shaded third turned into. Four pieces each means the numerator is multiplied by 4 too, giving 8/12.
Bigger numbers read as a bigger fraction
“8/12 is more than 2/3, because 8 is more than 2.”
Try this: Lay the 2/3 bar on top of the 8/12 bar so the shaded ends line up. More pieces, but each piece is smaller.
Where 4.NF.1 Fits
Practice 4.NF.1
Quick Check
- Fill in the missing number: 3/4 = ?/12
- Write two fractions equivalent to 2/5.
- Is 5/6 equivalent to 10/12? Explain.