4.NF.4: Multiply a Fraction by a Whole Number
Also written as 4.NF.B.4 and CCSS.MATH.CONTENT.4.NF.B.4 · Cluster: Build fractions from unit fractions.
The Official Wording
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Common Core State Standards, Grade 4, Number & Operations: Fractions · Read it at the source · Checked October 14, 2026
What 4.NF.4 Means in Plain English
Fourth graders read 7/3 as seven copies of 1/3, so 7/3 = 7 × 1/3 (part a). Then 4 × 2/3 becomes four groups of two thirds, eight thirds in all: 4 × 2/3 = 8 × 1/3 = 8/3 (part b).
Part c turns it into stories: 6 runners each drink 3/4 of a liter, so 6 × 3/4 = 18/4 = 4 2/4 liters, between 4 and 5. In 5th grade the whole number becomes a fraction too, as in 2/3 × 4/5 (5.NF.4).
4.NF.4 I Can Statements
- I can write a fraction like 7/3 as 7 × 1/3.
- I can multiply a whole number by a fraction, like 4 × 2/3.
- I can solve multiplication word problems with fractions, like 6 × 3/4 liters.
4.NF.4 Worked Example
A ribbon problem for part c, solved with the unit-fraction thinking of parts a and b.
Each of 5 students needs 2/3 of a yard of ribbon for a project. How much ribbon is that in all? Between which two whole numbers of yards is the answer?
- Five students each need the same amount, so this is 5 groups of 2/3.5 × 2/3
- Each 2/3 is two pieces of size 1/3. Five groups of 2 pieces is 10 pieces.5 × 2/3 = 10 × 1/3
- Ten thirds, written as one fraction. Only the number of pieces was multiplied. The pieces are still thirds.10 × 1/3 = 10/3
- Three thirds make one yard, so 9 thirds make 3 yards, with 1 third left over.10/3 = 9/3 + 1/3 = 3 1/3
Check it: Repeated addition gives the same total: 2/3 + 2/3 + 2/3 + 2/3 + 2/3 = 10/3. Each student needs less than a yard, so the total must be less than 5 yards.
Common Mistakes with 4.NF.4
Turning 5 × 2/3 into 10/15
5 × 2/3 = (5 × 2)/(5 × 3) = 10/15
Try this: Draw the five groups of 2/3 and count the pieces: there are 10 of them, and every piece is still a third.
Stopping at the improper fraction
6 × 3/4 = 18/4, and the student cannot say how many liters that is
Try this: Ask how many fourths make one whole, then count off groups of 4: 18/4 is 4 wholes and 2/4.
Expecting more than the whole number
“5 × 2/3 has to be more than 5, because multiplying makes things bigger.”
Try this: Compare with 5 × 1 first. Each group is less than one whole, so five groups must total less than 5.
Where 4.NF.4 Fits
Practice 4.NF.4
Quick Check
- Write 7/4 as a whole number times a unit fraction.
- 4 × 3/5
- A recipe uses 3/4 cup of oats per batch. How many cups do 7 batches need, and between which two whole numbers is that?