5.NF.6: Fraction Multiplication Word Problems
Also written as 5.NF.B.6 and CCSS.MATH.CONTENT.5.NF.B.6 · Cluster: Apply and extend previous understandings of multiplication and division.
The Official Wording
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Common Core State Standards, Grade 5, Number & Operations: Fractions · Read it at the source · Checked October 14, 2026
What 5.NF.6 Means in Plain English
Fifth graders multiply fractions inside a story. A recipe calls for 2 1/2 cups of flour and you make half: 1/2 × 2 1/2 = 1/2 × 5/2 = 5/4, so 1 1/4 cups. They decide multiplication fits, convert the mixed number, and answer in the story’s units.
5.NF.4 supplies the arithmetic and 5.NF.5 the size check (half a recipe needs less flour). This standard puts them to work: areas of rooms, distances at a fraction of the pace, portions of portions. In 6th grade the stories add division of fractions (6.NS.1) and ratios (6.RP.3).
5.NF.6 I Can Statements
- I can tell when a word problem calls for multiplying fractions.
- I can multiply mixed numbers by changing them to fractions first.
- I can check a fraction answer against the story and an estimate.
5.NF.6 Worked Example
A fabric problem with two mixed numbers, estimated first and then multiplied, with an answer that lands on a whole number.
A rectangular tablecloth is 2 1/4 yards long and 1 1/3 yards wide. How many square yards of fabric is that?
- Area is length times width, so this is a multiplication. Estimate first: a bit more than 2 times a bit more than 1, so somewhere near 3.2 1/4 × 1 1/3, about 3
- Turn each mixed number into a fraction. Two wholes are 8 fourths, plus 1 fourth is 9/4. One whole is 3 thirds, plus 1 third is 4/3.2 1/4 = 9/4, 1 1/3 = 4/3
- Multiply tops and bottoms.9/4 × 4/3 = 36/12
- Simplify. 36 twelfths is 3 wholes exactly.36/12 = 3
Check it: Against the estimate: near 3, yes. Against the story: a cloth a bit over 2 yards by a bit over 1 yard should cover between 2 and 3 square yards, and the extra fourth and third bring it right to 3.
Common Mistakes with 5.NF.6
Multiplying the parts separately
2 1/4 × 1 1/3 = (2 × 1) and (1/4 × 1/3) = 2 1/12
Try this: Convert to fractions first, 9/4 × 4/3, or draw an area model with all four boxes, including 2 × 1/3 and 1/4 × 1.
Dividing when the story says “of”
“1/2 of 2 1/2 cups” solved as 2 1/2 ÷ 1/2 = 5 cups
Try this: Estimate before choosing an operation: half a recipe needs less flour, not more. 5 cups fails, so multiply: 1/2 × 2 1/2.
Stopping at an improper fraction with no unit
36/12
Try this: Finish in the story’s words: 36/12 is 3, and the question asked for square yards, so the answer is 3 square yards.
Where 5.NF.6 Fits
Practice 5.NF.6
Quick Check
- A recipe needs 2 1/2 cups of flour. You make half the recipe. How much flour do you use?
- A rug is 3 1/2 feet by 2 1/4 feet. What is its area?
- A trail is 4 1/2 miles long. Sam has hiked 2/3 of it. How far has he hiked?