6.NS.1: Divide Fractions by Fractions
Also written as 6.NS.A.1 and CCSS.MATH.CONTENT.6.NS.A.1 · Cluster: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
The Official Wording
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.
Common Core State Standards, Grade 6, The Number System · Read it at the source · Checked October 14, 2026
What 6.NS.1 Means in Plain English
Sixth graders divide a fraction by a fraction and know what the answer means. How many 1/4-cup scoops fill 1 1/2 cups? Six, because 1 1/2 ÷ 1/4 = 6. They draw the model, write the equation, and explain why multiplying by the reciprocal gives the same result.
The word problems come in three shapes: sharing (4 people share 2/3 pound), measuring out servings, and finding a missing side from an area. This closes the fraction arithmetic that began in 5.NF.7. In 7th grade, 7.NS.2 extends division to negative fractions and 7.RP.1 to rates with fractions.
6.NS.1 I Can Statements
- I can divide a fraction by a fraction and simplify.
- I can draw a model that shows how many 3/4s fit in 2/3.
- I can write a story problem for a fraction division.
6.NS.1 Worked Example
A serving problem where the serving is bigger than the amount, so the answer is less than one, which is exactly where students stop trusting the rule.
A yogurt tub holds 2/3 cup. A serving is 3/4 cup. How many servings is that?
- “How many 3/4s are in 2/3?” is a division question.2/3 ÷ 3/4
- Estimate first. 3/4 is bigger than 2/3, so there is less than one serving in the tub. The answer must be under 1.2/3 < 3/4, so 2/3 ÷ 3/4 < 1
- Rewrite both with twelfths so the pieces match: 2/3 is 8 twelfths, 3/4 is 9 twelfths. The question becomes how many 9s are in 8.8/12 ÷ 9/12 = 8 ÷ 9 = 8/9
- Now the rule: dividing by 3/4 is multiplying by 4/3. Same answer, and now students know why it works.2/3 × 4/3 = 8/9
Check it: Multiply back: 3/4 of 8/9 is 24/36 = 2/3, the amount in the tub.
Common Mistakes with 6.NS.1
Flipping the wrong fraction
2/3 ÷ 3/4 = 3/2 × 3/4 = 9/8
Try this: Say the rule in full, “keep, change, flip”: the first fraction stays, the division sign changes, only the divisor flips.
Dividing straight across before the denominators match
2/3 ÷ 3/4 = (2 ÷ 3)/(3 ÷ 4)
Try this: Go back to common denominators: 8/12 ÷ 9/12 is 8 ÷ 9. Dividing top by top only works once the bottoms match.
Expecting division to make things smaller
“1/2 ÷ 1/8 can’t be 4, dividing makes numbers smaller”
Try this: Ask how many 1/8-cups fill a 1/2-cup measure. Four scoops, so dividing by a fraction under 1 gives a bigger number.
Where 6.NS.1 Fits
Practice 6.NS.1
Quick Check
- 5/6 ÷ 1/3
- Four friends share 2/3 of a pan of brownies equally. How much of the pan does each get?
- A garden bed has an area of 3/4 square yard and is 1/2 yard wide. How long is it?