CCSS.Math.Content.5.NF.B.7
The Standard
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
Common Core State Standards for Mathematics · Number and Operations—Fractions
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students divide a unit fraction by a nonzero whole number and divide a whole number by a unit fraction. They represent each situation with models, equations, and word problems.
What Mastery Looks Like
- Students correctly find quotients such as 1/3 ÷ 4 = 1/12 and 4 ÷ 1/3 = 12. They use equations, models, and context to explain why each answer makes sense.
Common Misconceptions
- Students may think division always makes a number smaller. They may invert the wrong number, divide the denominator by the whole number, or confuse the two division situations.
How to Assess It
- Use an exit ticket: solve 1/4 ÷ 3 and 3 ÷ 1/4, then draw a model and label what each quotient means.
Lesson moves
Ways to Teach It
Have students cut fraction strips to model sharing 1/2 among three people, then record the matching equation.
Ask students to explain why 5 ÷ 1/5 is greater than 5 using words, a drawing, and an equation.
Play a card sort matching division expressions, visual models, quotients, and word problems involving unit fractions.
Use measuring cups to determine how many 1/4-cup servings can be filled from 2 cups of rice.
Free download
Printable 5.NF.B.7 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.5.NF.B.7, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
See the whole path on the Number & Operations: Fractions progression map.
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.3.NF.A.1
Students must understand unit fractions as equal parts and a/b as quantities before interpreting division with unit fractions.
- CCSS.Math.Content.3.OA.A.2
Fraction division uses the same equal-sharing and equal-groups meanings of division, extended to fractional amounts and unit fractions.
- CCSS.Math.Content.4.NF.B.4
Multiplying fractions by whole numbers supports seeing fraction division through equal groups and inverse multiplication with unit fractions.
What This Unlocks
Mastery here sets students up for these next.
Keep exploring
Related Standards
- CCSS.Math.Content.5.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- CCSS.Math.Content.4.NF.B
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
- CCSS.Math.Content.6.NS.A
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- CCSS.Math.Content.5.NF.B
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
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