CCSS.Math.Content.7.NS.A.2c
The Standard
Apply properties of operations as strategies to multiply and divide rational numbers.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rearrange and group factors to make products easier, including fractions, decimals, and negative numbers. They rewrite division using reciprocals, then justify each step with a named property.
What Mastery Looks Like
- A student can simplify a multistep rational-number expression without changing its value. They choose useful pairings, distribute or factor correctly, and explain why each rewrite is valid.
Common Misconceptions
- Students may treat division as commutative or associative, so they reorder quotients incorrectly. They may distribute across multiplication instead of addition or lose a negative sign when using a reciprocal. Some think properties apply only to whole numbers.
How to Assess It
- Exit ticket: Simplify (-3/4) ÷ (3/8) × (-2). Replace division with multiplication, then label one property used to regroup or reorder factors.
Lesson moves
Ways to Teach It
Give groups signed fraction cards to build products, then physically reorder and regroup factors while recording the property used.
Ask: Why can 4 × (-3/5) × 5 be regrouped, but 4 ÷ (-3/5) ÷ 5 cannot?
Play a matching game pairing rational-number expressions with equivalent rewrites and property cards, awarding a point only after an explanation.
Compare calculating a 15 percent discount on three items separately with distributing 0.15 across the total price.
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Printable 7.NS.A.2c Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.7.NS.A.2c, with an answer key for the teacher on its own page. No account needed.
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Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.7.NS.A.2a
Students need the signed-number multiplication rules and operation properties from 2a to choose valid strategies in rational multiplication and division.
- CCSS.Math.Content.6.NS.A.1
Fraction division methods carry over when division extends to positive and negative rational numbers using operation properties.
- CCSS.Math.Content.6.EE.A.3
Using commutative, associative, and distributive properties in expressions supports choosing strategies for multiplying and dividing rational numbers.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.7.EE.B.3
Multiplying and dividing signed rational numbers with operation properties supports the target’s multi-step calculations and reasonableness checks.
- CCSS.Math.Content.HSN-VM.B.5
Scalar multiplication scales each vector component, so rational multiplication rules and properties help students compute and interpret component changes.
- CCSS.Math.Content.HSN-VM.C.7
Scalar matrix multiplication applies rational-number multiplication to each entry, so sign, fraction, and operation-property fluency supports the matrix work.
Keep exploring
Related Standards
- CCSS.Math.Content.7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- CCSS.Math.Content.3.OA.B.5
Apply properties of operations as strategies to multiply and divide.
- CCSS.Math.Content.7.NS.A.1d
Apply properties of operations as strategies to add and subtract rational numbers.
- CCSS.Math.Content.1.OA.B.3
Apply properties of operations as strategies to add and subtract.
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