CCSS.Math.Content.7.NS.A.2
The Standard
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Common Core State Standards for Mathematics · The Number System
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students multiply and divide positive and negative rational numbers written as integers, fractions, or decimals. They determine the sign, calculate the magnitude, and connect division to multiplication by a reciprocal.
What Mastery Looks Like
- Students accurately multiply and divide positive and negative integers, fractions, and decimals. They simplify results, use reciprocals correctly, and explain the sign using a rule or related multiplication equation.
Common Misconceptions
- Students often apply the addition sign rules to multiplication and division. They may forget to multiply by the reciprocal when dividing fractions or try to divide by zero. Some assume every rational-number quotient has a terminating decimal.
How to Assess It
- Give an exit ticket: Calculate (-3/4)(8/9) and (-2.4) ÷ 0.6, then explain how you determined each sign.
Lesson moves
Ways to Teach It
Give pairs fraction strips and sign cards to model magnitudes, assign signs, and check four rational-number products and quotients.
Ask students to explain why a negative divided by a negative is positive using a related multiplication equation.
Run a card sort matching rational-number expressions, simplified answers, and written sign explanations.
Have students calculate gains and losses per day from a weekly account change, including positive and negative fractional amounts.
Free download
Printable 7.NS.A.2 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.7.NS.A.2, 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 The Number System progression map.
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.6.NS.A.1
Fraction quotient models and equations carry over when dividing positive and negative rational numbers, especially signed fractions.
- CCSS.Math.Content.6.NS.C.6
Locating positive and negative rational numbers supports understanding signs and magnitudes when multiplying and dividing rational numbers.
- CCSS.Math.Content.5.NF.B.4
Multiplying fractions carries into rational-number multiplication, with grade 7 adding negatives and division rules.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.7.NS.A.3
Solving rational-number problems with all four operations requires knowing when and how to multiply and divide rational numbers.
- CCSS.Math.Content.HSN-VM.B.5b
Signed rational multiplication and absolute value support understanding how a scalar changes a vector’s length and reverses direction when negative.
- CCSS.Math.Content.HSN-RN.A.1
Multiplying and dividing rational numbers supports working with fractional exponents when extending integer exponent rules to radicals.
- CCSS.Math.Content.HSN-VM.B.5a
Component-wise vector scaling requires multiplying coordinates by positive, negative, and fractional scalars, including sign changes for direction reversal.
Keep exploring
Related Standards
- CCSS.Math.Content.6.NS.A
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- CCSS.Math.Content.7.NS.A
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
- CCSS.Math.Content.5.NF.B
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
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