7.NS.2: Multiply and Divide Rational Numbers
Also written as 7.NS.A.2 and CCSS.MATH.CONTENT.7.NS.A.2 · Cluster: Apply and extend previous understandings of operations with fractions.
The Official Wording
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Common Core State Standards, Grade 7, The Number System · Read it at the source · Checked October 14, 2026
What 7.NS.2 Means in Plain English
Seventh graders multiply and divide signed numbers and learn why the sign rules hold. Since 0 = -3 × (4 + (-4)) = -12 + (-3)(-4), the product (-3)(-4) has to be 12. Losing $15 a day for 4 days is 4 × (-15) = -60.
Division follows the same sign rules, and -(6/7) = (-6)/7 = 6/(-7). Long division turns any fraction into a decimal that stops, like 3/8 = 0.375, or repeats, like 0.1818… for 2/11. In 8th grade, 8.NS.1 meets numbers whose decimals do neither.
7.NS.2 I Can Statements
- I can multiply and divide positive and negative numbers.
- I can explain why a negative times a negative is positive.
- I can turn a fraction into a decimal using long division.
7.NS.2 Worked Example
One draining tank, two questions: a product of two negatives and a quotient of two negatives, each read back into the story so the sign means something.
A tank loses 2.5 gallons every minute, a rate of -2.5 gallons per minute. Compared with now, how much water was in the tank 4 minutes ago? How many minutes will it take to lose 15 gallons?
- Change in water is rate times time. Four minutes ago is time -4, so the product has two negative factors.(-2.5) × (-4)
- A negative times a negative is positive. Multiply the sizes: 2.5 × 4 = 10.(-2.5) × (-4) = 10
- Read the sign in the story: +10 means the tank held 10 more gallons 4 minutes ago, which fits a tank that is draining.10 gallons more than now
- For the second question, divide the change by the rate. Both are negative, so the quotient is positive.-15 ÷ (-2.5) = 6
- A positive time means the future: 6 minutes from now.6 minutes
Check it: Run it forward: 6 × (-2.5) = -15 gallons, the loss in the question. And 4 minutes of draining loses 4 × 2.5 = 10 gallons, which is why the tank had 10 more before.
Common Mistakes with 7.NS.2
Treating two negatives like an addition
(-6)(-3) = -18, because negative and negative make more negative
Try this: Separate the two rules out loud: adding two negatives goes further left, but multiplying two negatives gives a positive, so (-6)(-3) = 18.
Losing track of signs in a longer product
(-2)(-5)(-3) = 30
Try this: Count the negative factors before multiplying: three negatives give a negative product, so (-2)(-5)(-3) = -30.
Calling a rounded decimal exact
-5/6 = -0.83 exactly
Try this: Keep dividing until a remainder comes back: 5 ÷ 6 leaves 2 again and again, so -5/6 = -0.8333… with the 3 repeating.
Where 7.NS.2 Fits
Practice 7.NS.2
Quick Check
- Compute (-7)(-8) and (-56) ÷ 7.
- Use long division to write -3/11 as a decimal. Does it stop or repeat?
- Compute -4 × 2.5 × (-7) in the easiest order.