Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
These 20 problems cover standards 7.NS.A.2a, 7.NS.A.2b and 7.NS.A.2c: sign rules for products and quotients, why (−1)(−1) = 1, division by zero, and the signs in fractions.
You will use integers, decimals and fractions, then finish with real-world rates and short proofs. Count the negative signs before you multiply.
Standards: 7.NS.A.2a, 7.NS.A.2b, 7.NS.A.2c · Level: Grade 7
Problem 1 Five Products ★★★
Find each product.
- 6 × (−7)
- (−8) × 5
- (−9)(−4)
- (−12)(−1)
- 0 × (−15)
Problem 2 Four Quotients ★★★
Find each quotient.
- −56 ÷ 8
- 72 ÷ (−9)
- −45 ÷ (−5)
- 0 ÷ (−6)
Problem 3 Sign of a Long Product ★★★
Decide whether each product is positive or negative, and then find it.
- (−3)(−2)(−5)(4)
- (−2)(−6)(−1)(−3)
Problem 4 Jumps on a Number Line ★★★
Use the number line to model 4 × (−3) as four jumps from 0, each of size −3.
Problem 5 Falling Temperature ★★★
The temperature falls 3°F every hour for 5 hours, starting at 8°F. What is the temperature after 5 hours?
Problem 6 Pattern for Two Negatives ★★★
Complete the pattern, and explain what it shows about the product of two negative numbers.
Problem 7 Decimal Products ★★★
Find each product.
- (−2.5)(4.2)
- (−0.6)(−0.35)
Problem 8 Fraction Products ★★★
Find each product in simplest form.
- (−23)(910)
- (−58)(−415)
Problem 9 Fraction Quotients ★★★
Find each quotient in simplest form.
- (−34) ÷ 916
- (−56) ÷ (−512)
Problem 10 Division and Zero ★★★
Evaluate each expression, or write undefined.
- 0 ÷ (−8)
- −7 ÷ 0
- Explain, using multiplication, why −7 ÷ 0 has no answer.
Problem 11 Equivalent Forms of a Fraction ★★★
Which expressions equal −811? Check each one.
Problem 12 Distributive Property with a Negative ★★★
Evaluate −4 × (10 − 3) in two ways and compare the results.
Problem 13 Descending Drone ★★★
A drone descends 7.5 feet every second for 6 seconds, starting at a height of 120 feet. What is its change in height and its final height?
Problem 14 Average Change ★★★
Four daily temperature changes are −3°F, −7°F, 2°F and −4°F. Find the mean daily change.
Problem 15 Monthly Fees ★★★
A bank charges a fee of $4.25 per month. An account starts at $50.00 and gets no deposits for 7 months. Write the total change as a product, find the balance, and find how many fees add up to a total change of −$29.75 using division.
Problem 16 Evaluating with Variables ★★★
Evaluate each expression for a = −6, b = 4 and c = −2.
- ab ÷ c
- a ÷ (bc)
- abc
Problem 17 Mountain Temperatures ★★★
The air temperature falls 3.5°F for every 1,000 feet of climb. A hiker starts at 2,000 feet where it is 61°F and climbs to 9,000 feet. What is the temperature at 9,000 feet?
Problem 18 Stock Price Changes ★★★
A stock loses $1.35 per share each day for 6 days and then gains $0.90 per share each day for 4 days. It started at $42.00 per share. Find the net change per share, the final price, and the total change for 200 shares.
Problem 19 Why (−1)(−1) = 1 ★★★
Complete the reasoning that proves (−1)(−1) = 1. Start from 0 = (−1) × 0 = (−1) × (1 + (−1)). Use the distributive property and explain each step.
Problem 20 Submarine Rates ★★★
A submarine at −40 meters descends 12.5 meters per minute for 8 minutes, then rises 20 meters per minute for 3.5 minutes. Find its final position and its net change in position.
