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Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 7.NS.A.2a, 7.NS.A.2b, 7.NS.A.2c · Level: Grade 7
Problem 1 Five Products
(a) Different signs: −42.
(b) Different signs: −40.
(c) Same signs: 36.
(d) Same signs: 12.
(e) Zero times anything is 0.
Answer: −42, −40, 36, 12, 0
Problem 2 Four Quotients
(a) −7, since 8 × (−7) = −56.
(b) −8, since (−9)(−8) = 72.
(c) 9, since (−5)(9) = −45.
(d) 0.
Answer: −7, −8, 9, 0
Problem 3 Sign of a Long Product
(a) Three negative factors (odd), so negative: 3 × 2 × 5 × 4 = 120, giving −120.
(b) Four negative factors (even), so positive: 2 × 6 × 1 × 3 = 36.
Answer: −120 and 36
Problem 4 Jumps on a Number Line
Each jump moves 3 units left: −3, −6, −9, −12.
Answer: 4 × (−3) = −12
Problem 5 Falling Temperature
Change: 5 × (−3) = −15.
8 + (−15) = −7.
Answer: −7°F
Problem 6 Pattern for Two Negatives
The products rise by 2 each row: after −2 comes 0, then 2, then 4.
So 0 × (−2) = 0, (−1)(−2) = 2 and (−2)(−2) = 4.
Answer: 0, 2, 4; the product of two negative numbers is positive
Problem 7 Decimal Products
(a) 2.5 × 4.2 = 10.5, and the signs differ: −10.5.
(b) 0.6 × 0.35 = 0.21, and the signs match: 0.21.
Answer: −10.5 and 0.21
Problem 8 Fraction Products
(a) 23 × 910 = 1830 = 35; signs differ: −35.
(b) 58 × 415 = 20120 = 16; signs match: 16.
Answer: −35 and 16
Problem 9 Fraction Quotients
(a) −34 × 169 = −4836 = −43 = −1 13.
(b) 56 × 125 = 6030 = 2, positive because the signs match.
Answer: −1 13 and 2
Problem 10 Division and Zero
(a) 0 ÷ (−8) = 0, since (−8) × 0 = 0.
(b) −7 ÷ 0 is undefined.
(c) If −7 ÷ 0 = q, then q × 0 would have to equal −7. But any number times 0 is 0, so no such q exists.
Answer: 0; undefined; no number times 0 gives −7
Problem 11 Equivalent Forms of a Fraction
(a) 8−11: different signs, so negative, −811. Yes.
(b) −8−11: same signs, so 811. No.
(c) −(811) = −811. Yes.
(d) −(−811) = 811. No.
Answer: (a) and (c)
Problem 12 Distributive Property with a Negative
Way 1: −4 × 7 = −28.
Way 2: −4 × 10 + (−4) × (−3) = −40 + 12 = −28.
Answer: Both ways give −28
Problem 13 Descending Drone
Change: 6 × (−7.5) = −45.
Final height: 120 + (−45) = 75.
Answer: −45 feet; 75 feet
Problem 14 Average Change
Sum: −3 + (−7) + 2 + (−4) = −12.
−12 ÷ 4 = −3.
Answer: −3°F per day
Problem 15 Monthly Fees
Change: 7 × (−4.25) = −29.75.
Balance: 50.00 + (−29.75) = 20.25.
Number of fees: −29.75 ÷ (−4.25) = 7.
Answer: −$29.75; $20.25; 7 fees
Problem 16 Evaluating with Variables
(a) (−6)(4) = −24, and −24 ÷ (−2) = 12.
(b) bc = −8, and −6 ÷ (−8) = 34.
(c) (−6)(4)(−2) = 48.
Answer: 12, 34, 48
Problem 17 Mountain Temperatures
The climb is 9,000 − 2,000 = 7,000 feet, which is 7 thousands.
Change: 7 × (−3.5) = −24.5.
61 + (−24.5) = 36.5.
Answer: 36.5°F
Problem 18 Stock Price Changes
Losses: 6 × (−1.35) = −8.10. Gains: 4 × 0.90 = 3.60.
Net per share: −8.10 + 3.60 = −4.50.
Final price: 42.00 − 4.50 = 37.50.
200 shares: 200 × (−4.50) = −900.
Answer: −$4.50 per share; $37.50; −$900
Problem 19 Why (−1)(−1) = 1
1 + (−1) = 0, so (−1)(1 + (−1)) = (−1) × 0 = 0.
Distribute: (−1)(1) + (−1)(−1) = −1 + (−1)(−1).
So −1 + (−1)(−1) = 0. The number that must be added to −1 to give 0 is its opposite, 1.
Answer: (−1)(−1) = 1
Problem 20 Submarine Rates
Descent: 8 × (−12.5) = −100, so the position is −40 + (−100) = −140.
Rise: 3.5 × 20 = 70, so the position is −140 + 70 = −70.
Net change: −70 − (−40) = −30.
Answer: −70 meters; net change −30 meters