Integers — Previous Year Questions (Class 7 Mathematics)
Master integer operations including multiplication and division. Strengthen algebraic foundations with signed number rules.
TL;DR: Master integer operations including multiplication and division. Strengthen algebraic foundations with signed number rules.
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Master integer operations including multiplication and division. Strengthen algebraic foundations with signed number rules.
Integers — Previous Year Questions with Solutions
Q (2023, 2 marks): Multiply: (-8) × 5 and (-7) × (-6). Compare the results.
Answer: (-8) × 5 = -40
(-7) × (-6) = +42
Comparison: 42 > -40
Q (2022, 2 marks): Divide: (-36) ÷ 4 and (-45) ÷ (-9).
Answer: (-36) ÷ 4 = -9
(-45) ÷ (-9) = +5
Rules: Negative ÷ Positive = Negative; Negative ÷ Negative = Positive
Q (2023, 3 marks): Simplify: 8 + (-3) × 2 - 5 ÷ 1
Answer: 8 + (-3) × 2 - 5 ÷ 1
Applying order of operations (BODMAS):
= 8 + (-6) - 5
= 8 - 6 - 5
= 2 - 5
= -3
Q (2022, 2 marks): The product of two integers is -24. If one integer is 6, find the other.
Answer: Let the other integer be x.
6 × x = -24
x = -24 ÷ 6
x = -4
Verification: 6 × (-4) = -24 ✓
Q (2023, 3 marks): A lift goes down 5 meters per second. After 8 seconds, how many meters below the starting point is the lift?
Answer: Going down is represented as negative.
Distance per second: -5 meters
Time: 8 seconds
Total distance = (-5) × 8 = -40 meters
The lift is 40 meters below the starting point.
Q (2022, 3 marks): Verify: (-a) × b × c = -(abc), using a = 2, b = 3, c = 4
Answer: LHS: (-a) × b × c = (-2) × 3 × 4 = -24
RHS: -(abc) = -(2 × 3 × 4) = -24
LHS = RHS, hence verified.
Frequently Asked Questions
What are the multiplication rules for integers?
Positive × Positive = Positive; Negative × Negative = Positive; Positive × Negative = Negative; Negative × Positive = Negative. In short: Same signs give positive, different signs give negative.
Is the commutative property true for integer division?
No, integer division is not commutative. For example, 12 ÷ 4 = 3, but 4 ÷ 12 is not an integer. Division is not commutative for any numbers.
More Class 7 Mathematics PYQs
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