Operations with Integers — Question 15
Back to all questions(a) Maximum possible value = [(-2) – (3 + 5)] × (-6) = (-2 – 8) × (-6) = 60 (b) Minimum possible value = [3 – (-2) + 5)] × (-6) = (3 + 2 + 5) × -6 = -60
Key Concepts Covered
This question tests your understanding of the following concepts from the chapter Operations with Integers: Use, Numbers, Exactly, Once, Operations, Brackets. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.
A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This Question
Read the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to Remember
- Always show your working steps clearly.
- Verify your answer by substituting values back into the equation.
- Practice similar problems from the textbook exercises.
- Memorise important formulae and their conditions of applicability.
Practice more questions from Operations with Integers — Mathematics, Class 7 CBSE
Chapter Overview: Integers
This chapter covers multiplication and division of integers, extending the operations learned in Class VI. Students learn sign rules for multiplication and division, properties like closure, commutative, associative, and distributive, and apply integer operations to real-world contexts like temperature changes and financial transactions.
Exam Weightage: ~6 marks | Difficulty: Medium
Key Formulas
| Formula | When to Use |
|---|---|
| (+) × (+) = (+), (+) × (-) = (-) | Sign rule for multiplication |
| (-) × (+) = (-), (-) × (-) = (+) | Sign rule for multiplication |
| a × (b + c) = a×b + a×c | Distributive property |
| a × 1 = a; a × 0 = 0 | Identity and zero property |
| Division sign rules same as multiplication | Division of integers |
Must-Know Concepts
- Sign rules: same signs → positive, different signs → negative
- Closure property holds for multiplication but NOT for division:
- Commutative and associative properties hold for multiplication but NOT for division:
- Division by zero is undefined:
- Distributive property: a × (b + c) = a×b + a×c
Common Mistakes to Avoid
- Writing (-2) × (-3) = -6 instead of +6
- Claiming division is commutative
- Dividing by zero and writing 0 as the result
Scoring Tips
- Master sign rules first — they apply to both multiplication and division
- Use the pattern approach to understand why negative × negative = positive
- Practice with number line for visual understanding
- Memorize: even number of negatives = positive result
Frequently Asked Questions
Why is negative × negative = positive?
Look at the pattern: (-3)×3=-9, (-3)×2=-6, (-3)×1=-3, (-3)×0=0. Each step adds 3. So (-3)×(-1)=3, (-3)×(-2)=6. The pattern forces the result to be positive.
Why can't we divide by zero?
Division is the inverse of multiplication. If 6÷0 = x, then x×0 should equal 6. But anything times 0 is 0, never 6. So no answer exists — division by zero is undefined.
Does closure hold for division of integers?
No. For example, 7÷2 = 3.5, which is not an integer. So integers are not closed under division.