Operations with Integers — Class 7 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Operations with Integers" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Operations with Integers" — 8 important questions with detailed answers for CBSE bo…
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Key Questions Covered:
- What are integers? Explain with 5 examples and show them on a number line.
- Add: (-15) + (-8) and (-20) + 13. Explain your steps.
- Subtract: 12 - (-8) and (-5) - 6. Show the steps clearly.
- Multiply: (-6) × 5, (-4) × (-9), and 0 × (-15). Explain the sign rules.
- Divide: (-36) ÷ 6, (-48) ÷ (-8), and 0 ÷ (-5). State the sign rules for divis…
- Name and verify the commutative property for addition and multiplication usin…
- + 2 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| What are integers? Explain with 5 examples and show them … | ✓ Solved |
| Add: (-15) + (-8) and (-20) + 13. Explain your steps. | ✓ Solved |
| Subtract: 12 - (-8) and (-5) - 6. Show the steps clearly. | ✓ Solved |
| Multiply: (-6) × 5, (-4) × (-9), and 0 × (-15). Explain t… | ✓ Solved |
| Divide: (-36) ÷ 6, (-48) ÷ (-8), and 0 ÷ (-5). State the … | ✓ Solved |
| Name and verify the commutative property for addition and… | ✓ Solved |
Showing 6 of 8 questions
Q1: What are integers? Explain with 5 examples and show them on a number line.
Definition of Integers:
Integers are whole numbers including zero, positive numbers, and negative numbers. They do NOT include fractions or decimals.
Set of integers: {..., -3, -2, -1, 0, 1, 2, 3, ...}
5 Examples of Integers:
1. -5 (negative integer)
2. 0 (zero)
3. 7 (positive integer)
4. -12 (negative integer)
5. 100 (positive integer)
Number Line Representation:
← Negative ─────── Zero ────── Positive →
... -5 -4 -3 -2 -1 0 1 2 3 4 5 ...
Key Points:
• Integers on the right of 0 are positiv...
Q2: Add: (-15) + (-8) and (-20) + 13. Explain your steps.
Problem 1: (-15) + (-8)
Step 1: Identify the signs
Both numbers are negative.
When adding two negative integers, add their absolute values and keep the negative sign.
Step 2: Add absolute values
|-15| = 15
|-8| = 8
15 + 8 = 23
Step 3: Apply the negative sign
(-15) + (-8) = -23
Answer: -23
---
Problem 2: (-20) + 13
Step 1: Identify the signs
One number is negative, one is positive.
When adding integers with different signs, subtract the smaller absolute value from the larger and use the si...
Q3: Subtract: 12 - (-8) and (-5) - 6. Show the steps clearly.
Problem 1: 12 - (-8)
Step 1: Convert subtraction to addition
Subtracting a negative is the same as adding its positive.
12 - (-8) = 12 + 8
Step 2: Add
12 + 8 = 20
Answer: 20
Rule: a - (-b) = a + b
---
Problem 2: (-5) - 6
Step 1: Convert subtraction to addition
Subtracting a positive is adding its negative.
(-5) - 6 = (-5) + (-6)
Step 2: Add two negative numbers
Add their absolute values: 5 + 6 = 11
Keep the negative sign: -11
Answer: -11
Rule: a - b = a + (-b)
---
General Rule for Su...
Q4: Multiply: (-6) × 5, (-4) × (-9), and 0 × (-15). Explain the sign rules.
Problem 1: (-6) × 5
Step 1: Multiply absolute values
6 × 5 = 30
Step 2: Apply sign rule
Negative × Positive = Negative
(-6) × 5 = -30
Answer: -30
---
Problem 2: (-4) × (-9)
Step 1: Multiply absolute values
4 × 9 = 36
Step 2: Apply sign rule
Negative × Negative = Positive
(-4) × (-9) = +36 or 36
Answer: 36
---
Problem 3: 0 × (-15)
Step 1: Apply zero property
Any number multiplied by 0 equals 0, regardless of sign.
0 × (-15) = 0
Answer: 0
---
Sign Rules for Multiplication of Integers...
Q5: Divide: (-36) ÷ 6, (-48) ÷ (-8), and 0 ÷ (-5). State the sign rules for division.
Problem 1: (-36) ÷ 6
Step 1: Divide absolute values
36 ÷ 6 = 6
Step 2: Apply sign rule
Negative ÷ Positive = Negative
(-36) ÷ 6 = -6
Answer: -6
---
Problem 2: (-48) ÷ (-8)
Step 1: Divide absolute values
48 ÷ 8 = 6
Step 2: Apply sign rule
Negative ÷ Negative = Positive
(-48) ÷ (-8) = +6 or 6
Answer: 6
---
Problem 3: 0 ÷ (-5)
Step 1: Apply zero property
Zero divided by any non-zero integer equals 0.
0 ÷ (-5) = 0
Answer: 0
Note: We CANNOT divide by 0. Division by zero is undefined.
--...
Q6: Name and verify the commutative property for addition and multiplication using integers -3, 5.
Commutative Property: When we add or multiply two integers, the order does not matter.
---
Commutative Property of Addition:
For any integers a and b: a + b = b + a
Verification with -3 and 5:
Left side: (-3) + 5 = 2
Right side: 5 + (-3) = 2
Both sides equal 2 ✓
Therefore, (-3) + 5 = 5 + (-3)
---
Commutative Property of Multiplication:
For any integers a and b: a × b = b × a
Verification with -3 and 5:
Left side: (-3) × 5 = -15
Right side: 5 × (-3) = -15
Both sides equal -15 ✓
Therefore,...
Showing 6 of 8 questions. Visit the full page for complete solutions.
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