Important Questions Maths Chapter 2 Class 7 Ganita Prakash – II

Operations with Integers

1. Two integers have a sum of 27 and a difference of 9. Find the integers.
Answer:

Let the larger integer be a and the smaller integer be b.

Given:

• Sum = 27
• Difference = 9

Try pairs:

18 + 9 = 27

18 − 9 = 9

Therefore, the integers are 18 and 9.

Explanation:
The correct pair must satisfy both conditions at the same time. Here, 18 and 9 give the required sum and difference.

2. A carrom coin moves 6 units to the right and then 9 units to the left. What is its final position?
Answer:

Right movement = +6

Left movement = –9

Final position

= 6 + (–9)

= –3

Final position = –3

Explanation:
The negative sign shows that the coin is 3 units to the left of the starting point (0).

3. The first movement of a coin is –8 and the final position is 4. Find the second movement.
Answer:

Final Position = First Movement + Second Movement

4 = –8 + Second Movement

Second Movement = 4 + 8

= 12

Second movement = +12

Explanation: The coin first moved 8 units left. To reach 4, it must move 12 units right.

4. What is the additive inverse of –25? Explain.
Answer:

The additive inverse of a number is the number that makes the sum zero.

–25 + 25 = 0

Therefore, the additive inverse of –25 is 25.

Explanation: Every integer has an opposite number. Together they add up to zero.

5. Evaluate: 9 – 17
Answer:

Using additive inverse:

9 – 17
= 9 + (–17)
= –8
Answer = –8

Explanation: Subtracting a number is the same as adding its additive inverse.

6. Using integer multiplication rules, find 7 × (–8).
Answer:

7 × (–8)
= –56

Explanation: A positive integer multiplied by a negative integer gives a negative product.

7. Evaluate: (–9) × 6
Answer:

(–9) × 6
= –54

Explanation: One integer is negative and the other is positive, so the product is negative.

8. Evaluate: (–11) × (–4)
Answer:

(–11) × (–4)
= 44

Explanation: The product of two negative integers is always positive.

9. Without multiplying, find the value of (–123) × (–456) if 123 × 456 = 56088.
Answer:

The magnitudes remain the same.
123 × 456 = 56088
Both integers are negative.
Therefore,
(–123) × (–456) = 56088

Explanation: A negative multiplied by a negative gives a positive result.

10. Explain the sign of the product in each case.
Answer:

Explanation: The sign depends on whether the integers have the same sign or different signs.

11. An exam gives +5 marks for a correct answer and –2 marks for a wrong answer. A student gets 25 correct answers and 10 wrong answers. Find the score.
Answer:

Marks for correct answers
= 25 × 5
= 125

Marks for wrong answers
= 10 × (–2)
= –20

Total marks
= 125 + (–20)
= 105

Score = 105 marks

Explanation: Correct answers increase the score while wrong answers reduce it.

12. An elevator starts at ground level and moves downward at 3 metres per minute for 30 minutes. Find its position.
Answer:

Movement
= 30 × (–3)
= –90

Position = –90 metres
Explanation: The negative sign shows the elevator is below ground level.

13. Evaluate: (–100) ÷ 25
Answer:

25 × (–4) = –100

Therefore,
(–100) ÷ 25 = –4

Explanation: A negative number divided by a positive number gives a negative quotient.

14. Evaluate: (–84) ÷ (–12)
Answer:

(–84) ÷ (–12)
= 7

Explanation: A negative number divided by a negative number gives a positive quotient.

15. Verify the commutative property using integers –8 and 15.
Answer:

(–8) × 15
= –120
15 × (–8)
= –120
Therefore,
(–8) × 15 = 15 × (–8)

Explanation: Changing the order of multiplication does not change the product.

16. Verify the associative property for 2, –3 and 5.
Answer:

Left side:
(2 × –3) × 5
= –6 × 5
= –30

Right side:
2 × (–3 × 5)
= 2 × (–15)
= –30

Both sides are equal.

Explanation: The grouping of integers does not affect the product.

17. Use the distributive property to evaluate: –4 × (7 + (–2))
Answer:

= –4 × 5
= –20

Using distributive property:
= (–4 × 7) + (–4 × –2)
= –28 + 8
= –20

Answer = –20
Explanation: Both methods give the same result, proving the distributive property.

18. What is the value of –1 × 38?
Answer:

–1 × 38
= –38

Explanation: Multiplying any integer by –1 gives its additive inverse.

19. What is the sign of the product of five factors of –1?
Answer:

(–1) × (–1) × (–1) × (–1) × (–1)
There are 5 negative factors (an odd number).
Therefore, the product is negative.

Answer = –1

Explanation: An odd number of negative factors gives a negative product.

20. The temperature is 8°C and decreases by 5°C every hour. Write an expression and find the temperature after 4 hours.
Answer:

Decrease in 4 hours
= 4 × (–5)
= –20

Temperature after 4 hours
= 8 + (–20)
= –12°C

Answer = –12°C

Explanation: Each hour lowers the temperature by 5°C. After 4 hours, the total decrease is 20°C, resulting in –12°C.