Integers Questions with Solutions | Class 6 and 7

Integers are whole numbers that can be positive, negative or zero. This page covers integers questions with step-by-step solutions for Class 6 and 7 students. To understand the concept first, read our guide on integers.

Table of Contents

• Understanding Integer Operation
• Integer Questions - Easy Level
• Integer Questions - Medium Level
• Integer Questions - Advanced Level
• More Integer Questions with Solutions
• Practice Integer Questions
• Conclusion
• Frequently Asked Questions on Integer Questions

Understanding Integer Operation

Integers follow specific rules for addition, subtraction, multiplication, and division. Let’s explore these operations in detail.

1. Addition of Integers

Adding integers involves combining two numbers, either both positive or both negative, or one of each. Here are some basic rules:

• Positive + Positive: The sum of two positive integers is always positive.
  Example: 3 + 4 = 7

• Negative + Negative: The sum of two negative integers is always negative.
  Example: -3 + (-4) = -7

• Positive + Negative: The sum of a positive and a negative integer depends on the magnitude (absolute value) of the numbers.
  Example: 5 + (-3) = 2

• Zero + any integer: Adding zero to any integer leaves the integer unchanged.
  Example: 0 + 5 = 5

2. Subtraction of Integers

Subtraction of integers can be seen as the addition of a negative integer. Here’s how it works:

• Positive - Positive: If the number being subtracted is smaller, the result is positive; if it's larger, the result is negative.
  Example: 7 - 3 = 4

• Negative - Negative: The rule follows the same principle as positive subtraction.
  Example: -5 - (-3) = -2

• Adding the opposite: To subtract an integer, add its opposite.
  Example: 8 - (-4) = 12

3. Multiplication of Integers

The multiplication of integers follows a few key rules:

• Positive × Positive: The result is positive.
  Example: 3 × 4 = 12

• Negative × Negative: The result is positive.
  Example: (-3) × (-4) = 12

• Positive × Negative: The result is negative.
  Example: 3 × (-4) = -12

• Multiplying by zero: Any integer multiplied by zero equals zero.
  Example: 5 × 0 = 0

4. Division of Integers

Division works similarly to multiplication, with a few differences:

• Positive ÷ Positive: The result is positive.
  Example: 8 ÷ 4=2

• Negative ÷ Negative: The result is positive.
  Example: (-8) ÷ (-4) = 2

• Positive ÷ Negative: The result is negative.
  Example: 8 ÷ (-4) = -2

• Negative ÷ Positive: The result is negative.
  Example: (-8) ÷ 4 = -2

• Division by zero: Division by zero is undefined.

Know more on properties of integers

Question 1: Evaluate: (i) -35 + 48 (ii) 125 - (-45) (iii) -19 - (-32) (iv) -250 + (-150)

Solution:
(i) -35 + 48 = 13
(ii) 125 - (-45) = 125 + 45 = 170
(iii) -19 - (-32) = -19 + 32 = 13
(iv) -250 + (-150) = -400

Question 2: Find the additive inverse of:
(i) -91 (ii) 250 (iii) 0 (iv) -450

Solution:
(i) Additive inverse of -91 = 91
(ii) Additive inverse of 250 = -250
(iii) Additive inverse of 0 = 0
(iv) Additive inverse of -450 = 450

Question 3: True or False:
(i) -15 is smaller than -9.
(ii) 0 is an integer.
(iii) The sum of two negative integers is always negative.
(iv) -1 is the largest negative integer.

Solution:
(i) True - On a number line, -15 is further left than -9. 
(ii) True - zero is neither positive nor negative but it is an integer.
(iii) True - adding two negative integers always gives a negative result.
(iv) True - -1 is the closest negative integer to zero, making it the largest.

Question 4: Evaluate:
(i) (-3) × (-8) × (-5)
(ii) (-1) × (-1) × ... (50 times)
(iii) (-6) × 4 × (-2)

Solution: (i) 3 × 8 × 5 = 120, odd number of negatives = -120
(ii) (-1)⁵⁰ = 1 (even number of negatives gives positive)
(iii) (-6 × 4) × (-2) = -24 × -2 = 48

Question 5: Evaluate using properties:
(i) 120 + (-45) + (-55)
(ii) 450 - (225 - 75)
(iii) (65 - 15) × (65 + 15)

Solution: (i) 120 - 45 - 55 = 75 - 55 = 20
(ii) 450 - 150 = 300
(iii) 50 × 80 = 4000

Read more:

• Integers 
• Greatest Integer Function
• Addition and Subtraction of Integers
• Bodmas Rule Questions 

Integer Questions - Medium Level

Question 6: Verify the distributive property a × (b + c) = (a × b) + (a × c) for:
(i) a = -4, b = 5, c = -3
(ii) a = 7, b = -2, c = 8

Solution: (i) LHS = -4 × (5 + (-3)) = -4 × 2 = -8
RHS = (-4 × 5) + (-4 × -3) = -20 + 12 = -8
LHS = RHS

(ii) LHS = 7 × (-2 + 8) = 7 × 6 = 42
RHS = (7 × -2) + (7 × 8) = -14 + 56 = 42
LHS = RHS

Question 7: Simplify:
(i) (-18) + 25 + (-7) + 12
(ii) 36 + (-14) + (-22) + 8
(iii) (-45) + 30 + (-15) + 20

Solution: (i) (-18 - 7) + (25 + 12) = -25 + 37 = 12
(ii) (36 + 8) + (-14 - 22) = 44 - 36 = 8
(iii) (-45 - 15) + (30 + 20) = -60 + 50 = -10

Question 8: Find the missing integer: (i) ___ + (-15) = 10
(ii) ___ - (-8) = 20
(iii) ___ × (-4) = 36
(iv) ___ ÷ (-3) = -9

Solution: (i) 10 - (-15) = 10 + 15 = 25
(ii) 20 - 8 = 12
(iii) 36 ÷ (-4) = -9
(iv) -9 × (-3) = 27

Question 9: A number line shows points A at -6, B at 3 and C at -2.
(i) What is the distance between A and B?
(ii) What is the sum of A, B and C?
(iii) Which point is closest to zero?

Solution: (i) Distance = 3 - (-6) = 3 + 6 = 9 units
(ii) -6 + 3 + (-2) = -5
(iii) B (3) and C (-2) are both 2–3 units from zero. C at -2 is closest at 2 units.

Question 10: Arrange in ascending order:
(i) -8, 3, -1, 0, 5, -4
(ii) -15, 7, -3, 12, -9, 0

Solution: (i) -8, -4, -1, 0, 3, 5
(ii) -15, -9, -3, 0, 7, 12

Integer Questions - Advanced Level

Question 11: In a quiz, 4 marks are awarded for each correct answer and 2 marks are deducted for each wrong answer. A student answered 15 questions correctly and 5 incorrectly. What is the total score?

Solution: Marks for correct = 15 × 4 = 60 Marks deducted = 5 × 2 = 10 Total score = 60 - 10 = 50 marks

Question 12: The temperature in Leh was -8°C in the morning. It rose by 3°C by noon and then dropped by 5°C in the evening. What was the temperature in the evening?

Solution: Morning = -8°C After rise = -8 + 3 = -5°C After drop = -5 - 5 = -10°C

Question 13: A submarine is at 250 m below sea level. It descends another 150 m and then rises by 80 m. What is its final position?

Solution: Start = -250 m
After descent = -250 - 150 = -400 m
After rise = -400 + 80 = -320 m (320 m below sea level)

Question 14: A shopkeeper gains Rs. 12 on selling one notebook but loses Rs. 8 on selling one pen. If he sells 15 notebooks and 10 pens, what is his total profit or loss?

Solution: Profit from notebooks = 15 × 12 = Rs. 180
Loss from pens = 10 × 8 = Rs. 80
Net profit = 180 - 80 = Rs. 100 profit

Question 15: A football team scored 3 goals in the first half but conceded 5 goals. In the second half they scored 4 goals and conceded 1. What is their goal difference at the end of the match?

Solution: First half = 3 - 5 = -2
Second half = 4 - 1 = 3
Total goal difference = -2 + 3 = +1

More Integer Questions with Solutions

Question 1: Evaluate:

(i) -35 + 48
(ii) 125 - (-45)
(iii) -19 - (-32)
(iv) -250 + (-150)

Solution:
(i) -35 + 48 = 13
(ii) 125 - (-45) = 125 + 45 = 170
(iii) -19 - (-32) = -19 + 32 = 13
(iv) -250 + (-150) = -400

Question 2: Find the additive inverse of:

(i) -91
(ii) 250
(iii) 0
(iv) -450

Solution:
(i) Additive inverse of -91 = 91
(ii) Additive inverse of 250 = -250
(iii) Additive inverse of 0 = 0
(iv) Additive inverse of -450 = 450

Question 3: Verify: a × (b + c) = (a × b) + (a × c) for:

(i) a = -4, b = 5, c = -3
(ii) a = 7, b = -2, c = 8

Solution:

(i)
LHS = -4 × (5 + (-3)) = -4 × 2 = -8
RHS = (-4 × 5) + (-4 × -3) = -20 + 12 = -8 

(ii)
LHS = 7 × (-2 + 8) = 7 × 6 = 42
RHS = (7 × -2) + (7 × 8) = -14 + 56 = 42 

Question 4: Evaluate using properties:

(i) 120 + (-45) + (-55)
(ii) 450 - (225 - 75)
(iii) (65 - 15) × (65 + 15)

Solution:
(i) 120 - 45 - 55 = (120 - 45) - 55 = 75 - 55 = 20
(ii) 450 - (225 - 75) = 450 - 150 = 300
(iii) (65 - 15) × (65 + 15) = (50) × (80) = 4000 (difference of squares)

Question 5: True or False:

(i) -15 is smaller than -9.
(ii) 0 is an integer.
(iii) The sum of two negative integers is always negative.
(iv) -1 is the largest negative integer.

Solution:
(i) True
(ii) True
(iii) True
(iv) True

Question 6: Evaluate:

(i) (-3) × (-8) × (-5)
(ii) (-1) × (-1) × … (50 times)
(iii) (-6) × 4 × (-2)

Solution:
(i) - (3 × 8 × 5) = -120
(ii) (-1)^50 = 1
(iii) (-6 × 4) × (-2) = -24 × -2 = 48

Question 7: In a quiz, 4 marks are awarded for each correct answer, and 2 marks are deducted for each wrong answer. A student answered 18 questions and scored 44 marks. How many correct answers did the student give?

Solution:
Let correct answers = x
Wrong answers = 18 - x

Score: 4x - 2(18 - x) = 44
4x - 36 + 2x = 44
6x - 36 = 44
6x = 80
x = 80 ÷ 6 = 13.33 (Not possible - check: marks suggest the student had 14 correct answers if integers are considered.)

Question 8: The temperature in Leh was -8°C in the morning. It rose by 3°C by noon, and then dropped by 5°C in the evening. What was the temperature in the evening?

Solution:
Morning temperature = -8°C
After rise = -8 + 3 = -5°C
After drop = -5 - 5 = -10°C
Final temperature = -10°C

Question 9: A submarine is at 250 m below sea level. It descends another 150 m and then rises by 80 m. Where is it now?

Solution:
Start: -250 m
After descent: -250 -150 = -400 m
After rise: -400 + 80 = -320 m
Final position = 320 m below sea level

Question 10: A shopkeeper gains ₹12 on selling one notebook but loses ₹8 on selling one pen. If he sells 15 notebooks and 10 pens, what is his total profit or loss?

Solution:
Profit from notebooks = 15 × 12 = ₹180
Loss from pens = 10 × 8 = ₹80
Net profit = 180 - 80 = ₹100

Practice Integer Questions

1. What is the value of (-9) + 6?
2. 14 - (-7) = ____
3. Multiply: (-5) × (-3) = ____
4. (-20) ÷ 4 = ____
5. Add: (-7) + (-3) + 5 = ____
6. Find the result of (-8) + (-4)
7. 15 + (-9) = ____
8. What is (-6) × 7?
9. (-24) ÷ (-6) = ____
10. Work out: 10 + (-3) + (-7)

Answers:

1. -3
2. 21
3. 15
4. -5
5. -5
6. -12
7. 6
8. -42
9. 4
10. 0

Conclusion

Integers are a crucial concept in mathematics, and understanding how to manipulate them using the basic operations - addition, subtraction, multiplication, and division - lays the foundation for more advanced topics. Whether you’re working with financial calculations, measuring temperatures, or solving algebraic equations, integers are an essential tool for solving real-world problems.

Frequently Asked Questions on Integer Questions

Q1: What is the difference between a positive integer and a negative integer?

Answer: Positive integers are greater than zero, while negative integers are less than zero.

Q2: How do you multiply integers with different signs?

Answer: If the signs are different, the product is always negative.

Q3: What happens if you divide by zero?

Answer: Division by zero is undefined.

Q4: Can you add two negative integers?

Answer: Yes, when you add two negative integers, the sum will always be negative.

By mastering integer questions, you’ll enhance your mathematical skills and gain confidence in handling a wide variety of problems.Learn more at orchids International.