NCERT Solutions for Class 7 Maths Chapter 1 Integers

This page provides NCERT Class 7 Maths Chapter 1 solutions, exercise-wise answers, important integer rules, solved examples and extra practice questions. It is useful for homework, revision and exam preparation.

Edition note: This page covers the earlier NCERT Class 7 Maths chapter titled Integers, which matches the chapter and search intent represented by this URL. In the current 2026-27 NCERT Ganita Prakash textbook, Chapter 1 is Large Numbers Around Us, while integer operations are covered in Chapter 10, Operations with Integers.

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Class 7 Maths Chapter 1 Integers at a Glance

Topic	What you learn
Integers	Positive integers, negative integers and zero
Number line	Representing and comparing integers
Addition	Adding integers with the same or different signs
Subtraction	Subtracting an integer by adding its opposite
Multiplication	Sign rules and properties of multiplication
Division	Sign rules and properties of division
Word problems	Temperature, profit and loss, elevation and scores

NCERT Solutions for Class 7 Maths Chapter 1 Integers

The older NCERT chapter is divided into four exercises. Each exercise focuses on a different part of integer operations.

Exercise 1.1: Addition and Subtraction of Integers

Question 1: Temperature on a Number Line

The temperatures shown on the number line are:

• Lahulspiti = -8°C
• Srinagar = -2°C
• Shimla = 5°C
• Ooty = 14°C
• Bengaluru = 22°C

(a) Temperature difference between the hottest and coldest places

Hottest temperature = 22°C
Coldest temperature = -8°C

22 - (-8) = 22 + 8 = 30°C

Answer: 30°C

(b) Temperature difference between Lahulspiti and Srinagar

-2 - (-8) = -2 + 8 = 6°C

Answer: 6°C

(c) Temperature at Srinagar and Shimla taken together

-2 + 5 = 3°C

Since 3°C is less than 5°C but greater than -2°C, the combined temperature is less than Shimla's temperature but not less than Srinagar's temperature.

Question 2: Quiz Scores

Jack's scores are:

25, -5, -10, 15 and 10

Total score:

25 + (-5) + (-10) + 15 + 10
= 25 - 5 - 10 + 15 + 10
= 35

Answer: Jack's total score is 35.

Question 3: Change in Temperature

Monday temperature = -5°C

Tuesday:

-5 - 2 = -7°C

Wednesday:

-7 + 4 = -3°C

Answer:

• Tuesday = -7°C
• Wednesday = -3°C

Question 4: Plane and Submarine

Height of plane = 5000 m
Depth of submarine = -1200 m

Vertical distance:

5000 - (-1200)
= 5000 + 1200
= 6200 m

Answer: 6200 m

Question 5: Bank Deposit and Withdrawal

Deposit = +₹2000
Withdrawal = -₹1642

Balance:

2000 + (-1642) = ₹358

Answer: The balance is ₹358.

Question 6: Movement Towards East and West

East is represented by a positive integer.

Therefore, west is represented by a negative integer.

Rita travels:

20 km east and 30 km west.

Final position from A:

20 + (-30) = -10 km

Answer: Rita is 10 km west of point A, represented by -10 km.

Question 7: Magic Square

A magic square has the same sum in every row, column and diagonal.

For the first square, one diagonal does not have the same sum as the other rows, columns and diagonal.

Therefore, it is not a magic square.

For the second square, every row, column and diagonal has the sum -9.

Answer: The second square is a magic square.

Question 8: Verify a - (-b) = a + b

(i) a = 21, b = 18

LHS:

21 - (-18) = 21 + 18 = 39

RHS:

21 + 18 = 39

Therefore:

LHS = RHS

The identity is verified.

The same method gives:

• (ii) a = 118, b = 125: LHS = RHS = 243
• (iii) a = 75, b = 84: LHS = RHS = 159
• (iv) a = 28, b = 11: LHS = RHS = 39

Question 9: Compare the Expressions

(a)

(-8) + (-4) = -12
(-8) - (-4) = -4

Therefore:

-12 < -4

Answer: <

(b)

(-3) + 7 - 19 = -15

15 - 8 + (-9) = -2

Therefore:

-15 < -2

Answer: <

(c)

23 - 41 + 11 = -7

23 - 41 - 11 = -29

Therefore:

-7 > -29

Answer: >

(d)

39 + (-24) - 15 = 0

36 + (-52) - (-36) = 20

Therefore:

0 < 20

Answer: <

(e)

-231 + 79 + 51 = -101

-399 + 159 + 81 = -159

Therefore:

-101 > -159

Answer: >

Exercise 1.2: Properties of Addition of Integers

Question 1

Write a pair of integers satisfying each condition.

(a) Sum = -7

-4 + (-3) = -7

Answer: -4 and -3

(b) Difference = -10

-25 - (-15) = -10

Answer: -25 and -15

(c) Sum = 0

4 + (-4) = 0

Answer: 4 and -4

Question 2

(a) Two negative integers whose difference is 8

(-5) - (-13) = 8

Answer: -5 and -13

(b) A negative and positive integer whose sum is -5

-25 + 20 = -5

Answer: -25 and 20

(c) A negative and positive integer whose difference is -3

-2 - 1 = -3

Answer: -2 and 1

Question 3: Quiz Scores

Team A:

-40 + 10 + 0 = -30

Team B:

10 + 0 + (-40) = -30

Both teams scored the same.

This also illustrates the commutative property of addition. Integers can be added in a different order without changing the sum.

Answer: Both teams scored -30. Yes, integers can be added in any order.

Question 4: Fill in the Blanks

(i)
(-5) + (-8) = (-8) + (-5)

(ii)
-53 + 0 = -53

(iii)
17 + (-17) = 0

(iv)
[13 + (-12)] + (-7) = 13 + [(-12) + (-7)]

(v)
(-4) + [15 + (-3)] = [-4 + 15] + (-3)

These examples demonstrate the commutative, additive identity and associative properties of addition.

Exercise 1.3: Multiplication of Integers

Question 1: Find the Products

Expression	Answer
3 × (-1)	-3
(-1) × 225	-225
(-21) × (-30)	630
(-316) × (-1)	316
(-15) × 0 × (-18)	0
(-12) × (-11) × 10	1320
9 × (-3) × (-6)	162
(-18) × (-5) × (-4)	-360
(-1) × (-2) × (-3) × 4	-24
(-3) × (-6) × (-2) × (-1)	36

Question 2: Verify the Distributive Property

(a)

18 × [7 + (-3)]

= 18 × 4
= 72

Right side:

(18 × 7) + [18 × (-3)]

= 126 - 54
= 72

Therefore:

LHS = RHS

(b)

(-21) × [(-4) + (-6)]

= (-21) × (-10)
= 210

Right side:

[(-21) × (-4)] + [(-21) × (-6)]

= 84 + 126
= 210

Therefore:

LHS = RHS

Question 3: Multiplication by -1

For any integer a:

(-1) × a = -a

Therefore:

• If the product is -22, the required integer is 22
• If the product is 37, the required integer is -37
• If the product is 0, the required integer is 0

Question 4: Why is (-1) × (-1) = 1?

Consider:

(-1) × 5 = -5
(-1) × 4 = -4
(-1) × 3 = -3
(-1) × 2 = -2
(-1) × 1 = -1
(-1) × 0 = 0

The product increases by 1 each time the second factor decreases by 1.

Therefore:

(-1) × (-1) = 1

This explains why the product of two negative integers is positive.

Question 5: Use Properties to Calculate

(a)

26 × (-48) + (-48) × (-36)

= -48[26 + (-36)]
= -48(-10)
= 480

(b)

8 × 53 × (-125)

= 8 × (-125) × 53
= -1000 × 53
= -53,000

(c)

15 × (-25) × (-4) × (-10)

= 15 × 100 × (-10)
= -15,000

(d)

(-41) × 102

= (-41) × (100 + 2)
= -4100 - 82
= -4182

(e)

625 × (-35) + (-625) × 65

= 625[(-35) + (-65)]
= 625 × (-100)
= -62,500

(f)

7 × (50 - 2)

= 350 - 14
= 336

(g)

(-17) × (-29)

= (-17) × (-30 + 1)
= 510 - 17
= 493

(h)

(-57) × (-19) + 57

= 57 × 19 + 57
= 57 × 20
= 1140

Question 6: Freezing Process

Initial temperature = 40°C

Decrease per hour = 5°C

Decrease in 10 hours:

5 × 10 = 50°C

Final temperature:

40 - 50 = -10°C

Answer: -10°C

Question 7: Class Test

Correct answer = +5 marks
Incorrect answer = -2 marks

(i) Mohan

4 correct:

4 × 5 = 20

6 incorrect:

6 × (-2) = -12

Total:

20 - 12 = 8 marks

(ii) Reshma

5 correct:

5 × 5 = 25

5 incorrect:

5 × (-2) = -10

Total:

25 - 10 = 15 marks

(iii) Heena

2 correct:

2 × 5 = 10

5 incorrect:

5 × (-2) = -10

Total:

10 - 10 = 0 marks

Question 8: Profit and Loss

Profit on one white cement bag = ₹8
Loss on one grey cement bag = ₹5

(a)

3000 white bags:

3000 × 8 = ₹24,000 profit

5000 grey bags:

5000 × (-5) = -₹25,000

Net result:

24,000 - 25,000 = -₹1,000

Answer: Loss of ₹1,000

(b)

If 6400 grey bags are sold:

6400 × 5 = ₹32,000 loss

Let x be the number of white bags.

8x - 32,000 = 0

8x = 32,000

x = 4000

Answer: 4000 white cement bags

Question 9: Complete the Statements

(a)
(-3) × (-9) = 27

(b)
5 × (-7) = -35

(c)
7 × (-8) = -56

(d)
(-11) × (-12) = 132

Exercise 1.4: Division of Integers

Question 1: Evaluate

Expression	Answer
(-30) ÷ 10	-3
50 ÷ (-5)	-10
(-36) ÷ (-9)	4
(-49) ÷ 49	-1
13 ÷ [(-2) + 1]	-13
0 ÷ (-12)	0
(-31) ÷ [(-30) + (-1)]	1
[(-36) ÷ 12] ÷ 3	-1
[(-6) + 5] ÷ [(-2) + 1]	1

Remember:

• Positive ÷ positive = positive
• Negative ÷ negative = positive
• Positive ÷ negative = negative
• Negative ÷ positive = negative
• 0 ÷ any non-zero integer = 0

Question 2: Division Is Not Distributive Over Addition

For a = 12, b = -4 and c = 2:

LHS:

12 ÷ (-4 + 2)
= 12 ÷ (-2)
= -6

RHS:

(12 ÷ -4) + (12 ÷ 2)
= -3 + 6
= 3

Therefore:

-6 ≠ 3

So,

a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

For a = -10, b = 1 and c = 1:

LHS = -10 ÷ 2 = -5

RHS = -10 + (-10) = -20

Again, LHS ≠ RHS.

Question 3: Fill in the Blanks

Statement	Missing integer
369 ÷ ___ = 369	1
(-75) ÷ ___ = -1	75
(-206) ÷ ___ = 1	-206
-87 ÷ ___ = 87	-1
___ ÷ 1 = -87	-87
___ ÷ 48 = -1	-48
20 ÷ ___ = -2	-10
___ ÷ 4 = -3	-12

Question 4: Five Integer Pairs with a ÷ b = -3

Examples:

• 15 ÷ (-5) = -3
• (-15) ÷ 5 = -3
• 18 ÷ (-6) = -3
• (-18) ÷ 6 = -3
• 21 ÷ (-7) = -3

Answer: Any five valid integer pairs can be used.

Question 5: Temperature Change

Initial temperature at noon = 10°C

Decrease each hour = 2°C

The temperature reaches -8°C after:

10 → 8 → 6 → 4 → 2 → 0 → -2 → -4 → -6 → -8

This takes 9 hours.

Answer: 9 p.m.

At midnight, 12 hours have passed:

10 + (12 × -2)
= 10 - 24
= -14°C

Answer: Midnight temperature = -14°C

Question 6: Class Test

Correct answer = +3 marks
Incorrect answer = -2 marks

(i) Radhika

12 correct answers:

12 × 3 = 36

Her total score is 20.

Marks from incorrect answers:

20 - 36 = -16

Number of incorrect answers:

-16 ÷ -2 = 8

Answer: 8 incorrect answers

(ii) Mohini

7 correct answers:

7 × 3 = 21

Total score = -5

Marks from incorrect answers:

-5 - 21 = -26

Number of incorrect answers:

-26 ÷ -2 = 13

Answer: 13 incorrect answers

Question 7: Elevator in a Mine

Initial position = 10 m above ground
Final position = -350 m

Distance descended:

-350 - 10 = -360 m

Rate of descent = -6 m/min

Time:

360 ÷ 6 = 60 minutes

Answer: 60 minutes or 1 hour

Important Rules for Integers

Rule 1: Addition

When two integers have the same sign, add their absolute values and keep the common sign.

Example:

(-7) + (-5) = -12

When the signs are different, subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.

Example:

-9 + 4 = -5

Rule 2: Subtraction

Subtracting an integer is the same as adding its opposite.

a - b = a + (-b)

Example:

8 - (-3) = 8 + 3 = 11

Rule 3: Multiplication

Signs	Result
+ × +	+
+ × -	-
- × +	-
- × -	+

Rule 4: Division

Division follows the same sign pattern as multiplication.

Signs	Result
+ ÷ +	+
+ ÷ -	-
- ÷ +	-
- ÷ -	+

Rule 5: Zero

For every integer a:

a + 0 = a

and, when a ≠ 0:

0 ÷ a = 0

Number Line and Integers

A number line helps you visualise positive and negative integers.

• Positive integers lie to the right of zero.
• Negative integers lie to the left of zero.
• Zero lies between positive and negative integers.
• Moving right means the value increases.
• Moving left means the value decreases.

For example:

-5 < -2 < 0 < 3 < 7

A common mistake is to think that -5 is greater than -2 because 5 is greater than 2. On the number line, -5 lies to the left of -2, so -5 is smaller.

Properties of Integers

Closure Property

The sum, difference and product of two integers are integers.

For example:

7 + (-10) = -3

Commutative Property

Addition and multiplication are commutative:

a + b = b + a

a × b = b × a

Subtraction and division are not generally commutative.

Associative Property

Addition and multiplication are associative:

(a + b) + c = a + (b + c)

(a × b) × c = a × (b × c)

Distributive Property

Multiplication distributes over addition and subtraction:

a × (b + c) = a × b + a × c

a × (b - c) = a × b - a × c

Class 7 Maths Chapter 1 Integers Worksheet with Answers

Try these questions before checking the answers.

Questions

1. Find: -18 + 25.
2. Find: -32 - (-14).
3. Arrange in ascending order: 4, -7, 0, -2, 9.
4. Find: (-8) × 7.
5. Find: (-12) × (-6).
6. Find: 84 ÷ (-7).
7. Find: (-96) ÷ (-12).
8. A temperature of 4°C falls by 11°C. What is the new temperature?
9. A bank account has ₹750. A withdrawal of ₹925 is made. Represent the transaction and find the resulting balance.
10. Verify: 18 - (-7) = 18 + 7.
11. Find two integers whose sum is -12.
12. Find two integers whose difference is 9.
13. Evaluate: (-5) + 12 - 8.
14. A lift is at 6 m above ground and descends 18 m. What is its final position?
15. Find x: (-9) × x = 63.

Worksheet Answers

1. 7
2. -18
3. -7, -2, 0, 4, 9
4. -56
5. 72
6. -12
7. 8
8. -7°C
9. ₹750 + (-₹925) = -₹175
10. 25 = 25
11. Example: -5 and -7
12. Example: 12 and 3
13. -1
14. -12 m
15. x = -7

Extra Questions on Integers for Class 7

1. Why is -9 smaller than -4?

On a number line, -9 lies to the left of -4. Numbers become smaller as we move left.

Answer: -9 < -4

2. What is the additive inverse of -15?

The additive inverse of a number is the number that gives zero when added to it.

-15 + 15 = 0

Answer: 15

3. What is the multiplicative identity for integers?

The multiplicative identity is 1 because:

a × 1 = a

4. Is subtraction commutative?

No.

For example:

8 - 3 = 5

but

3 - 8 = -5

Therefore:

8 - 3 ≠ 3 - 8

5. Is division commutative?

No.

For example:

12 ÷ 3 = 4

but

3 ÷ 12 = 1/4

Therefore, division is not commutative.

6. What happens when a negative integer is multiplied by -1?

The sign changes.

Example:

(-18) × (-1) = 18

7. Find the value of:

(-15) + (-8) + 20

= -23 + 20

= -3

8. A temperature is -6°C. It rises by 14°C. What is the new temperature?

-6 + 14 = 8°C

9. A person owes ₹600 and pays ₹250. Represent the remaining amount using an integer.

-600 + 250 = -350

The person still owes ₹350.

10. Find:

(-4) × [6 + (-2)]

= (-4) × 4

= -16

Class 7 Maths Chapter 1 Integers: Quick Revision

Before a test, remember these points:

• Integers include negative numbers, zero and positive numbers.
• Zero is neither positive nor negative.
• Numbers farther to the right on a number line are greater.
• Subtracting a negative number means adding its positive opposite.
• Same signs give a positive result in multiplication and division.
• Different signs give a negative result in multiplication and division.
• Zero multiplied by any integer is zero.
• Zero divided by a non-zero integer is zero.
• Addition and multiplication are commutative.
• Subtraction and division are not commutative.
• Addition and multiplication are associative.
• Multiplication is distributive over addition and subtraction.
• Always check the sign before finalising an answer to an integer word problem.

Class 7 Maths Chapter 1 Solutions PDF

If you need a PDF copy of these solutions for revision, open the page in your browser and choose Print → Save as PDF. This creates a personal PDF copy of the page without requiring a separate download claim.

For the current 2026–27 NCERT Ganita Prakash textbook, students should check the new chapter numbering before using older Chapter 1 Integers material.

Related Class 7 Maths Chapters

• NCERT Solutions for Class 7 Maths Chapter 2
• NCERT Solutions for Class 7 Maths Chapter 3
• NCERT Solutions for Class 7 Maths Chapter 4
• NCERT Solutions for Class 7 Maths Chapter 5
• NCERT Solutions for Class 7 Maths Chapter 6
• NCERT Solutions for Class 7 Maths Chapter 7