Integers Worksheet for Class 6

Integers worksheet for Class 6 students, learning integers is very important because it helps to solve real life problems like temperature going below zero, money borrowed (negative) or money saved (positive). A class 6 integers worksheet is a good way to practice and understand these ideas in a simple and easy manner.

This worksheet on integers for class 6 with answers pdf free is prepared to help students learn step by step. It is made with simple examples and practice sums so that students can improve speed and accuracy. An integers class 6 worksheet with answers is also very useful for self checking and correction. Students can also use integers worksheet for class 6 with answers for revision before class 6 exams.

Integers class 6 worksheet ncert style so that it matches school CBSE syllabus. This class 6 integers worksheet with answers also builds confidence in solving problems of addition, subtraction, multiplication and division of integers. So with this integers class 6 worksheet, students can practice more and make learning of integers easy, interesting and useful in daily life.

What are Integers?

Integers are numbers that include positive numbers, negative numbers, and zero. They do not include fractions or decimals.

Examples of integers are: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,

In simple words, integers are whole numbers with both positive and negative values.

Types of Integers

• Positive Integers: 1, 2, 3, 4, 5…
• Negative Integers: -1, -2, -3, -4, -5…
• Zero: 0 is also an integer. It is neither positive nor negative.

Download Integers worksheet for class 6 with answers PDF

Students can download the Integers Worksheet for Class 6 PDF and practice anytime. The worksheet includes basic to advanced-level questions with answers.

Integers worksheet for class 6 with Answers

Q. Write an appropriate integer for each of the following:

(i) A loss of Rs.35

(ii) 75° above zero degree

(iii) 24° below zero

(iv) Depositing Rs.680 in a bank

(iii) Gaining Rs.555

(vi) Losing Rs.324

(vii) Withdrawing Rs.1560 from a bank

Solution:

(i) A loss of Rs. 35

Loss is represented by a negative integer.

So, Rs. 35 loss = -35

Answer: -35

(ii) 75° above zero degree

Above zero is represented by a positive integer.

So, 75° above zero = +75

Answer: +75

(iii) 24° below zero

Below zero is represented by a negative integer.

So, 24° below zero = -24

Answer: -24

(iv) Depositing Rs. 680 in a bank

Depositing money means money is added, so it is represented by a positive integer.

So, depositing Rs. 680 = +680

Answer: +680

(v) Gaining Rs. 555

Gain is represented by a positive integer.

So, gaining Rs. 555 = +555

Answer: +555

(vi) Losing Rs. 324

Losing money is represented by a negative integer.

So, losing Rs. 324 = -324

Answer: -324

(vii) Withdrawing Rs. 1560 from a bank

Withdrawing money means money is taken out, so it is represented by a negative integer.

So, withdrawing Rs. 1560 = -1560

Answer: -1560

Q. In each of the following pairs, state which integer is greater:

(i) -5, -7

(ii) -7, 5

(iii) 0, 8

(iv) 0, -3

(v) 27, -315

(vi) -37, -25

(vii) -15, 0

(viii) -1, -53

Solution: 

(i) -5, -7

On the number line, -5 is to the right of -7.

So, -5 > -7

Answer: -5

(ii) -7, 5

A positive integer is always greater than a negative integer.

So, 5 > -7

Answer: 5

(iii) 0, 8

8 is a positive integer and it is greater than 0.

So, 8 > 0

Answer: 8

(iv) 0, -3

Zero is greater than any negative integer.

So, 0 > -3

Answer: 0

(v) 27, -315

A positive integer is always greater than a negative integer.

So, 27 > -315

Answer: 27

(vi) -37, -25

Both are negative integers. The number closer to zero is greater.

-25 is closer to zero than -37.

So, -25 > -37

Answer: -25

(vii) -15, 0

Zero is greater than any negative integer.

So, 0 > -15

Answer: 0

(viii) -1, -53

Both are negative integers. The number closer to zero is greater.

-1 is closer to zero than -53.

So, -1 > -53

Answer: -1

Q. Add the following integers:

(i) +84 and +45

(ii) -63 and -23

(iii) -44 and +35

(iv) +12 and -20

(v) +2245 and -1013

(vi) -260 and 0

Solution: 

(i) +84 and +45

Both integers are positive, so we add them and keep the positive sign.

+84 + +45 = +129

Answer: +129

(ii) -63 and -23

Both integers are negative, so we add the numbers and keep the negative sign.

-63 + -23 = -86

Answer: -86

(iii) -44 and +35

One integer is negative and the other is positive.

Subtract the smaller number from the bigger number:

44 - 35 = 9

The bigger number is 44, and its sign is negative.

So,

-44 + 35 = -9

Answer: -9

(iv) +12 and -20

One integer is positive and the other is negative.

Subtract the smaller number from the bigger number:

20 - 12 = 8

The bigger number is 20, and its sign is negative.

So,

+12 + -20 = -8

Answer: -8

(v) +2245 and -1013

One integer is positive and the other is negative.

Subtract the smaller number from the bigger number:

2245 - 1013 = 1232

The bigger number is 2245, and its sign is positive.

So,

+2245 + -1013 = +1232

Answer: +1232

(vi) -260 and 0

Adding zero to any integer gives the same integer.

So,

-260 + 0 = -260

Answer: -260

Q. Find the sum of the following:

(i) -4761 and 9999

(ii) 2345, 793 and 1447

(iii) -3167, -445 and 2208

(iv) 3141, -1000 and 5345

Solution: 

(i) -4761 and 9999

-4761 + 9999 = 9999 - 4761

9999 - 4761 = 5238

Answer: 5238

(ii) 2345, 793 and 1447

2345 + 793 + 1447

2345 + 793 = 3138

3138 + 1447 = 4585

Answer: 4585

(iii) -3167, -445 and 2208

Calculation:

-3167 + (-445) + 2208

-3167 + (-445) = -3612

-3612 + 2208 = -(3612 - 2208)

3612 - 2208 = 1404

So, -3612 + 2208 = -1404

Answer: -1404

(iv) 3141, -1000 and 5345

3141 + (-1000) + 5345

3141 + 5345 = 8486

8486 - 1000 = 7486

Answer: 7486

Q. Find the additive inverse of each of the following integers:

(i) 45

(ii) 0

(iii) -167

(iv) 8

(v) 1

Solution: The additive inverse of a number is the number which gives 0 when added to the original number.

For example:

5 + (-5) = 0

So, the additive inverse of 5 is -5.

(i) 45

45 + (-45) = 0

So, the additive inverse of 45 is -45.

Answer: -45

(ii) 0

0 + 0 = 0

So, the additive inverse of 0 is 0.

Answer: 0

(iii) -167

Calculation:

-167 + 167 = 0

So, the additive inverse of -167 is 167.

Answer: 167

(iv) 8

Calculation:

8 + (-8) = 0

So, the additive inverse of 8 is -8.

Answer: -8

(v) 1

Calculation:

1 + (-1) = 0

So, the additive inverse of 1 is -1.

Answer: -1

Q. Find the successor of each of the following integers.

(i) -670

(ii) -115

(iii) 999

(iv) -1

(v) -200

Solution: The successor of an integer is the number that comes just after it.

To find the successor, we add 1 to the given integer.

Successor = Given integer + 1

(i) -670

-670 + 1 = -669

Answer: -669

(ii) -115

-115 + 1 = -114

Answer: -114

(iii) 999

999 + 1 = 1000

Answer: 1000

(iv) -1

-1 + 1 = 0

Answer: 0

(v) -200

-200 + 1 = -199

Answer: -199

Q. Find the predecessor of each of the following integers:

(i) 0

(ii) -45

(iii) -1000

(iv) -128

(v) -500

Solution: The predecessor of an integer is the number that comes just before it.

To find the predecessor, subtract 1 from the given integer.

Predecessor = Given integer - 1

(i) 0

Calculation:

0 - 1 = -1

Answer: -1

(ii) -45

Calculation:

-45 - 1 = -46

Answer: -46

(iii) -1000

Calculation:

-1000 - 1 = -1001

Answer: -1001

(iv) -128

Calculation:

-128 - 1 = -129

Answer: -129

(v) -500

Calculation:

-500 - 1 = -501

Answer: -501

Q. Simplify the following:

(i) (-105) + (-64) + 115 + (-47)

(ii) (392) + (-115) + 675 + (-205) + (-645)

(iii) (-360) + 111 + (-342) + 88 + (-20)

(iv) (-1) + 52 + (-896) + (-65) + 2410

Solution: 

(i) (-105) + (-64) + 115 + (-47)

(-105) + (-64) + 115 + (-47)

First add the negative integers:

-105 + (-64) + (-47) = -216

Now add 115:

-216 + 115 = -101

Answer: -101

(ii) 392 + (-115) + 675 + (-205) + (-645)

392 + (-115) + 675 + (-205) + (-645)

First add the positive integers:

392 + 675 = 1067

Now add the negative integers:

(-115) + (-205) + (-645) = -965

Now simplify:

1067 + (-965) = 1067 - 965 = 102

Answer: 102

(iii) (-360) + 111 + (-342) + 88 + (-20)

(-360) + 111 + (-342) + 88 + (-20)

First add the positive integers:

111 + 88 = 199

Now add the negative integers:

(-360) + (-342) + (-20) = -722

Now simplify:

199 + (-722) = -(722 - 199)

722 - 199 = 523

So,

199 + (-722) = -523

Answer: -523

(iv) (-1) + 52 + (-896) + (-65) + 2410

(-1) + 52 + (-896) + (-65) + 2410

First add the positive integers:

52 + 2410 = 2462

Now add the negative integers:

(-1) + (-896) + (-65) = -962

Now simplify:

2462 + (-962) = 2462 - 962 = 1500

Answer: 1500

Q. State whether the following statements are true (T) or false (F).

(i) The sum of two integers can be zero.

(ii) The addition of three distinct integers is zero if one of integer is zero.

(iii) The addition of a negative (-ve) integer and a positive (+ve) integer is always a negative (-ve) integer.

(iv) The addition of an integer and its opposite is zero.

(v) The addition of two negative (-ve) integers is always a positive (+ve) integer.

Solution: (i) The sum of two integers can be zero.

This is true.

Example:

5 + (-5) = 0

Answer: True (T)

(ii) The addition of three distinct integers is zero if one integer is zero.

This is false.

Example:

0 + 2 + 3 = 5

Here, one integer is zero, but the sum is not zero.

Answer: False (F)

(iii) The addition of a negative integer and a positive integer is always a negative integer.

This is false.

Example:

-4 + 10 = 6

Here, the answer is positive, not negative.

Answer: False (F)

(iv) The addition of an integer and its opposite is zero.

This is true.

Example:

8 + (-8) = 0

Answer: True (T)

(v) The addition of two negative integers is always a positive integer.

This is false.

Example:

-6 + (-4) = -10

The sum of two negative integers is always negative.

Answer: False (F)

Q. Find an integer n such that

(i) n + 57 = 0;

(ii) n + (-89) = 0

Solution: 

(i) n + 57 = 0

n + 57 = 0

To find n, move 57 to the other side:

n = 0 - 57

n = -57

Check:

-57 + 57 = 0

Answer: n = -57

(ii) n + (-89) = 0

n + (-89) = 0

This means:

n - 89 = 0

To find n, move -89 to the other side:

n = 0 + 89

n = 89

Check:

89 + (-89) = 0

Answer: n = 89

Q. Word Problems on Addition of Integers:

(i) A private car traveled 48 km to the north of California and then further traveled 215 km to the south from there. How far was the car finally from California?

Let north direction be positive and south direction be negative.

Solution:

48 km north = +48

215 km south = -215

So,

+48 + (-215) = 48 - 215

48 - 215 = -167

The negative sign shows that the car is in the south direction.

Answer: The car was finally 167 km south of California.

(ii) Nairitee opened her bank account on 1st August 2023 by depositing Rs. 7896. A week later she withdrew Rs. 3562 and finally on the last day of August 2023 she deposited Rs. 4569. What would be her bank balance on the first day of September 2023?

Depositing money is positive and withdrawing money is negative.

Solution:

First deposit = +7896

Withdrawal = -3562

Second deposit = +4569

So,

7896 + (-3562) + 4569

7896 - 3562 = 4334

4334 + 4569 = 8903

Her bank balance on 1st September 2023 would be Rs. 8903.

(iii) Two integers have a difference of 6 and a sum of -40. What are the integers?

Solution: Let the two integers be x and y.

Given:

x - y = 6

x + y = -40

Add both equations:

x - y + x + y = 6 + (-40)

2x = -34

x = -34 ÷ 2

x = -17

Now put x = -17 in the equation:

x + y = -40

-17 + y = -40

y = -40 + 17

y = -23

Check:

Difference: -17 - (-23) = -17 + 23 = 6

Sum: -17 + (-23) = -40

The two integers are -17 and -23.

Q. Subtract the following:

(i) +9 from +12

(ii) +15 from -21

(iii) -42 from +74

(iv) -10 from +25

(v) 7 from 15

(vi) +7 from -15

(vii) -7 from +15

(viii) -7 from 15

Solution: 

(i) +9 from +12

+12 - (+9) = 12 - 9

= 3

(ii) +15 from -21

-21 - (+15) = -21 - 15

= -36

(iii) -42 from +74

+74 - (-42) = 74 + 42

= 116

(iv) -10 from +25

+25 - (-10) = 25 + 10

= 35

(v) 7 from 15

15 - 7 = 8

(vi) +7 from -15

-15 - (+7) = -15 - 7

= -22

(vii) -7 from +15

+15 - (-7) = 15 + 7

= 22

(viii) -7 from 15

15 - (-7) = 15 + 7

= 22

Q. Fill in the blanks

(i) 0 × 9 = ______

Calculation:

0 × 9 = 0

Answer: 0

(ii) 9 × 0 = ______

Calculation:

9 × 0 = 0

Answer: 0

(iii) 0 × (-9) = ______

Calculation:

0 × (-9) = 0

Answer: 0

(iv) 15 × 13 = ______

Calculation:

15 × 13 = 195

Answer: 195

(v) 13 × 15 = ______

Calculation:

13 × 15 = 195

Answer: 195

(vi) (-13) × 15 = ______

Calculation:

(-13) × 15 = -195

Answer: -195

Q. Find the value of the products

(i) 4 × 12

Calculation:

4 × 12 = 48

Answer: 48

(ii) 11 × 5

Calculation:

11 × 5 = 55

Answer: 55

(iii) (-4) × 12

Calculation:

(-4) × 12 = -48

Answer: -48

(iv) (-3) × (-12)

Calculation:

(-3) × (-12) = 36

Answer: 36

(v) 8 × 0

Calculation:

8 × 0 = 0

Answer: 0

(vi) 7 × 4 × 3

Calculation:

7 × 4 × 3 = 28 × 3

28 × 3 = 84

Answer: 84

(vii) 7 × (-4) × 3

Calculation:

7 × (-4) × 3 = -28 × 3

-28 × 3 = -84

Answer: -84

(viii) (-7) × 3 × (-3)

Calculation:

(-7) × 3 × (-3) = -21 × (-3)

-21 × (-3) = 63

Answer: 63

(ix) (-7) × (-3) × (-3)

Calculation:

(-7) × (-3) × (-3) = 21 × (-3)

21 × (-3) = -63

Answer: -63

(x) (-8) × (-8) × (-8)

Calculation:

(-8) × (-8) × (-8) = 64 × (-8)

64 × (-8) = -512

Answer: -512