# NCERT Class 6 Maths Chapter 6 ‘Integers’: Notes and Solutions (Free PDF)

In this chapter, students will understand everything related to integers. Students will learn to compare, order and apply different functions on integers. Through the Chapter 6 of Class 6 Maths, students will learn the different additive and subtractive properties of integers. Read through for CBSE NCERT Class 6 Maths Chapter 6 Integers Notes, Exercise and Important Questions.

## CBSE NCERT Class 6 Maths Notes for Chapter 6 Integers- Free PDF Download

Below we have given topic-wise notes for the CBSE NCERT Class 6 Maths for Chapter 6 Integers. We have also provided a downloadable free PDF at the end of these notes so you can download and take a printout to study later when you need quick revision before going to the exam hall.

### Topic 1: Integers

• Integers: Whole numbers and negative numbers are collectively known as integers. There are two kinds of integers – positive and negative.
• Positive Integers: All positive numbers among the whole list of integers beginning with 1, 2, 3,.. and so on are called positive integers.
• Negative Integers: All negative numbers among the whole list of integers going down below the value of -1, -2, -3,.. and so on are called negative integers.

### Topic 2: Representation of Integers on the Number Line

• Number Line: On a number line, the numbers are represented at a fixed distance from each other.

### Topic 3: Ordering Integers on the Number Line

• Ordering of Integers: On the Number Line, 0 is placed at the centre. On the right of zero, all the positive integers are written in an increasing order starting from zero. All the negative integers are written on the left of zero in decreasing order.

### Topic 4: Addition of Integers

1. You add when you have two positive integers.

For eg, (+3) + (+2) = +5 [= 3 + 2].

1. You also add when you have two negative integers but the answer will take a minus (–) sign.

For eg, (–2) + (–1) = – (2+1) = –3.

1. When you have one positive and one negative integer, you must subtract, but the answer will take the sign of the bigger integer.

For eg, (+ 5) + (– 8) = (+ 5) + (– 5) + (– 3)

= 0 + (– 3) = (– 3)

### Topic 5: Subtraction of Integers

• Subtraction of Integers: To subtract an integer from another integer, it is enough to add the additive inverse of the integer that is being subtracted, to the other integer.

For eg, (– 10) – (– 4) = (– 10) + (additive inverse of – 4)

= –10 + 4 = – 6

## Important Questions in NCERT Class 6 Maths Chapter 6: Free PDF Download

Below we have provided some important exercise questions and their solutions from Chapter 6 of Maths for Class 6.

### Exercise 6.1

Q 1. Write opposites of the following :

1. Increase in weight
2. 30 km north
3. Loss of Rs 700
4. 100 m above sea level

Ans. The opposites of each of the given cases are given below.

1. The opposite of an increase in weight is a decrease in weight.
2. The opposite of 30 km north is 30 km south.
3. The opposite of the loss of Rs 700 is the gain of Rs 700.
4. The opposite of 100 m above sea level is 100 m below the sea level.

Q 2. Represent the following numbers as integers with appropriate signs.

1. An aeroplane is flying at a height two thousand metre above the ground.
2. A submarine is moving at a depth, eight hundred metre below the sea level.
3. A deposit of rupees two hundred.
4. Withdrawal of rupees seven hundred.

Ans. Let us write each case in numbers with appropriate signs as:

1. +2000 m
2. -800 m
3. + Rs 200
4. – Rs 200

Q 3. In each of the following pairs, which number is to the right of the other on the

number line?

1. 2, 9
2. – 3, – 8 >
3. 0, – 1

Ans. On the number line, all the numbers (whether positive or negative) are placed in an increasing order from left to right. The number to the right in each case is given below.

1. Since 2 < 9, 9 lies on the right side of 2 on the number line.
2. In this case, -3 > -8, so -3 lies on the right of -8 on the number line.
3. Again, 0 > -1, so 0 lies on the right of -1 on the number line.

Q 4. For the following statements, write True (T) or False (F). If the statement is false,

correct the statement.

1. – 8 is to the right of – 10 on a number line.
2. – 100 is to the right of – 50 on a number line.
3. The smallest negative integer is – 1.
4. – 26 is greater than – 25

Ans. The answers in each case are given below.

1. True, because -8 > -10.
2. False, -100 < -50. So, -100 is to the left of -50 on the number line.
3. False, -1 is the greatest negative integer.
4. False, -26 < -25.

### Exercise 6.2

Q 1.  Find the sum of :

1. 137 and – 354
2. – 52 and 52
3. – 312, 39 and 192
4. – 50, – 200 and 300

Ans. Let us add the given integers below.

1. 137 + (-354) = -217
2. -52 + 52 = 0
3. -312 + 39 + 192 = -312 + 231 = -81
4. -50 + (-200) + 300 = -50 -200 +300 = -250 + 300 = 50

Q 2. Add without using a number line.

1. 11+ (-7)
2. -13 + (+18)
3. -10 + (+19)
4. -250 + (+150)
5. -380 + (-270)
6. -217 + (-100)

Ans. Let us add the given integers below:-

1. 11 – 7= 4
2. -13 + 18= 5
3. -10 + 19= 9
4. -250 + 150= -100
5. -380 – 270= -650
6. -217 – 100= -317

Q 3. Find the sum

1. -7 + (-9) + 4 + 16
2. 37 + (-2) + (-65) + (-8)

Ans. 1. -7 + (-9) + 4 = 16

-7 -9 +4 +16

-16 + 4 +16

-12 +16= 4

2. 37 + (-2) + (-65) + (-8)

37 – 2 – 65 – 8

35 – 65 – 8

-30-8= -38

### Exercise 6.3

Q 1. Fill in the blanks with >, < or = sign.

1. (– 3) + (– 6) ______ (– 3) – (– 6)
2. (– 21) – (– 10) _____ (– 31) + (– 11)
3. 45 – (– 11) ______ 57 + (– 4)
4. (– 25) – (– 42) _____ (– 42) – (– 25)

Ans. The answers are given below.

1. <
2. >
3. >
4. >

Q 2.  Fill in the blanks.

1. (– 8) + _____ = 0
2. 13 + _____ = 0
3. 12 + (– 12) = ____
4. (– 4) + ____ = – 12
5. ____ – 15 = – 10

1. 8
2. -13
3. 0
4. -8
5. 5

Q 3. Find:-

1. 35-(20)
2. 72- (90)
3. -15 – (-18)
4. -20 – (13)
5. 23 – (-12)
6. -32 – (-40)

Ans. 1. 15

2. -18

3. -33

4. -33

5. 35

6. 8

Q 4. Find

1. -7 – 8 – (-25)
2. -13 + 32 -8 -1
3. -7 + (-8) + (-90)
4. 50 – (-40) – (-2)

Ans. 1. -7-8+25

-7+17= 10

2. -13 + 32 -8 -1

19-8-1

19-9= 10

3. -7 + (-8) + (-90)

-7 -8 -90= -105

4. 50 – (-40) – (-2)

50 + 40 + 2 = 92

Also See:

CBSE NCERT Class 6 Maths Chapter 1 Knowing Our Numbers Notes and Important Questions – Free PDF

CBSE NCERT Class 6 Maths Chapter 2 Whole Numbers Notes, Exercise and Important Questions – Free PDF

CBSE NCERT Class 6 Maths Chapter 3 Playing With Numbers Notes and Important Exercise Questions and Answers – Free PDF

CBSE NCERT Class 6 Maths Chapter 4 Basic Geometrical Ideas Notes and Important Exercise Questions and Answers – Free PDF

CBSE NCERT Class 6 Maths Chapter 5 Understanding Elementary Shapes Notes and Important Exercise Questions and Answers – Free PDF

## FAQs

Q.1. What are integers?

Ans: Whole numbers and negative numbers are collectively known as integers.

Q.2. How many types of integers are there?

Ans: There are two kinds of integers – positive and negative.

Q.3. What is the order of representing the integers on a number line?

Ans: On the number line, all the integers (whether positive or negative) are placed in an increasing order from left to right.

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