### NATIONAL COUNSIL OF EDUCATIONAL RESEARCH AND TRAINING BOOK.

# NCERT SOLUTIONS FOR CLASS 6 TH MATHS CHAPTER 6,INTEGERS

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**CHAPTER – 6, INTEGERS**

1. The positive numbers, negative numbers and zero are called integers.

2. The collection of numbers infinity to … – 3, – 2,- 1, 0 1, 2, 3 …….. to infinity are called integers.

3. The numbers that we go below zero on the number line are called negative integers. Examples -1, -2, – 3 ……

4. The numbers that we go above zero on the number line are called positive integers. Examples 1, 2, 3, ……..

5. We have seen that one more than given number gives a successor.

6. We have also seen that one less than given number gives a predecessor.

7. Add two integers, their sum is a positive integer.

8. Add two negative integers, their sum is a negative integer.

9. When a positive integer is added to an integer, the resulting integer becomes greater than the given integer.

10. When a negative integer is added to an integer, the resulting integer becomes less than the given integer.

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

12. 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.

## NCERT SOLUTIONS FOR MATHS CLASS 6 TH CHAPTER 6, INTEGERS

**CHAPTER – 6, INTEGERS**

**EXERCISE – 6.1**

**Problem 1**

1. Write opposites of the following

a. Increase in weight

b. 30 km north

c. 326 BC

d. Loss of Rs. 700

e. 100 m above sea level.

**Answers :**

a. Decrease in weight.

b. 30 km south

c. 326 AD

d. Gain of Rs. 700

e. 100 m below sea level.

**Problem 2**

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

a. An aeroplane is flying at a height two thousand meters above the ground.

b. A submarine is moving at a depth eight hundred meters below the sea level.

c. A deposit of rupees two hundred.

d. Withdrawal of rupees seven hundred.

**Answers**

a. + 2000

b. – 800

c. + 200

d. – 700

**Problem 3**

3. Represent the following numbers on a number line.

a. + 5

b. – 10

c. + 8

d. – 1

e. – 6

**Answers :**

**Problem 4**

4. Below figure is a vertical number line, representing integers, observe it and locate the following points.

a. If point D is + 8,then which point is – 8.

b. Is point G a negative integer or a positive integer ?

c. Write integers for points B and E

d. Which point marked in this number line has the least value.

e. Arrange all the points in decreasing order of value.

**Answers :**

a. The point + 8 is F.

b. The point G is a negative integer ( – 6 ).

c. The point P represents 4 and the point E represents – 10.

d. The point on this number line has the least value is E.

e. D > C > B > A > O H > G > F > E

**Problem 5**

5. Following is the list of temperatures of five places in India on a particular day of the year.

Place …………….Temperature …………….

a. Siachin………….10° below 0° ……………..

b. Shimla…………..2° below 0° ………………

c. Ahmedabad…….30° above 0° ……………

d. Delhi ………………20° above 0° ……………

e. Srinagar …………..5° below 0° ……………

a. Write the temperatures of these places in the form of integers in the blank column.

b. Following is the number line representing the temperature in degree Celsius.

Plot the name of the city against its temperature.

c. Which is the coolest place?

d. Write the names of the places where the temperatures are above 10°.

**Answers :**

Place …………….Temperature

a. Siachin …………. 10° below 0° … -10° c

b. Shimla ………….. 2° below 0°b….. – 2°c

c. Ahmedabad ……. 30° above 0° … + 30°c

d. Delhi ………… 20° above 0° … + 20°c

e).Srinagar ……. 5° below 0° ……… – 5°

b).

c. Siachin is the coolest place.

d. Delhi, Ahmedabad

**Problem 6**

6. In each of the fallowing pairs,which number is to the right of the others on the number line.

a. 2, 9

b. – 3, – 8

c. 0, – 1

d. – 11, 10

e. – 6, 6

f. 1, -100

**Answers :**

a. 2, 9 ….. 2 < 9

9 is the right side of 2

b. – 3, – 8 …… – 3 > – 8

– 3 is the right side of – 8

c. 0, – 1 …… 0 > – 1

0 is the right side of – 1

d. – 11, 10 ….. – 11 < 10

10 is the right side of – 11

e. – 6, 6 …… – 6 < 6

6 is the right side of – 6

f. 1, – 100 ….. 1 > – 100

1 is the right side of – 100

**Problem 7**

**7. **Write all the integers between the given pairs. ( Write them in the increasing order)

a. 0 and – 7

b. – 4 and 4

c. – 8 and -15

d. – 30 and – 23

**Answers :**

a. 0 and – 7

*– *6 < – 5 < – 4 < – 3 < – 2 < – 1

b. – 4 and 4

*– *3 < – 2 < – 1 < 0 < 1 < 2 < 3

*c. – 8 and – 15*

14 < – 13 < – 12 < – 11 < – 10 < – 9

*d. – 30 and – 23*

29 < – 28 < – 27 < – 26 < – 25 < – 24

**Problem 8**

8. a. Write four negative integers greater than – 20.

b. Write four negative integers less than – 10.

**Answers :**

a.The four negative integers greater than – 20. are – 19 ,- 18 ,- 17 ,- 16

b.The four negative integers less than – 10 are-11, – 12 , – 13 , – 14.

9. For the fallowing statements write true ( T ) or false ( F ).If the statement is false, correct the statement.

a. – 8 is to the right of – 10 on a number line.

b. – 100 is to the right of – 50 on a number line.

c. Smallest negative integer is – 1.

d. – 26 is greater than – 25.

**Answers :**

a. – 8 is to the right of – 10 on a number line.

True

b. -100 is to the right of – 50 on a number line.

False

– 100 is the left side of – 50 on a number line.

c. Smallest negative integer is – 1.

False

Greatest negative integer is – 1.

d. – 26 is greater than – 25.

False

– 26 is smaller than – 25.

10. Draw a number line and answer the fallowing.

a. Which number will we reach if we move four numbers to the right of – 2?

b. Which number will we reach if we move five numbers to the right of – 4?

c. If we are at – 8 on the number line, in which direction should we move to reach – 13 ?

d. If we are at – 6 on the number line, in which direction should we move to reach – 1 ?

**Answers :**

a. If we move four numbers to the right of – 2 ,we will reach + 2 on a number line.

b. If we move five numbers to the right of – 4 ,we will reach + 1 on a number line.

c. If we are at -8 on the number line, we should move to left reach – 13

d. If we are at – 6 on the number line, we should move to right reach – 1

## CBSE SOLUTIONS FOR CLASS 6TH MATHS CHAPTER 6

**CHAPTER – 6 INTEGERS**

**EXERCISE 6.2**

**Problem 1**

1. Using the number line write the integers which is

a. 3 more than 5

b. 5 more than – 5

c. 6 less than 2

d. 3 less than – 2

**Answers :**

a. 3 more than 5 is 8.

b. 5 more than -5 is 0.

c. 6 less than 2 is – 4.

d. 3 less than – 2 is – 5.

**Problem 2**

2. Use number line and add the fallowing integers

a. 9 + ( – 6 )

b. 5 + ( – 11 )

c. ( – 1 ) + ( – 7 )

d. ( – 5 ) + 10

e. ( – 1 ) + ( – 2 ) +( – 3 )

f. ( – 2 ) + 8 + ( – 4 )

**Answers :**

a. 9 + ( – 6 ) = 3

b. 5 + ( – 11 ) = – 6

c. ( – 1 ) + ( – 7 ) = – 8

d. ( – 5 ) + 10 = 5

e. ( – 1 ) + ( – 2 ) + ( – 3 ) = – 6

f. ( – 2 ) + 8 + ( – 4 ) = 2

**Problem 3**

3. Add without using number line.

a. 11 + ( – 7 )

b. ( – 13 ) + ( + 18 )

c. ( – 11 ) + ( + 19 )

d. – 250 + ( + 150 )

e. ( – 380 ) + ( – 270 )

f. ( – 217 ) + ( – 100 )

**Answers :**

a. 11 + ( – 7 )

11 – 7 = + 4

b. ( – 13 ) + ( + 18 )

– 13 + 18 = + 5

c. ( – 11 ) + ( + 19 )

– 11 + 19 = + 8

d. – 250 + ( + 150 )

– 250 + 150 = – 100

e. ( – 380 ) + ( – 270 )

– 380 – 270 = – 650

f. ( – 217 ) + ( – 100 )

– 217 – 100 = – 317

**Problem 4**

4. Find the sum of

a. 137 and – 354

137 + ( -354 )

137 – 354 = – 217

b. – 52 and 52

– 52 + 52 = 0

c. – 312, 39 and 192

– 312 + 39 + 192 = – 81

d. -50, – 200 and 300

– 50 + ( – 200 ) + 300

– 50 – 200 + 300 = 50

**Problem 5**

5. Find the sun

a. – 7 + ( – 9 ) + 4 + 16

b. 37 + ( – 2 ) + ( – 65 ) + ( – 8 )

**Answers :**

*a. – 7 + ( – 9 ) + 4 + 16*

– 7 – 9 + 4 + 16

– 16 + 20 = + 4

*b. 37 + ( – 2 ) + ( – 65 ) + ( – 8 )*

37 – 2 – 65 – 8

37 – 75 = – 38

**NCERT SOLUTIONS FOR MATHS CLASS 6 TH CHAPTER 6**

**CHAPTER – 6 INTEGERS**

**EXERCISE 6.3**

**Problem 1**

1. Find

a. 35 – ( 20 )

b. 72 – ( 90 )

c. ( – 15 ) – ( – 18 )

d. ( – 20 ) – ( 13 )

e. 23 – ( – 12 )

f. – 32 – ( – 40 )

**Answers :**

a. 35 – ( 20 )

= 35 – 20 = 15

b. 72 – ( 90 )

= 72 – 90 = – 18

c. ( – 15 ) – ( – 18 )

= – 15 + 18 = + 3

d. ( – 20 ) – ( 13 )

= – 20 – 13 = – 33

e. 23 – ( – 18 )

= 23 + 18 = 41

f. – 32 – ( – 40 )

= – 32 + 40 = + 8

**Problem**

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

a. ( – 3 ) + ( – 6 ) …….. ( – 3 ) – ( – 6 )

b. ( – 21 ) – ( – 10 ) ……… ( – 31 ) + ( – 11 )

c. 45 – ( -11 ) ……… 57 + ( – 4 )

d. – 25 – ( – 42 ) ……….. ( – 42 ) – ( – 25 )

**Answers :**

a. ( – 3 ) + ( – 6 ) ……..( – 3 ) – ( – 6 )

– 3 – 6 ………… – 3 + 6

– 9 ……………….. + 6

– 9 < 6, Therefore, ( – 3 ) + ( – 6 ) < ( – 3 ) – ( – 6 )

b. ( – 21 ) – ( – 10 ) ……… ( – 31 ) + ( – 11 )

– 21 + 10 …………… – 31 – 11

– 11 …………………. – 41

– 11 > – 41, Therefore, ( – 21 ) – ( – 10 ) > ( – 31 ) + ( – 11 )

c. 45 – ( – 11 ) ……… 57 + ( – 4 )

45 + 11 …………… 57 – 4

57 …………………. 53

57 > 53, Therefore, 45 – ( – 11 ) > 57 + ( – 4 )

d. – 25 – ( – 42)………..( – 42) – ( – 25)

– 25 + 42 …………… – 42 + 25

17 ……………………. – 17

17 > – 17, Therefore, – 25 – ( – 42 ) > ( – 42 ) – ( – 25 )

**Problem 3**

3. Fill in the blanks

a. – 8 + ….. = 0

b. 13 + …… = 0

c. 12 + ( – 12 ) = …..

d. ( – 4 ) + …… = – 12

e. ….. – 15 = – 10

**Answers :**

a. – 8 + 8 = 0

b. 13 + ( – 13 ) = 0

c. 12 + ( – 12 ) = 0

d. ( – 4 ) + ( – 8 ) = -12

e. 5 – 15 = – 10

**Problem 4**

*4. Find*

*a. ( – 7 ) – 8 – ( – 25 )*

*b. – 13 + 32 – 8 – 1*

*c. ( – 7 ) + ( – 8 ) + ( – 90 )*

*d. 50 – ( – 40 ) – ( – 2 )*

**Answers :**

( – 7 ) – 8 – ( – 25 )

= – 7 – 8 + 25

= – 15 + 25 = + 10

b. – 13 + 32 – 8 – 1

– 13 + 32 – 9

– 22 + 32 = + 10

c.( – 7 ) + ( – 8 ) + ( – 90 )

= – 7 – 8 – 90 = – 105

d.50 – ( – 40 ) – ( – 2 )

= 50 + 40 + 2 = 92

**6TH CLASS MATHS SOLUTIONS CHAPTER 6 CBSE**

**CHAPTER – 6 INTEGERS**

Integers is a important chapter. This is very useful in our life.

**Note** : Observe the solutions of integers and try them in your own methods.

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