NCERT Solutions Class 6 Maths

Chapter - 6: Integers

Exercise 6.1

1. Write opposites of the following:

(a) Increase in weight

Answer: Decrease in weight

Explanation: Decrease is the opposite of increase

(b) 30 km north

Answer: 30 km South

Explanation: South is the opposite direction of North

(c) 80 m east

Answer: 80 m west

Explanation: West is the opposite direction of East

(d) Loss of Rs 700

Answer: Gain of Rs 700

Explanation: Gain is the opposite of loss

(e) 100 m above sea level

Answer: 100 m below sea level

Explanation: Below is the opposite of above

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

(a) An aeroplane is flying at a height two thousand metre above the ground.

Answer: + 2000

Explanation: Ground level is considered at level 0. The level above the ground level is positive, while the level below the ground level is negative. Hence, 2000 m above the ground can be represented as +2000.

(b) A submarine is moving at a depth, eight hundred metre below the sea level.

Answer: - 800

Explanation: Sea level is considered at level 0. The level above the sea level is positive, while the level below the sea level is negative. Hence, 800 m below the ground can be represented as -800.

(c) A deposit of rupees two hundred.

Answer: +200

Explanation: Deposit means to submit the amount in the respective account. The value deposited is added to the total amount. Hence, it represented as positive.

(d) Withdrawal of rupees seven hundred.

Answer: -700

Explanation: Withdraw means to take out the amount from the respective account. The value taken is subtracted from the total amount. Hence, it represented as negative.

3. Represent the following numbers on a number line:

(a) + 5

(b) - 10

(c) + 8

(d) - 1

(e) - 6

4. Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points:

The equivalent diagram showing the numbers on the number line is shown below:

(a) If point D is + 8, then which point is - 8?

Answer: F

The above diagram shows that F is the point that has the value equivalent to -8.

(b) Is point G a negative integer or a positive integer?

Answer: Negative

G has the value equivalent to -6. Hence, it is a negative integer.

(c) Write integers for points B and E.

Answer: 4, -10

B has the value equivalent to 4 and E has the value equivalent to -10.

(d) Which point marked on this number line has the least value?

Answer: E

E has the least value of -10.

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

Answer: D, C, B, A, H, G, F, E

D has the highest value of 8 and E has the lowest value of -100. Thus, the decreasing order from highest integer to the lowest integer is D, C, B, A, H, G, F, E.

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

Siachin 10°C           below 0°C  
Shimla 2°C             below 0°C 
Ahmedabad 30°C         above 0°C 
Delhi 20°C             above 0°C 
Srinagar 5°C           below 0°C 

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

The temperatures below 0°C are represented with the negative sign, while the temperatures above 0°C are represented with the positive sign.

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

Plot the name of the city against its temperature.

The cities with positive temperature are represented on the right side of the number line, while the cities with negative temperatures are represented on the left side of the number line.

Answer:

(c) Which is the coolest place?

Answer: Siachin

The city with the lowest temperature is considered as the coolest place.

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

Answer: Delhi and Ahmedabad

Delhi has the temperature of 20 degrees Celsius, while Ahmedabad has the temperature of 30 degrees Celsius.

6. In each of the following pairs, which number is to the right of the other on the number line?

Positive number is always represented on the right side of the number line, while negative numbers are represented on the left side. 0 is the centre of the number line.

(a) 2, 9

Answer: 9

9 is to the right of the number 2

(b) - 3, - 8

Answer: -3

-3 is to the right of the number -8

(c) 0, - 1

Answer: 0

0 is to the right of the number -1

(d) - 11, 10

Answer: 10

10 is the right of the number -11

(e) - 6, 6

Answer: 6

6 is the right of the number --6

(f) 1, - 100

Answer: 1

1 is the right of the number --100

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

(a) 0 and - 7

Answer: -6, -5, -4, -3, -2, -1

These numbers on the number line will appear as:

(b) - 4 and 4

Answer: -3, -2, -1, 0, 1, 2, 3

These numbers on the number line will appear as:

(c) - 8 and - 15

Answer: -14, -13, -12, -11, -10, -9

(d) - 30 and - 23

Answer: -29, -28, -27, -26, -25, -24

8. (a) Write four negative integers greater than - 20.

Answer: -19, -18, -17, -16

Note: In the case of negative numbers, the numbers starting from -1 to -2, -3, and so on are in the decreasing order. It means that -2 is smaller than -1. The same is reverse in case of the positive numbers. The numbers starting from 1 to 2, 3, 4 and so on are in the increasing order. It means that 2 is greater than 1.

(b) Write four integers less than - 10.

Answer: -11, -12, -13, -14

9. For the following 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.

Answer: True

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

Answer: False

Correct statement: - 50 is to the right of - 100 on a number line.

(c) Smallest negative integer is - 1.

Answer: False

Correct statement: Largest negative integer is - 1.

(d) - 26 is greater than - 25.

Answer: False

Correct statement: - 25 is greater than - 26.

10. Draw a number line and answer the following:

(a) Which number will we reach if we move 4 numbers to the right of - 2.

Answer: 2

Number line:

(b) Which number will we reach if we move 5 numbers to the left of 1.

Answer: -4

Number line:

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

Answer: left

Explanation: The numbers smaller than -8 are present on its left side. -13 is smaller than -8.

(d) If we are at - 6 on the number line, in which direction should we move to

reach - 1?

Answer: Right

Explanation: The numbers greater than -6 are present on its right side. -1 is greater than -6.

Exercise 6.2

1. Using the number line write the integer which is:

(a) 3 more than 5

Answer: 8

(b) 5 more than -5

Answer: 0

(c) 6 less than 2

Answer: -4

(d) 3 less than -2

Answer: -5

2. Use number line and add the following integers:

(a) 9 + (- 6)

Answer: 3

(b) 5 + (- 11)

Answer: -6

(c) (- 1) + (- 7)

Answer: -8

(d) (- 5) + 10

Answer: 5

(e) (- 1) + (- 2) + (- 3)

Answer: -6

(f) (- 2) + 8 + (- 4)

Answer: 2

3. Add without using number line:

(a) 11 + (- 7)

Answer: 11 - 7 = 4

Adding + and - is equal to -

(b) (- 13) + (+ 18)

Answer: -13 + 18 = 5

Adding + and + is equal to +

(c) (- 10) + (+ 19)

Answer: -10 + 19 = 19 - 10 = 9

(d) (- 250) + (+ 150)

Answer: -250 + 150 = 150 - 250 = -100

The sign of the greater integer comes with the answer. If the greater number is positive, the answer is positive. If the greater number is negative, the answer is negative.

Here, the number 250 is greater than 150.

(e) (- 380) + (- 270)

Answer: -380 - 270 = -650

Same sign numbers are always added. Both the numbers are added because of the same negative sign. The answer will be an added number with the negative sign.

(f) (- 217) + (- 100)

Answer: -217 - 100 = -317

4. Find the sum of:

(a) 137 and - 354

Answer: -217

137 + (-354)

= 137 - 354

= -217

(b) - 52 and 52

Answer: 0

-52 + 52

= 0

(c) - 312, 39 and 192

Answer: -81

-312 + 39 + 192

= -312 + 231

= 231 - 312

= -81

(d) - 50, - 200 and 300

Answer: 50

-50 + (-200) + 300

= -50 - 200 + 300

= -250 + 300

= 300 - 250

= 50

5. Find the sum:

(a) (- 7) + (- 9) + 4 + 16

Answer: 4

- 7 - 9 + 4 + 16

= -16 + 20

(Adding the numbers with same sign first)

= 20 - 16

= 4

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

Answer: -38

= 37 - 2 - 65 - 8

(Adding the numbers with same sign first)

= 37 - 75

= -38

Exercise 6.3

1. Find

(a) 35 - (20)

Answer: 15

35 - 20

= 15

(b) 72 - (90)

Answer: -18

72 - 90

= -18

(c) (- 15) - (- 18)

Answer: 3

-15 + 18

= 18 - 15

= 3

Adding - and - is equal to -

(d) (-20) - (13)

Answer: -33

-20 - 13

= -33

(e) 23 - (- 12)

Answer: 35

23 + 12

= 35

(f) (-32) - (- 40)

Answer: 8

-32 + 40

= 40 - 32

= 8

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

(a) (- 3) + (- 6) < (- 3) - (- 6)

Explanation:

LHS (Left Hand Side)

(- 3) + (- 6)

= -3 - 6

= -9

RHS (Right Hand Side)

(- 3) - (- 6)

= -3 + 6

= 3

Thus,

LHS < RHS

(b) (- 21) - (- 10) > (- 31) + (- 11)

Explanation:

LHS

(- 21) - (- 10)

-21 + 10

= -11

RHS

(- 31) + (- 11)

-31 - 11

= -42

Thus,

LHS > RHS

(c) 45 - (- 11) > 57 + (- 4)

Explanation:

LHS

45 - (- 11)

45 + 11

= 56

RHS

57 + (- 4)

= 57 - 4

= 53

Thus,

LHS > RHS

(d) (- 25) - (- 42) > (- 42) - (- 25)

Explanation:

LHS

(- 25) - (- 42)

= -25 + 42

= 42 - 25

= 17

RHS

(- 42) - (- 25)

= -42 + 25

= -17

Thus,

LHS > RHS

3. Fill in the blanks.

(a) (- 8) + 8 = 0

(b) 13 + (- 13) = 0

(c) 12 + (- 12) = 0

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

(e) 5 - 15 = - 10

4. Find

(a) (- 7) - 8 - (- 25)

Answer: 10

-7 -8 + 25

= -15 + 25

= 10

(b) (- 13) + 32 - 8 - 1

Answer: 10

-13 + 32 - 8 - 1

= 32 - 13 - 8 - 1

Adding numbers with the same negative sign first

= 32 - 22

= 10

(c) (- 7) + (- 8) + (- 90)

Answer: -105

-7 -8 - 90

Adding numbers with the same negative sign

= - 105

(d) 50 - (- 40) - (- 2)

Answer: 92

50 + 40 + 2

= 92