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Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 1 www.embibe.com CBSE NCERT Solutions for Class 6 Mathematics Chapter 6

Back of Chapter Questions

Exercise 6.1

1.Write opposite of the following:

(A)Increase in weight (B)30 km north (C)ͺͲ East (D)Loss of ൟ700 (E)ͳͲͲ above sea level

Solution:

(A)Decrease in weight(B)30 km south (C)ͺͲ West (D)Profit of ൟ700 (E)ͳͲͲ below sea level 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.

Solution:

(A)ሺ൅ሻʹͲͲͲ meters Since, the aeroplane is flying above the ground, the height is taken to be positive. (B)ሺെሻͺͲͲ metersSince, the submarine is below the sea level, the depth is taken to be negative. (C)ሺ൅ሻʹͲͲ Rupees

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 2 www.embibe.com Deposition of money is considered to be positive while expenditure is

considered negative. (D) ሺെሻ͹ͲͲ Rupees Deposition of money is considered to be positive while expenditure is considered negative.

3. Represent the following numbers on number line:

(A) ൅ͷ (B) െͳͲ (C) ൅ͺ (D) െͳ (E) െ͸

Solution:

(A) ൅ͷ is greater than 0, hence it appears towards the right of zero. (B) െͳͲ is lesser than 0, hence it appears towards the left of zero. (C) ൅ͺ is greater than 0, hence it appears towards the right of zero. (D) െͳ is lesser than 0, hence it appears towards the left of zero. (E) െ͸ is lesser than 0, hence it appears towards the left of zero.

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 3 www.embibe.com

4. Adjacent figure is a vertical number line, representing integers. Observe it and

locate the following points: (A) If point D is ൅ͺ then which point is െͺ? (B) Is point a negative integer or a positive integer? (C) Write integers for points and . (D) Which point marked on this number line has the least value? (E) Arrange all the points in decreasing order of values.

Solution:

Let us draw a rough number line and locate points according to the given figure. (A) From the above figure, If point is ൅ͺ, then െͺ will appear at a point :

ͺ units (from ൅ͺ to Ͳ) ൅ͺ units (from Ͳ to െͺ) ൌͳ͸ units from .

Hence, point represents െͺ.

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 4 www.embibe.com (B) From the above figure,

Point G represents a negative integer.

Counting the integers from point D, we can observe that point O represents 0. Therefore, all the numbers below point O represent negative integers. (C) From the above figure, Point B lies 4 units below ሺ൅ሻͺ Therefore, the integer value of B is ሺ൅ሻͺȂͶൌሺ൅ሻͶ Now, point E lies ͳͺ units below ൅ૡ. Until point , we have ͺ units. Therefore ͳͺെͺൌͳͲ will be the number of units below zero. ൌሺ൅ሻͶൌሺെሻͳͲ Hence, point E represents െͳͲ and point represents ൅Ͷ (D) From the above figure, Since, down the line the value of integers decreases, point has the least value. (E) From the above figure, The point at the top of the number line has the highest value.

The value decreases down the number line.

Hence, the points arranged in the decreasing order of their values will be as follows: ǡǡǡǡǡǡǡǡ

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

the year.

Place Temperature

Siachin ͳͲι below Ͳι ______________

Shimla ʹι below Ͳι ______________

Ahmedabad ͵Ͳι above Ͳι ______________

Delhi ʹͲι above Ͳι ______________

Srinagar ͷι below Ͳι ______________

(A) Write the temperature of these places in the form of integers in the blank column. (B) Following is the number line representing the temperature in degree

Celsius.

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 5 www.embibe.com Plot the name of the city against its temperature.

(C) Which is the coolest place? (D) Write the names of the place where temperatures are above ͳͲ୭.

Solution:

(A) In the below table, the temperature values are shown in integers form.

Place Temperature Temperature

Siachin ͳͲι below Ͳι ሺെሻͳͲι Shimla ʹι below Ͳι ሺെሻʹι Ahmedabad ͵Ͳι above Ͳι ሺ൅ሻ͵Ͳι Delhi ʹͲι above Ͳι ሺ൅ሻʹͲι Srinagar ͷι below Ͳι ሺെሻͷι (B) Number line represents name of the cities against its temperature. (C) From Siachin is the coldest place with the least temperature ofሺെሻͳͲι. Minimum number will be the smallest negative number. So,ሺെሻͳͲι is on the left of the line which is the smallest negative number. (E) From the table we can observe that, Ahmedabad with a temperature of ሺ൅ሻ͵Ͳι and Delhi with a temperature of ሺ൅ሻʹͲι have temperatures above ሺ൅ሻͳͲι.

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

number line? (A) ʹǡͻ (B) െ͵ǡെͺ (C) Ͳǡെͳ (D) െͳͳǡͳͲ (E) െ͸ǡ͸

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 6 www.embibe.com (F) ͳǡെͳͲͲ

Solution:

(A) Since 9 is greater than 2, the integer 9 is to the right of 2.

(B) Since െ͵ is greater than െͺ, the integer െ͵ is to the right of െͺ.

(C) Since 0 is greater than െͳ, the integer Ͳ is to the right of െͳ (D) Since 10 is greater than െͳͳ, the integer ͳͲ is to the right of െͳͳ (E) Since 6 is greater than െ͸, the integer ͸ is to the right of െ͸

(F) Since 1 is greater than െͳͲͲ, the integer ͳ is to the right of െͳͲͲ

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

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 7 www.embibe.com (A) Ͳ and െ͹ (B) െͶ and Ͷ (C) െͺ and െͳͷ (D) െ͵Ͳ and െʹ͵

Solution:

The following are the integers between the given pairs, in the increasing order. (A) െ͸ǡെͷǡെͶǡെ͵ǡെʹǡെͳ (B) െ͵ǡെʹǡെͳǡͲǡͳǡʹǡ͵

(C) െͳͶǡെͳ͵ǡെͳʹǡെͳͳǡെͳͲǡെͻ

(D) െʹͻǡെʹͺǡെʹ͹ǡെʹ͸ǡെʹͷǡെʹͶ

8. (A) Write four negative integers greater than െʹͲ.

(B) Write four negative integers less than െͳͲ.

Solution:

Farther a number from zero on the left, smaller is its value. Hence,

(A) െͳͻǡെͳͺǡെͳ͹ǡെͳ͸ are the examples of the numbers that are greater than

െʹͲ

(B) െͳͳǡെͳʹǡെͳ͵ǡെͳͶ are the examples of the numbers that are lesser than

െͳͲǤ

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

correct the statement: (A) െͺ is to the right of െͳͲ on a number line. (B) െͳͲͲ is to the right of െͷͲ on a number line. (C) Smallest negative integer is െͳ. (D) െʹ͸ is larger than െʹͷ.

Solution:

(A) True Since െͺ is greater than െͳͲ, the integer െͺ lies towards the right of

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 8 www.embibe.com െͳͲ. (B) False

Since െͷͲ is greater than െͳͲͲ, the integer െͷͲ lies towards the right of

െͳͲͲ. (C) False Farther the number from zero on the left, smaller is its value. Therefore, െͳ is the greatest negative integer. (D) False Farther the number from zero on the left, smaller is its value.

So, െʹ͸൏െʹͷ

Since െʹͷ lies closer to zero than െʹ͸, the integer െʹͷ is larger than

െʹ͸.

10. Draw a number line and answer the following:

(A) Which number will we reach if we move Ͷ numbers to the right of െʹ. (B) Which number will we reach if we move ͷ numbers to the left of ͳ. (C) If we are at െͺ on the number line, in which direction should we move to reach െͳ͵? (D) If we are at െ͸ on the number line, in which direction should we move to reach െͳ?

Solution:

(A) L

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 9 www.embibe.com We will reach 2 if we move 4 numbers to the right of െʹ.

(B) We will reach െͶ if we move ͷ numbers to the left of ͳ. (C)

Since െͺ is greater than െͳ͵, the integer െͺ will lie to the right of െͳ͵.

Hence, we need to move towards the left on the number line from െͺ to reach െͳ͵. (D) Since െͳ is greater than െ͸, the integer െͳ will lie on the right side of െ͸. Hence, we need to move towards the right on the number line from െ͸ to reach െͳ.

Exercise 6.2

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

(A) 3 more than ͷ (B) 5 more than െͷ (C) 6 less than ʹ (D) 3 less than െʹ

Solution:

Farther a number from zero on the right, larger is its value. Farther a number from zero on the left, smaller is its value.

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 10 www.embibe.com (A) Let us consider any number line to plot integers,

Since, we need to arrive at a number that is 3 more than 5, we move towards the right of 5 by three units. The number obtained is 8. (B) Let us consider the number line to plot integers, Since, we need to arrive at a number that is ͷ more than െͷ, we move towards the right of െͷ by ͷ units. The number obtained is Ͳ. (C) Let us consider the number line to plot integers, Since, we need to arrive at a number that is ͸ less than ʹ, we move towards the left of ʹ by ͸ units. The number obtained will be െͶ. (E) Let us consider the number line to plot integers, Since, we need to arrive at a number that is three less than െʹ, we move towards the left of െʹ by ͵ units. The number obtained will be െͷ.

2. Use number line and add the following integers:

(A) ͻ൅ሺെ͸ሻ (B) ͷ൅ሺെͳͳሻ (C) ሺെͳሻ൅ሺെ͹ሻ (D) ሺെͷሻ൅ͳͲ (E) ሺെͳሻ൅ሺെʹሻ൅ሺെ͵ሻ (F) ሺെʹሻ൅ͺ൅ሺെͶሻ

Solution:

(A) Let us consider the number line, First, we move to 9 steps to right on the number line from 0 and retreat by

6 units towards left, hence obtaining 3.

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 11 www.embibe.com ͻ൅ሺെ͸ሻൌ͵ (B) Let us consider the number line, Now first we move to 5 steps right from 0 on the number line and retreat by 11 units, hence obtaining െ͸. ͷ൅ሺെͳͳሻൌെ͸ (C) Let us consider the number line, First, we move to 1 step left from 0 on the number line and then move ͹ units from െͳ towards left, hence obtaining െͺ. ሺെͳሻ൅ሺെ͹ሻൌെͺ (D) Let us consider the number line, Now first we move 5 units to the left of 0 to obtain െͷ and then move 10 units forward from െͷ, hence obtaining 5. ሺെͷሻ൅ͳͲൌͷ (E) We first move one unit to the left of 0 to obtain െͳ and then move 2 and 3 steps subsequently, hence obtaining െ͸. ሺെͳሻ൅ሺെʹሻ൅ሺെ͵ሻൌെ͸

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 12 www.embibe.com (F) We first move ʹ units to the left of zero, to obtain െʹ. Then we move ͺ units forward from െʹ, thereby reaching 6. From ͸ retreat by 4 units to obtain ʹ. ሺെʹሻ൅ͺ൅ሺെͶሻൌʹ

3. Add without using number line:

(A) ͳͳ൅ሺെ͹ሻ (B) ሺെͳ͵ሻ൅ሺ൅ͳͺሻ (C) ሺെͳͲሻ൅ሺ൅ͳͻሻ (D) ሺെʹͷͲሻ൅ሺ൅ͳͷͲሻ (E) ሺെ͵ͺͲሻ൅ሺെʹ͹Ͳሻ (F) ሺെʹͳ͹ሻ൅ሺെͳͲͲሻ

Solution:

(A) ͳͳ൅ሺെ͹ሻ ൌͳͳെ͹ ൌͶ (B) ሺെͳ͵ሻ൅ͳͺ ൌͳͺെͳ͵ ൌͷ (C) ሺെͳͲሻ൅ሺ൅ͳͻሻ ൌെͳͲ൅ͳͻ ൌͻ (D) ሺെʹͷͲሻ൅ሺ൅ͳͷͲሻ ൌെʹͷͲ൅ͳͷͲ ൌെͳͲͲ

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 13 www.embibe.com (E) ሺെ͵ͺͲሻ൅ሺെʹ͹Ͳሻ

ൌെ͵ͺͲെʹ͹Ͳ ൌെ͸ͷͲ (F) ሺെʹͳ͹ሻ൅ሺെͳͲͲሻ ൌെʹͳ͹െͳͲͲ ൌെ͵ͳ͹

4. Find the sum of:

(A) ͳ͵͹ and െ͵ͷͶ (B) െͷʹ and ͷʹ (C) െʹͳ͵ǡ͵ͻ and ͳͻʹ (D) െͷͲǡെʹͲͲ and ͵ͲͲ

Solution:

(A) ͳ͵͹൅ሺെ͵ͷͶሻ ൌͳ͵͹െ͵ͷͶ ൌെʹͳ͹ (E) ሺെͷʹሻ൅ͷʹൌͲ [Additive inverses] (C) ሺെ͵ͳʹሻ൅͵ͻ൅ͳͻʹ ൌെ͵ͳʹ൅ʹ͵ͳ ൌെͺͳ (D) ሺെͷͲሻ൅ሺെʹͲͲሻ൅͵ͲͲ ൌെͷͲെʹͲͲ൅͵ͲͲ ൌെʹͷͲ൅͵ͲͲ ൌͷͲ

5. Find the value of:

(A) ሺെ͹ሻ൅ሺെͻሻ൅Ͷ൅ͳ͸

(B) ͵͹൅ሺെʹሻ൅ሺെ͸ͷሻ൅ሺെͺሻ

Solution:

(A) ሺെ͹ሻ൅ሺെͻሻ൅Ͷ൅ͳ͸

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 14 www.embibe.com ൌെ͹െͻ൅Ͷ൅ͳ͸

ൌെͳ͸൅ʹͲ ൌͶ

(B) ͵͹൅ሺെʹሻ൅ሺെ͸ͷሻ൅ሺെͺሻ

ൌ͵͹െʹെ͸ͷെͺ ൌ͵͹െ͹ͷ ൌെ͵ͺ

Exercise 6.3

1. Find:

(A) ͵ͷെሺʹͲሻ (B) ͹ʹെሺͻͲሻ (C) ሺെͳͷሻെሺെͳͺሻ (D) ሺെʹͲሻെሺͳ͵ሻ (E) ʹ͵െሺെͳʹሻ (F) ሺെ͵ʹሻെሺെͶͲሻ

Solution:

(A) ͵ͷെሺʹͲሻ ൌ͵ͷെʹͲ ൌͳͷ (B) ͹ʹെሺͻͲሻ ൌ͹ʹെͻͲ ൌെͳͺ (C) ሺെͳͷሻെሺെͳͺሻ ൌെͳͷ൅ͳͺ ൌ͵ (D) ሺെʹͲሻെሺͳ͵ሻ ൌെʹͲെͳ͵ ൌെ͵͵ (E) ʹ͵െͳʹ

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 15 www.embibe.com ൌʹ͵൅ͳʹ ൌ͵ͷ (F) ሺെ͵ʹሻെሺെͶͲሻ ൌെ͵ʹ൅ͶͲ ൌͺ

2. Fill in the blanks with ൐ǡ൏ or = sign:

(A) ሺെ͵ሻ൅ሺെ͸ሻ ____________ ሺെ͵ሻെሺെ͸ሻ

(B) ሺെʹͳሻെሺെͳͲሻǤ__________ ሺെ͵ͳሻ൅ሺെͳͳሻ

(C) Ͷͷെሺെͳͳሻ ___________ ͷ͹൅ሺെͶሻ

(D) ሺെʹͷሻെሺെͶʹሻǤ___________ ሺെͶʹሻെሺെʹͷሻ

Solution:

(A) Given, LHS: ሺെ͵ሻ൅ሺെ͸ሻൌሺെͻሻ RHS: ሺെ͵ሻെሺെ͸ሻൌ͵

Clearly, RHS൐LHS

So, ͵൐ሺെͻሻ

Therefore,ሺെ͵ሻ൅ሺെ͸ሻ൏ሺെ͵ሻെሺെ͸ሻ

(B) Given, LHS: ሺെʹͳሻെሺെͳͲሻൌሺെͳͳሻ RHS: ሺെ͵ͳሻ൅ሺെͳͳሻൌሺെͶʹሻ

Clearly, LHS൐RHS

So,ሺെͳͳሻ൐ሺെͶʹሻ

Therefore, ሺെʹͳሻെሺെͳͲሻ൐ሺെ͵ͳሻ൅ሺെͳͳሻ

(C) Given,

LHS: Ͷͷെͳͳൌͷ͸

RHS: ͷ͹൅ሺെͶሻൌͷ͵

Clearly, RHS൏LHS

So, ͷ͸൐ͷ͵

Hence, Ͷͷെሺെͳͳሻ൐ͷ͹൅ሺെͶሻ

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 16 www.embibe.com (D) Given, LHS: ሺെʹͷሻെሺെͶʹሻൌͳ͹ RHS: ሺെͶʹሻെሺെʹͷሻൌሺെͳ͹ሻ

Clearly, RHS൏LHS

So, ͳ͹൐ሺെͳ͹ሻ

Therefore, ሺെʹͷሻെሺെͶʹሻ൐ሺെͶʹሻെሺെʹͷሻ

3. Fill in the blanks:

(A) ሺെͺሻ൅ __________ ൌͲ (B) ͳ͵൅ ___________ ൌͲ (C) ͳʹ൅ሺെͳʹሻൌ _________ (D) ሺെͶሻ൅ _________ ൌെͳʹ (E) ___________ െͳͷൌെͳͲ

Solution:

(A) Additive inverse of ሺെͺሻ is 8.

So, ሺെͺሻ൅ͺൌͲ

Hence, 8 is the required answer.

(B) Additive inverse of ͳ͵ is ሺെͳ͵ሻ. So, ͳ͵൅ሺെͳ͵ሻൌͲ Hence, ሺെͳ͵ሻ is the required answer. (C) ͳʹ and ሺെͳʹሻ are additive inverses of each other. Hence, upon adding its sum will be equal to zero. ͳʹ൅ሺെͳʹሻൌͲ Therefore, ሺെͳʹሻ is the required answer. (D) Since, ሺെͳʹሻ൅Ͷൌሺെͺሻ. So, ሺെͶሻ൅ሺെͺሻൌെͳʹ Hence, ሺെͺሻ is the required answer. (E) Since, ሺെͳͲሻ൅ͳͷൌͷ,

So, ͷെͳͷൌെͳͲ

Therefore, 5 is the required answer.

Class- VI-CBSE-Mathematics Integers

Practice more on Integers Page - 17 www.embibe.com 4. Find: (A) ሺെ͹ሻെͺെሺെʹͷሻ (B) ሺെͳ͵ሻ൅͵ʹെͺെͳ (C) ሺെ͹ሻ൅ሺെͺሻ൅ሺെͻͲሻ (D) ͷͲെሺെͶͲሻെሺെʹሻ

Solution:

(A) ሺെ͹ሻെͺെሺെʹͷሻ ൌെ͹െͺ൅ʹͷ ൌെͳͷ൅ʹͷ ൌͳͲ (B) ሺെͳ͵ሻ൅͵ʹെͺെͳ ൌെͳ͵൅͵ʹെͺെͳ ൌ͵ʹെʹʹ ൌͳͲ (C) ሺെ͹ሻ൅ሺെͺሻ൅ሺെͻͲሻ ൌെ͹െͺെͻͲ ൌെͳͲͷ (D) ͷͲሺെͶͲሻെሺെʹሻ ൌͷͲ൅ͶͲ൅ʹ ൌͻʹ

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