NCERT Solutions for Class 6 Maths Chapter 6: Integers - Exercise 6.2

Exercise 6.2

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

(i) 3 more than 5

Ans: Integer is a set of both positive and negative numbers including 0.

A number line is a line on which the numbers are marked at equal intervals.

We are given a statement, ‘3 more than 5’. We are required to find the integer using the number line. 

To do so, we will interpret the given statement. The given statement says three more than five. This means three places to the right of 5. So, we will first locate 5 on the number line. We will then move three places to the right of 5. 

This can be expressed on the number line as follows,

Therefore, using the number line we have found that the integer 3 more than 5 is 8. 

(ii) 5 more than $ - 5$

Ans: Integer is a set of both positive and negative numbers including 0.

A number line is a line on which the numbers are marked at equal intervals.

We are given a statement, ‘5 more than $ - 5$’. We are required to find the integer using the number line. 

To do so, we will interpret the given statement. The given statement says five more than $ - 5$. This means five places to the right of $ - 5$. So, we will first locate $ - 5$ on the number line. We will then move five places to the right of $ - 5$. 

This can be expressed on the number line as follows,

Therefore, using the number line we have found that the integer 5 more than $ - 5$ is 0. 

(iii) 6 less than 2

Ans: Integer is a set of both positive and negative numbers including 0.

A number line is a line on which the numbers are marked at equal intervals.

We are given a statement, ‘6 less than 2’. We are required to find the integer using the number line. 

To do so, we will interpret the given statement. The given statement says six less than 2. This means six places to the left of 2. So, we will first locate 2 on the number line. We will then move six places to the left of 2. 

This can be expressed on the number line as follows,

Therefore, using the number line we have found that the integer 6 less than 2 is $ - 4$. 

(iv) 3 less than $ - 2$

Ans: Integer is a set of both positive and negative numbers including 0.

A number line is a line on which the numbers are marked at equal intervals.

We are given a statement, ‘3 less than$ - 2$’. We are required to find the integer using the number line. 

To do so, we will interpret the given statement. The given statement says three less than$ - 2$. This means three places to the left of $ - 2$. So, we will first locate $ - 2$ on the number line. We will then move three places to the left of$ - 2$. 

This can be expressed on the number line as follows,

Therefore, using the number line we have found that the integer 3 less than $ - 2$ is $ - 5$. 

2. Use number line and add the following integers:

(i) $9 + \left( { - 6} \right)$

Ans: Integer is a set of both positive and negative numbers including 0.

A number line is a line on which the numbers are marked at equal intervals.

We are required to add the expression $9 + \left( { - 6} \right)$ using a number line.

To do so, we will first locate 9 on the number line starting from 0. After this, we will move six places to the left of 9. 

This can be expressed on the number line as follows,

Therefore, using the number line we have found that the value of the given expression $9 + \left( { - 6} \right)$ is 3. 

(ii) $5 + \left( { - 11} \right)$

Ans: Integer is a set of both positive and negative numbers including 0.

A number line is a line on which the numbers are marked at equal intervals.

We are required to add the expression $5 + \left( { - 11} \right)$ using a number line.

To do so, we will first locate 5 on the number line starting from 0. After this, we will move eleven places to the left of 5. 

This can be expressed on the number line as follows,

Therefore, using the number line we have found that the value of the given expression $5 + \left( { - 11} \right)$ is $ - 6$. 

(iii) $\left( { - 1} \right) + \left( { - 7} \right)$

Ans: Integer is a set of both positive and negative numbers including 0.

A number line is a line on which the numbers are marked at equal intervals.

We are required to add the expression $\left( { - 1} \right) + \left( { - 7} \right)$ using a number line.

To do so, we will first locate $ - 1$ on the number line starting from 0. After this, we will move seven places to the left of $ - 1$. 

This can be expressed on the number line as follows,

Therefore, using the number line we have found that the value of the given expression $\left( { - 1} \right) + \left( { - 7} \right)$ is $ - 8$. 

(iv) $\left( { - 5} \right) + 10$

Ans: Integer is a set of both positive and negative numbers including 0.

A number line is a line on which the numbers are marked at equal intervals.

We are required to add the expression $\left( { - 5} \right) + 10$ using a number line.

To do so, we will first locate $ - 5$ on the number line starting from 0. After this, we will move ten places to the right of $ - 5$. 

This can be expressed on the number line as follows,

Therefore, using the number line we have found that the value of the given expression $\left( { - 5} \right) + 10$ is 5. 

(v) $\left( { - 1} \right) + \left( { - 2} \right) + \left( { - 3} \right)$

Ans: Integer is a set of both positive and negative numbers including 0.

A number line is a line on which the numbers are marked at equal intervals.

We are required to add the expression $\left( { - 1} \right) + \left( { - 2} \right) + \left( { - 3} \right)$ using a number line.

To do so, we will first locate $ - 1$ on the number line starting from 0. After this, we will move two places to the left of $ - 1$ to reach a number. Finally, we will move three places to the left of the number reached earlier. 

This can be expressed on the number line as follows,

Therefore, using the number line we have found that the value of the given expression $\left( { - 1} \right) + \left( { - 2} \right) + \left( { - 3} \right)$ is $ - 6$.

(vi) $\left( { - 2} \right) + 8 + \left( { - 4} \right)$

Ans: Integer is a set of both positive and negative numbers including 0.

A number line is a line on which the numbers are marked at equal intervals.

We are required to add the expression $\left( { - 2} \right) + 8 + \left( { - 4} \right)$ using a number line.

To do so, we will first locate $ - 2$ on the number line starting from 0. After this, we will move eight places to the right of $ - 2$ to reach a number. Finally, we will move four places to the left of the number reached earlier. 

This can be expressed on the number line as follows,

Therefore, using the number line we have found that the value of the given expression $\left( { - 2} \right) + 8 + \left( { - 4} \right)$ is 2.

3. Add without using number line:

(i) $11 + \left( { - 7} \right)$

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given an expression $11 + \left( { - 7} \right)$, and we are required to add the terms without using the number line by solving them.

To do so, we will first simplify the signs. 

$11 + \left( { - 7} \right) = 11 - 7$

We will now subtract the numbers.

$11 - 7 = 4$

Therefore, the value of the given expression $11 + \left( { - 7} \right)$ is 4.

(ii) $\left( { - 13} \right) + \left( { + 18} \right)$

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given an expression $\left( { - 13} \right) + \left( { + 18} \right)$, and we are required to add the terms without using the number line by solving them.

To do so, we will first simplify the signs. 

$\left( { - 13} \right) + \left( { + 18} \right) = \left( { - 13} \right) + 18$

We will now subtract the numbers.

$\left( { - 13} \right) + 18 = 5$

Therefore, the value of the given expression $\left( { - 13} \right) + \left( { + 18} \right)$ is 5.

(iii) $\left( { - 10} \right) + \left( { + 19} \right)$

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given an expression $\left( { - 10} \right) + \left( { + 19} \right)$, and we are required to add the terms without using the number line by solving them.

To do so, we will first simplify the signs. 

$\left( { - 10} \right) + \left( { + 19} \right) = \left( { - 10} \right) + 19$

We will now subtract the numbers.

$\left( { - 10} \right) + 19 = 9$

Therefore, the value of the given expression $\left( { - 10} \right) + \left( { + 19} \right)$ is 9.

(iv) $\left( { - 250} \right) + \left( { + 150} \right)$

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given an expression $\left( { - 250} \right) + \left( { + 150} \right)$, and we are required to add the terms without using the number line by solving them.

To do so, we will first simplify the signs. 

$\left( { - 250} \right) + \left( { + 150} \right) = \left( { - 250} \right) + 150$

We will now subtract the numbers.

$\left( { - 250} \right) + 150 =  - 100$

Therefore, the value of the given expression $\left( { - 250} \right) + \left( { + 150} \right)$ is $ - 100$.

(v) $\left( { - 380} \right) + \left( { - 270} \right)$

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given an expression $\left( { - 380} \right) + \left( { - 270} \right)$, and we are required to add the terms without using the number line by solving them.

To do so, we will first simplify the signs. 

$\left( { - 380} \right) + \left( { - 270} \right) = \left( { - 380} \right) - 270$

We will now add the numbers.

$\left( { - 380} \right) - 270 =  - 650$

Therefore, the value of the given expression $\left( { - 380} \right) + \left( { - 270} \right)$ is $ - 650$.

(vi) $\left( { - 217} \right) + \left( { - 100} \right)$

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given an expression $\left( { - 217} \right) + \left( { - 100} \right)$, and we are required to add the terms without using the number line by solving them.

To do so, we will first simplify the signs. 

$\left( { - 217} \right) + \left( { - 100} \right) = \left( { - 217} \right) - 100$

We will now add the numbers.

$\left( { - 217} \right) - 100 =  - 317$

Therefore, the value of the given expression $\left( { - 217} \right) + \left( { - 100} \right)$ is $ - 317$.

4. Find the sum of:

(i) 137 and $ - 354$

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given two numbers, 137 and $ - 354$. We are required to find the sum of the two given numbers. To do so, we will first write an expression out of it. The required expression will be,

$137 + \left( { - 354} \right)$

We will now solve the expression. For that we will first simplify the signs. 

$137 + \left( { - 354} \right) = 137 - 354$

We will now add the numbers.

$137 - 354 =  - 217$

Therefore, the sum of the given two numbers 137 and $ - 354$is $ - 217$.

(ii) $ - 52$ and 52

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given two numbers,$ - 52$ and 52. We are required to find the sum of the two given numbers. To do so, we will first write an expression out of it. The required expression will be,

$\left( { - 52} \right) + \left( { + 52} \right)$

We will now solve the expression. For that we will first simplify the signs. 

$\left( { - 52} \right) + \left( { + 52} \right) = \left( { - 52} \right) + 52$

We will now add the numbers.

$\left( { - 52} \right) + 52 = 0$

Therefore, the sum of the given two numbers $ - 52$and 52 is 0.

(iii) $ - 213$, 39 and 192

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given three numbers, $ - 213$, 39 and 192. We are required to find the sum of the three given numbers. To do so, we will first write an expression out of it. The required expression will be,

$\left( { - 213} \right) + \left( { + 39} \right) + \left( { + 192} \right)$

We will now solve the expression. For that we will first simplify the signs. 

$\left( { - 213} \right) + \left( { + 39} \right) + \left( { + 192} \right) = \left( { - 213} \right) + 39 + 192$

We will now add the numbers with the same sign.

$\left( { - 213} \right) + 39 + 192 = \left( { - 213} \right) + 231$

Finally, we will solve the remaining expression. On doing so,

$\left( { - 213} \right) + 231 = 18$

Therefore, the sum of the given two numbers $ - 213$, 39 and 192 is 18.

(iv) $ - 50$, $ - 200$ and 300

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given three numbers, $ - 50$, $ - 200$ and 300. We are required to find the sum of the three given numbers. To do so, we will first write an expression out of it. The required expression will be,

$\left( { - 50} \right) + \left( { - 200} \right) + \left( { + 300} \right)$

We will now solve the expression. For that we will first simplify the signs. 

$\left( { - 50} \right) + \left( { - 200} \right) + \left( { + 300} \right) = \left( { - 50} \right) - 200 + 300$

We will now add the numbers with the same sign.

$\left( { - 50} \right) - 200 + 300 = \left( { - 250} \right) + 300$

Finally, we will solve the remaining expression. On doing so,

$\left( { - 250} \right) + 300 = 50$

Therefore, the sum of the given two numbers $ - 50$, $ - 200$ and 300 is 50.

5. Find the value of:

(i) $\left( { - 7} \right) + \left( { - 9} \right) + 4 + 16$

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given an expression $\left( { - 7} \right) + \left( { - 9} \right) + 4 + 16$, and we are required to find the value of the given expression. 

To do so, we will first simplify the signs. 

$\left( { - 7} \right) + \left( { - 9} \right) + 4 + 16 = \left( { - 7} \right) - 9 + 4 + 16$

After this, we will now add the terms with the same signs. 

$\left( { - 7} \right) - 9 + 4 + 16 =  - 16 + 20$

We will now add the numbers.

$ - 16 + 20 = 4$

Therefore, the value of the given expression $\left( { - 7} \right) + \left( { - 9} \right) + 4 + 16$ is 4.

(ii) $37 + \left( { - 2} \right) + \left( { - 65} \right) + \left( { - 8} \right)$

Ans: Integer is a set of both positive and negative numbers including 0. 

We are given an expression $37 + \left( { - 2} \right) + \left( { - 65} \right) + \left( { - 8} \right)$, and we are required to find the value of the given expression. 

To do so, we will first simplify the signs. 

$37 + \left( { - 2} \right) + \left( { - 65} \right) + \left( { - 8} \right) = 37 - 2 - 65 - 8$

After this, we will now add the terms with the same signs. 

$37 - 2 - 65 - 8 = 37 - 75$

We will now add the numbers.

$37 - 72 =  - 38$

Therefore, the value of the given expression $37 + \left( { - 2} \right) + \left( { - 65} \right) + \left( { - 8} \right)$ is $ - 38$.

NCERT Solutions for Class 6 Maths Chapter 6 Integers Exercise 6.2

Opting for the NCERT solutions for Ex 6.2 Class 6 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 6.2 Class 6 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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