Chapter - 6 - EXERCISE 6.2 - Integers (NCERT Class 6th Maths Solution)

Using the number line write the integer which is :
(a) 3 more than 5
(b) 5 more than –5
(c) 6 less than 2
(d) 3 less than –2

Solution/Explanation:

More means moving right on the number line and less mean moving left on the Number line
a)

So answer is -5

Q2. Use number line and add the following integers : 

(a) 9 + (– 6)                                           (b) 5 + (– 11) 

(c) (– 1) + (– 7)                                     (d) (– 5) + 10 

(e) (– 1) + (– 2) + (– 3)                         (f) (– 2) + 8 + (– 4)

Solution/Explanation:

Two important things to remember
When we add positive integer, we move to the right
When we add negative integer, we move to the right
a) $9+(-6)$
We start with number 9 and move to left six steps and we reach the number 3

b) $5+(-11)$
We start with number 5 and move to left 11 steps and we reach the number -6

c) $(-1)+(-7)$
We start with number -1 and move to left 7 steps and we reach the number -8

d) $(-5)+10$
We start with number -5 and move to right 10 steps and we reach the number 5

e) $(-1)+(-2)+(-3)$
We start with number -1 and move to left 2 steps and we reach the number -3. Then again we move to left 3 steps and we reach finally -6

f) $(-2)+8+(-4)$
We start with number -2 and move to right 8 steps and we reach the number 6. Then again we move to left 4 steps and we reach finally 2

Q3. Add without using number line : 

(a) 11 + (– 7) (b) (– 13) + (+ 18)

(c) (– 10) + (+ 19) 

(d) (– 250) + (+ 150) 

(e) (– 380) + (– 270) 

(f) (– 217) + (– 100)

Solution/Explanation:

Q4. Find the sum of : 

(a) 137 and – 354                                     (b) – 52 and 52 

(c) – 312, 39 and 192                               (d) – 50, – 200 and 300

Solution/Explanation:

We have to take important note of this principle
1) When one positive and one negative integers are added, we subtract the smaller number from bigger number and put the sign of the bigger integer. The bigger integer is decided by ignoring the signs of the integers
For example, (+11) + (–5) = + 6 and (–12) + (+ 1) = – 11
2) When two negative integers are added, we add both the number and put the negative sign on the number=
For example, (-11) + (–5) = -16 and (–12) + (- 1) = – 13
Also when three or more numbers are present, we start with first pair of 2 number, the answer from first pair is added to the third Number and it goes on.

a)	137 and −354	Subtracting 137 from 354= 217 -217
b)	− 52 and 52	Subtracting 52 from 52= 0 0
c)	− 312, 39 and 192	1) Taking number -312 and 39 first Subtracting 39 from 312= 273 -273 2) Taking the number -273 and 192 Subtracting 192 from 273= 81 -81
d)	− 50, − 200 and 300	1) Taking number -50 and -200 first Adding 50 and 200= 250 -250 2) Taking the number -250 and 300 Subtracting 250 from 300=50 50

Q5. Find the sum : 

(a) (– 7) + (– 9) + 4 + 16 

(b) (37) + (– 2) + (– 65) + (– 8)

Solution/Explanation:

a. $(-7)+(-9)+4+16=(-16)+\left(20\right)=4$$b.\; (37)+(-2)+(-65)+(-8)=(37)+(-75)=(-38)$