The rules to add integers are as follows:

Rule I:

When the two integers have the positive sign, add the integers and assign the (+) sign to the sum.

1. Combination One:

(positive + positive) or (+ plus +)

For example:

Find the sum of the integers.

(i) 8 + 19 = 27

(ii) 33 + 25 = 58

(iii) 42 + 91 = 133

(iv) 59 + 87 = 146

Note:

Here, we have two integers having the same (+) sign. So, we add the numbers and attach (+) sign to the sum.

﻿﻿Rule II:

When the two integers have the negative sign, add the integers and assign the (-) sign to the sum.

2. Combination Two:

(negative + negative) or (- plus -)

For example:

Find the sum of the integers.

(i) (-7) + (-9) = -16

(ii) (-23) + (-15) = -38

(iii) (-41) + (-57) = -98

(iv) (-119) + (-137) = -256

Note:

Here, both the integers have the same (-) sign. So, we add the numbers and attach the (-) sign to the sum.

Combination of Rule I and Rule II:

From the above two rules (Rule I and Rule II) we can conclude that,

To add two integers of like signs (both positive or both negative), add their values regardless of their signs and give the sum their common sign.

For example:

(i) 23 + 46 = 69

(ii) (-12) + (-21) = -33

Rule III:

When the two integers have opposite sign [one positive (+) and other negative (-)], find the difference of the numbers and to the difference assign the sign of the integer having greater value.

3. Combination Three:

(negative + positive) or (- plus +)

For example:

Find the sum of the integers.

(i) (-17) + 29

= -17 + 29

[Here, two integers are with unlike signs – and +.We find the difference of the numbers is 12 and to the difference attach the sign of the integer having greater value; so the answer is positive 12].

= 12

(ii) (-81) + (+35)

= -81 + 35

[Here, two integers are with unlike signs – and +.We find the difference of the numbers is 46 and to the difference attach the sign of the integer having greater value; so the answer is negative 46].

= -46

4. Combination Four:

(positive + negative) or (+ plus -)

For example:

Find the sum of the integers.

(i) (+79) + (-57)

= 79 – 57

[Here, two integers are with unlike signs + and -.We find the difference of the numbers is 22 and to the difference attach the sign of the integer having greater value; so the answer is positive 22].

= 22

(ii) (+85) + (-121)

= 85 – 121

[Here, two integers are with unlike signs + and -.We find the difference of the numbers is 36 and to the difference attach the sign of the integer having greater value; so the answer is negative 36].

= -36

Rue III in other words,

To add two integers of unlike signs (one positive and the other negatives, find the difference between their numerical values regardless of their signs and give the sign of the greater integer to this difference.

For example: (i) -48 + 26 = -22;

(ii) 72 + (-16) = 56

Solved Examples on Rules For Addition of Integers:

1. Add the integers (i) + 45 and + 88;     (ii) -124 and -63

Solution:

According to the rule for addition of integers, to add two integers of like signs, their numerical values are added regardless of their signs and the sum is given their common sign. Therefore, we have

(i) + 45 and + 88 = (+ 45) + (+ 88) = + (45 + 88) = +133 = 133

(ii) -124 and -63 =  (-124) + (-63) = - (124 + 63)= - 187

2.  Add (i) -69 + 45;     (ii) 246 + (- 87)

Solution:

According to the rule for addition of integers, to add two integers of unlike signs, the difference between their numerical values is found and the sign of the integer with greater value is given to this difference.

Therefore, we have

(i) -69 + 45 = -(69 - 45) = -24

(ii) 246 + (- 87) = +(246 - 87) = +159 = 159

Representation of Integers on a Number Line.

Addition of Integers on a Number Line.

Rules to Subtract Integers.

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