Page 94 - Maths Class 06

Clearly B represents the integer -9.
\ (-3 ) (+ -6 ) = -9
From the above examples, we obtain certain rules for addition of integers, which are given
below.

Rules for Addition of Integers
To add two integers, we use the following rules:

(a) When two inte gers have the same sign (both posi tive or both nega tive), add the abso lute values of
the integers and assign the common sign to them.
For example, +13 and +26
|+ 13 |= 13 and | + 26 | = 26
Q 13 26+ = 39

\ + 13 + + 26( ) = + 39 or 39
and | – 5 | = 5 and |-23 |= 23

5 23+ = 28
\ (-5 ) (+ -23 ) = -28
(b) When two inte gers have oppo site signs (one posi tive and another nega tive), find the differ ence of
the abso lute values and to the differ ence assign the sign of the inte ger having greater abso lute
value.

For example, –12 and + 9
|- 12 |= 12 and |+ 9 |= 9
Difference of 12 and 9 = 3

Q – 12 has greater absolute value,
\ -12 + + 9( ) = -3
| + 92 | = 92 and |-116 |= 116

Difference of 92 and 116 = 24
Q -116 has greater absolute value.

\ + 92 + -116( ) = -24

Properties of Addition of Integers
Prop erty 1. Let us con sider any two in te gers

(a) (-15 ) (+ 12 ) = -3, which is an integer.
(b) (-9 ) (+ -16 ) = -25, which is an integer.
(c) (-3 ) ( )+ 3 = 0, which is an integer.

Hence, if a and b are any two integers, then a b+ is also an integer.
Prop erty 2. Let us con sider any two in te gers and add them by chang ing their or der.

(a) (20 ) ( 7+ - ) 13= and (-7 ) (+ 20 ) = 13
(b) (-110 )+ 10 = -100 and 10 + -( 110 = -) 100

94