Page 95 - Maths Class 06

(c) (-8 ) (+ -7 ) = -15 and (-7 ) (+ -8 ) = -15
Thus, we see that sum of the two integers remains the same, no matter in which order we
add them.
Hence, if a and b are any two integers, then a b+ = b a+ .
Property 3. Let us consider the sum of three integers.

(a) (-3 )+ 6 + (-11 )
We add these integers in the order:

[(-3 )+ 6 ] (+ -11 ) = +3 (-11 ) = -8
(b) Now we add these integers in the order:
)]
(-3 ) [+ 6 + (-11 = -( 3 ) + -( 5 ) = -8
Thus, while adding three integers they need not be added in the order in which they are
given. We can group them in easy combinations and find their sum.
Hence, if a b, and c are any three integers, then (a b+ ) c+ = +a ( b + c).
Property 4. Let us consider the result of adding zero to any integer.

(a) 0 + -( 7 = -) 7 (b) 6 + 0 = 6
Thus, we have seen that when zero is added to any integer, the result is the integer itself.
Hence, if a is an integer, then a + 0 = 0 + a = a.
Property 5. We know that

(+5 ) (+ -5 ) = 0 and (-11 ) (+ +11 ) = 0
Thus, for any integer there exists an integer which when added to the original integer
makes the sum zero. Each is called the additive inverse of the other.

Hence, if a is an integer then there is an integer -a such that a + -( a =) 0.
Property 6. We have studied earlier that by adding 1 to any whole number, we get the successor of that
number and by subtracting 1 from any whole number we get predecessor of that number.
The same rule applies to integers also.
(a) -3 is the successor of -4 (b) 0 is the successor of -1
(c) 4 is the predecessor of 5 (d) -7 is predecessor of -6
Thus, if a is any number then a + 1 is its successor and a -1 is its predecessor.

Exercise 6.2

1. Represent the following on a number line:
(a) (+3 ) (+ +7 ) = +10 (b) (-3 ) (+ +7 ) = + 4
(c) (-3 ) (+ -7 ) = -10 (d) (+3 ) (+ -7 ) = -4

2. Find:
(a) 200 + -( 174 + -) ( 26) (b) 4 + -( 99 + -) ( 101 +) 96
(c) (-18 ) (+ +25 ) (+ -37 ) (d) (-100 ) (+ -99 ) (+ -98 )+ 98 99 + 100
+
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