Page 28 - Revised Maths Wisdom Class - 6

26 MATHS

● While adding negative integer to negative integer we move towards left. For example, (–3) + (–2) = –5

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

Properties for Addition of Integers
1. Closure Property: For any two integers a and b, their sum (a + b) is also an integer. For example, the sum
of 3 and 5 is 8.

2. Commutative Property: For any two integers a and b, a + b = b + a
For example, 4 + (–3) = (–3) + 4 = 1

3. Associative Property: For any three integers a, b and c, a + (b + c) = (a + b) + c
For example, –3 + [2 + (– 4)] = –3 – 2 = –5; (–3 + 2) + (– 4) = (–1) + (– 4) = –5
4. Additive Identity: For any integer a, a + 0 = 0 + a = a

For example, 0 + (–7) = –7; –7 + 0 = –7
5. Additive Inverse: For any integer a, a + (–a) = (–a) + a = 0

Here, ‘–a’ is called the additive inverse of a.
For example, 2 + (–2) = 0; –8 + 8 = 0

6. Successor and Predecessor of an Integer: For any integer a,
Its successor is given by a + 1 and
Its predecessor is given by a – 1
For example, Successor of –5 is –5 + 1 = – 4

Predecessor of 8 is 8 – 1 = 7.

ILLUSTRATIONS

Example 1: Using the number line, write the integer that is 6 more than –3.
Solution: To find the required integer, we start from –3 and move 6 steps towards right

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
Hence, the required number is 3.

Example 2: Complete the following:
(a) The additive inverse of –13 is _______. (b) The successor of –89 is _______.
(c) The predecessor of 102 is _______.

Solution: (a) The additive inverse of –13 is 13. [–13 + 13 = 0]
(b) The successor of –89 is –88. [–89 + 1 = –88]

(c) The predecessor of 102 is 101. [102 – 1 = 101]

Example 3: Find the sum of the following:
(a) (–6) + (13) + (–3) + 18 (b) 68 + (–2) + (–7) + (–80)