Page 17 - ICSE Math 7

Example 3: Add the following.
(a) (–95) and (–55) (b) (+121), (–30) and (–45) (c) (+35), (–25), (+111) and (–124)

Solution: (a) |–95| = 95 and |–55| = 55
|–95| + |–55| = 95 + 55 = 150
\ (–95) + (–55) = –150

(b) |–30| + |–45| = 30 + 45 = 75
(–30) + (–45) = –75
\ (+121) + (–30) + (–45) = +121 – 75 = 46
(c) |+35| + |+111| = 35 + 111 = 146

Also, |–25| + |–124| = 25 + 124 = 149
\ (+35) + (–25) + (+111) + (–124) = (+35) + (+111) + (–25) + (–124)
= 146 – 149 = –3

Properties of addition of integers
• Closure property

If a and b are any two integers, then a + b is also an integer. For example, –5 + 9 = 4 which is an
integer.
• Commutative property
If a and b are any two integers, then a + b = b + a. For example, 110 + (–4) = 106 = (–4) + 110

• Associative property
If a, b and c are any three integers, then (a + b) + c = a + (b + c) = a + b + c. For example,
{13 + (–2)} + 5 = {13 – 2} + 5 = 11 + 5 = 16 and 13 + {(–2) + 5} = 13 + {–2 + 5}= 13 + 3 = 16
\ {13 + (–2)} + 5 = 13 + {(–2) + 5}
• Existence of additive identity

If a is any integer, then a + 0 = a = 0 + a. We say, 0 is an additive identity of integers. For example,
(–36) + 0 = –36 = 0 + (–36)
• Existence of additive inverse
If a is any integer, then a + (–a) = 0 = (–a) + a. We say, a and –a are Maths Info
additive inverse of each other. For example, 9 + (–9) = 0 = (–9) + 9 0 is the only integer which is
additive inverse of itself, i.e.,
• Cancellation law self inverse.
If a, b and c are any three integers, then a + c = b + c ⇒ a = b.
For example, x + 91 = (–27) + 91 ⇒ x = –27
Subtraction
Subtraction is the inverse of addition. Thus, to subtract integers, change the sign of the integers to be
subtracted and then add them.

Example 4: Subtract the following.
(a) 26 from 9 (b) (–13) from 25 (c) 17 from (–10) (d) (–11) from (–95)
Solution: (a) 9 – (26) = 9 – 26 = –17 (b) 25 – (–13) = 25 + 13 = 38
(c) (–10) – (17) = –10 – 17 = –27 (d) (–95) – (–11) = –95 + 11 = –84

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