Page 19 - ICSE Math 7

Multiplication

For multiplication of integers, we have two cases: Maths Info
(a) When both the integers to be multiplied have the same sign, i.e., (+) × (+) = (+)
either both are positive or both are negative, then their product is (–) × (–) = (+)
a positive integer with value equal to the product of their absolute (–) × (+) = (–)
values. (+) × (–) = (–)
(b) When one of the integers is positive and the other is negative, then their product is a negative
integer with value equal to the product of their absolute values.

Points to remember

• Product of any number of positive integers is positive.
• Product of even number of negative integers is positive.
• Product of odd number of negative integers is negative.
• Product of any integer and zero is always zero.

Example 7: Evaluate the following.
(a) 12 × (–2) × 3 (b) (–3) × (–5) × 4 (c) (–25) × 15 × (–3) × (–11)

Solution: (a) 12 × (–2) × 3
= –(12 × 2 × 3) (Since there is only one negative integer,
the product is negative.)
= –72
(b) (–3) × (–5) × 4
= 3 × 5 × 4 (Since there are two negative integers,
the product is positive.)
= 60
(c) (–25) × 15 × (–3) × (–11)
= –(25 × 15 × 3 × 11) (Since there are three negative integers, the
product is negative.)
= –(375 × 33) = –12,375

Properties of multiplication of integers
• Closure property
If a and b are any two integers, then a × b is also an integer. For example, (–3) × 5 = –15 which
is an integer.
• Commutative property
If a and b are any two integers, then a × b = b × a. For example, 4 × (–8) = –32 = (–8) × 4
• Associative property

If a, b and c are any three integers, then (a × b) × c = a × (b × c) = a × b × c.
For example, {4 × (–5)} × 2 = (–20) × 2 = – 40 and 4 × {(–5) × 2} = 4 × (–10) = –40
\ {4 × (–5)} × 2 = 4 × {(–5) × 2}
• Existence of multiplicative identity
If a is any integer, then a × 1 = a = 1 × a. So, 1 is called the multiplicative identity of integers.
For example, 13 × 1 =13 = 1 × 13 = 13

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