Page 35 - ICSE Math 6

• Let ‘a’, ‘b’ and ‘c’ be three whole numbers such that a – b = c, then a = b + c.
For example, 7 – 3 = 4, then 7 = 3 + 4

III. Multiplication
• Closure property

The product of two whole numbers is always a whole number, i.e., if ‘a’ and ‘b’ are two whole
numbers then ‘a × b’ is also a whole number. This property is known as the closure property of
multiplication of whole numbers. For example, 3 and 6 are whole numbers and 3 × 6 = 18 is also
a whole number.

• Commutative property
The product of two whole numbers remains the same irrespective of the order in which they are
multiplied, i.e., if ‘a’ and ‘b’ are two whole numbers then a × b = b × a. This property is known
as the commutative property of multiplication of whole numbers.
For example, 5 × 3 = 15 = 3 × 5
• Associative property
The product of whole numbers remains the same even if their grouping is changed, i.e., if ‘a’, ‘b’
and ‘c’ are any three whole numbers then (a × b) × c = a × (b × c). This property is known as the
associative property of multiplication of whole numbers. For example, (2 × 3) × 4 = 6 × 4 = 24
and 2 × (3 × 4) = 2 × 12 = 24
• Existence of multiplicative identity
When a whole number is multiplied by 1 we get the same number, i.e., if ‘a’ is a whole number
then a × 1 = a = 1 × a. Thus, 1 is the multiplicative identity of whole numbers.
For example, 7 × 1 = 7 = 1 × 7
• Multiplicative inverse

If a × b = 1, then we say that b is the multiplicative inverse of a and a is the multiplicative inverse
of b.
1
1
Since for any given whole number a, a × = 1 but is not a whole number (except a = 1), the
a a
multiplicative inverse of whole numbers does not exist.
• Property of zero
The product of 0 and a whole number is always 0, i.e., if ‘a’ is a whole number, then a × 0 = 0 =
0 × a. This is known as the property of zero under multiplication.
For example, 4 × 0 = 0 = 0 × 4
• Distributive property of multiplication over addition
Let ‘a’, ‘b’ and ‘c’ be any three whole numbers, then a × (b + c) = a × b + a × c.
Thus, for whole numbers, multiplication distributes over addition.

For example, 4 × (5 + 7) = 4 × 5 + 4 × 7
LHS = 4 × (5 + 7) = 4 × 12 = 48
RHS = 4 × 5 + 4 × 7 = 20 + 28 = 48

• Distributive property can also be written as, (b + c) × a = b × a + c × a.

• For whole numbers, multiplication distributes over subtraction also, as a × (b – c) = a × b – a × c,
provided b ≥ c.

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