Multiplicative Identity: <\/strong>For any integer a, (a \u00d7 1) = a = (1 \u00d7 a). Thus, we see that when we multiply one with any integer, we get the same integer. Thus, we say that\u00a0 1 is the multiplicative identity for integers.\u00a0<\/li>\n<\/ol>\n\n\n\n(a \u00d7 1) = (1 \u00d7 a) = a<\/p>\n\n\n\n
\n- Associativity for Multiplication: <\/strong>for any three integers a, b and c, [(a \u00d7 b) \u00d7 c] = [a \u00d7 (b \u00d7 c)]. Thus, like whole numbers, the product of three integers does not depend upon the grouping of integers and this is called the associative property for multiplication of integers.<\/li>\n\n\n\n
- Distributive Property:<\/strong> For any three integers a, b and c, [a \u00d7 (b + c)] = (a \u00d7 b + a \u00d7 c). Thus, we say that the multiplication of integers is distributive over addition.<\/li>\n<\/ol>\n\n\n\n
Topic 5: Division of Integers<\/h3>\n\n\n\n
When we divide a negative integer by a positive integer, we divide them as whole numbers and then put a minus sign (\u2013) before the quotient. We, thus, get a negative integer.<\/p>\n\n\n\n
In general, for any two positive integers a and b,<\/p>\n\n\n\n
a \u00f7 (\u2013 b) = (\u2013 a) \u00f7 b, where b \u2260 0<\/p>\n\n\n\n
Similarly, when we divide a negative integer by a negative integer, we first divide them as whole numbers and then put a positive sign (+). That is, we get a positive integer.<\/p>\n\n\n\n
In general, for any two positive integers a and b,<\/p>\n\n\n\n
(\u2013 a) \u00f7 (\u2013 b) = (a \u00f7 b), where b \u2260 0<\/p>\n\n\n\n
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