Multiplication of Integers
Product of a negative integer and a positive integer is always a negative integer.
10×−2=−20
Product of two negative integers is a positive integer.
−10×−2=20
Product of even number of negative integers is positive.
(−2)×(−5)=10
Product of an odd number of negative integers is negative.
(−2)×(−5)×(6)=−60
Properties of Multiplication of Integers
Closure under Multiplication
- Integer * Integer = Integer
Commutativity of Multiplication
- For any two integers a and b, a × b = b × a.
Associativity of Multiplication
- For any three integers a, b and c, (a × b) × c = a × (b × c).
Distributive Property of Integers
- Under addition and multiplication, integers show the distributive property.
- For any integers a, b and c, a × (b + c) = a × b + a × c.
Multiplication by Zero
- For any integer a, a × 0 = 0 × a = 0.
Multiplicative Identity
- 1 is the multiplicative identity for integers.
a × 1 = 1 × a = a
Division of Integers
(positive integer/negative integer)or(negative integer/positive integer)
⇒ The quotient obtained is a negative integer.
(positive integer/positive integer)or(negative integer/negative integer)
⇒ The quotient obtained is a positive integer.
Properties of Division of Integers
For any integer a,
- a/0 is not defined
- a/1=a
Integers are not closed under division.
Example:
(–9)÷(–3)=3 result is an integer but
(−3)÷(−9)=−3−9=13=0.33 which is not an integer.