Integers
Integers are a big collection of numbers which include whole numbers and negaative numbers.
Operations with Integers
- Multiplying 2 integers with the same sign, the result will be positive. ( 3 * 2 = 6 , -3*-2 = 6 )
Multiplying 2 integers with different signs, the result will be negative. ( -5 * 3 = -15 ) - Dividing 2 integers with the same sign, the result will be positive. ( 6 ÷ 3 = 2 , -6 ÷ -3 = 2 )
Dividing 2 integers with different signs, the result will be negative. (-15 ÷ 3 = -5 ) - When we add 2 positive integers, the result will be positive. ( 5 + 3 = 8 )
When we add 2 negative integers, the result will be negative. ( -5 + -3 = -8 )
When we add 2 integers with different signs, the result can either be positive or negative. ( -5 + 3 = -2 , 5+ -3 = 2 ) - When we subtract 2 positive integers, the result can either be positive or negative. ( 5-3 = 2, 3-5 = -2 )
When we subtract 2 negative integers, the result can either be positive or negative. ( -5 - -3 = -2 , -8 - - 14 = 6 )
When we subtract 2 integers with different signs, the result can either be positive or negative. ( -5 - 3 = -8 , 5- -3 = 8 )
Properties of Integers
- Commutative Property
Commutative Property of Addition : 2 integers can be added in any order, the result will be same. ( 3+5 = 5+3 )
Commutative Property of Multiplication : 2 integers can be multiplied in any order, the result will be same. ( 3*5 = 5*3 )
Commutative Property of Division : This is not possible with division. When we divide 2 integers in any order, the result may differ. ( 6÷2 is not equal to 2 ÷ 6 )
Commutative Property of Subtraction : This is not possible with subtraction. When we subtract 2 integers in any order, the result may differ.
- Associative Property
Associative Property of Addition : 3 or more integers can be added in any order.
Associative Property of Multiplication : 3 or more integers can be multiplied in any order.
Associative Property of Division : This is not possible with division. When we divide 3 or more integers in any order, the result may differ.
Associative Property of Subtraction : This is not possible with subtraction. When we subtract 3 or more integers in any order, the result may differ.
Identities
- Multiplicative identity : Any number multiplied by 1, the result will be the same.
- Additive identity : Any number added by 0, the result will be the same.
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