properties of addition and subtraction of integers
- 1. Properties of Addition and Subtraction of Integers
- 2. 1. Closure property a. Closure under Addition 1. Closure under Addition For the closure property the sum of two integers must be an integer then it will be closed under addition. Example 2 + 3 = 5 2+ (-3) = -1 (-2) + 3 = 1 (-2) + (-3) = -5 As you can see that the addition of two integers will always be an integer, hence integers are closed under addition. If we have two integers p and q, p + q is an integer.
- 3. b. Closure under Subtraction If the difference between two integers is also an integer then it is said to be closed under subtraction. Example 7 – 2 = 5 7 – (- 2) = 9 - 7 – 2 = – 9 - 7 – (- 2) = – 5 As you can see that the subtraction of two integers will always be an integer, hence integers are closed under subtraction. For any two integers p and q, p - q is an integer.
- 4. 3. Commutative Property a. Commutative Property under addition If we change the order of the integers while adding then also the result is the same then it is said that addition is commutative for integers. For any two integers p and q p + q = q + p Example 23 + (-30) = – 7 (-30) + 23 = – 7 There is no difference in answer after changing the order of the numbers.
- 5. b. Commutative Property under subtraction If we change the order of the integers while subtracting then the result is not the same so subtraction is not commutative for integers. For any two integers p and q p – q ≠ q – p will not always equal. Example 23 - (-30) = 53 (-30) - 23 = -53 The answer is different after changing the order of the numbers