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Properties of Real Numbers - Coggle Diagram
Properties of Real Numbers
Addition Properties
Closure
Property : a +b is a real number.
Description : If you add two real numer, the sum is also a real number.
Example: 3 + 9 = 12 where 12 (the sum of 3 ad 9) is a real number.
Commutative
Property : a + b = b + a
Description : If you add two real numbers in any order, the sum will always be the same
or equal.
Example : 5 + 2 = 2+ 5 = 10
Associative
Property: (a +b)+c = a + (b +c)
Description : If you are adding three real number, the sum is always the same regardless of their grouping.
Example :(1+2)+3 = 1+(2+3) = 6
Additive Identity
Property : a+0 =a
Description : If you add a real number to zero, the sum will be the original number itself.
Example : 3 + 0 = 3 or 0 +3 = 3
Additive Inverse
Property : a + ( - a) = 0
Description : If you add a real number and its opposite, you will always get zero.
Example : 13 + (-13) = 0
Multiplication Properties
Closure
Property : a x b is a real number.
Description : If you multiply two real numbers, the product is also a real number.
Example : 6 x 7 = 42
Commutative
Property : a x b = b x a
Description : If you are multiplying three real number, the product is always the same regardless of their grouping.
Example : 9 x 4 = 4 x 9 = 36
Associative
Property : (a x b) x c = a x (b x c)
Description : If you are multiplying three real number, the product is always the same regardless of their grouping
Example : ( 5 x 3) x 2 = 5 x (3x2) = 30
Multiplicative Identity
Property : a x 1 = a
Description : If you multiply a real number to one (1), you will get the original number itself
Eaxmple : 25 x 1 = 25 or 1 x 25 = 25
Multiplicative Inverse
Property : a x (1/a) = 1 but a ≠ 0
Description : If you multiply a nonzero real number by its inverse or reciprocal the product will always be one (1)
Example : 2 x (1/2) = 1