Properties of Real Numbers!

One type of problem that appears on nearly every UIL Mathematics test deals with different properties of real numbers. We've compiled a list of the properties that appear most often:

1) Assosiative Property - Changing the grouping of numbers does not change the result of the equation. This works for both addition and multiplication. For example:

(4 + 7) + 13 = 4  + (7+13) = 24
(a + b) + c = a + (b + c) = a + b + c

2) Commutative Property - Multiplying/adding numbers in any order still produces the same result. For example:

7*4 = 4*7 = 28
ab = ba

8+9 = 9+8
a + b = b + a

3) Distributive Property - Multiplying a single term times two or more terms inside a set of parentheses produces the same result as multiplying a single term times each number in the parentheses. For example:

3(4+5) = 3(4) + 3(5) = 27
a(b+c) = a(b) + a(c)

4) Identity Property - Adding a zero to any number does not change the number; multiplying a number by 1 does not change the number. (Hint: The number will retain its identity!) For example:

5 + 0 = 5
a + 0 = a

7 * 1 = 7
a * 1 = a

5) Inverse Property - For every real number not equal to zero, the Inverse Property is another real number, called the Inverse Number. There are two types of Inverse Properties: Additive Inverses and Multiplicative Inverses. For example:

Additive Inverse: 1 + (-1) = 0  (1 is the number, -1 is the Inverse Number.)

Multiplicative Inverse: 6 * (1/6) = 1 (6 is the number, 1/6 is the Inverse Number.)