The Real Number System

According to the Order of Operations, perform the operations with the parenthesis first, next evaluate the power (exponents), multiply and divide from left to right (direction in which reading is done). Last add and/or subtract from left to right.

The product of a number and its reciprocal always equals one because the reciprocal of a number is the number that, when multiplied by the original number, gives a product of 1. This is a fundamental property of reciprocals, where any non-zero number multiplied by its reciprocal will result in the multiplicative identity, which is 1. Therefore, the statement is true.

The absolute value is the distance that a number is from zero (0) on the number line. Distance is always thought of as positive, therefore the absolute value of a number is always positive.

Additive Inverse Property states that the sum of a number and its additive inverse (opposite) will always equal zero (0).

Turn the fraction upside down and keep the sign.

The order in which the two numbers is different, therefore the commutative property is illustrated.

The two operations present are multiplication and addition. The Distributive Property is the only property of real numbers that involves two mathematical operations.

The Commutative Property deals with the order in which numbers are added or multiplied. The Associative Property deals with the grouping of numbers when adding or multiplying. The Distributive Property involves 2 operations, one of which must be multiplication the other operation can be addition or subtraction. The Additive identity states that when zero (0) is added to a number, the results is the original number.

Irrational numbers cannot be written as fractions, are not repeating or terminating decimals.

Read as the opposite of the absolute value of 45, the answer is -45. Remember that the opposite of any positive number is negative.