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# 1.1/1.2 Properties of Real Numbers

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### 1.1/1.2 Properties of Real Numbers

1. 1. Chapter1: Expressions, Equations, and Inequalities<br />1.1 Patterns and Expressions<br />1.2 Properties of Real Numbers <br />
2. 2. Definitions<br />A mathematical quantity is anything that can be measured or counted.<br />Quantities whose value stay the same are constants<br />Quantities whose values change or vary are called variable quantities<br />
3. 3. Definitions<br />A variable is a symbol, usually a letter, that represents one or more numbers.<br />Examples: and <br />A numerical expression is a mathematical phrase that contains numbers and operation symbols.<br />Examples: and <br />An algebraic expression is a mathematical phrase that contains one or more variables.<br />Examples: and <br />
4. 4. Sets of Numbers<br />Real Numbers can be graphed on a number line and contain several subsets<br />Natural Numbersare the counting numbers: <br /> 1, 2, 3, 4, …<br />Whole numbersare the natural numbers and zero<br /> 0, 1, 2, 3, 4 ….<br />Integers are the positive and negative whole numbers and zero<br />
5. 5. Sets of Numbers<br />Rational numbersare number that can be written as a ratio of two integers (this includes fractions, terminating decimals, and repeating decimals)<br />Irrational Numbers cannot be written as a ratio of two integers and have decimal representations that do not terminate or repeat<br />
6. 6. Sets of Numbers<br />This diagram shows how subsets of the real numbers are related.<br />
7. 7. Example: Graph each number on the number line and classify each number.<br />
8. 8. Properties of Real Numbers<br />The properties of real numbers are relationships that are true for all real numbers (except in one case, zero)<br />The opposite (additive inverse) of any number a is –a. <br />The Additive Inverse: The sum of a number and its opposite is 0.<br />Thereciprocal (multiplicative inverse) of any <br /> nonzero number is <br />The Multiplicative Inverse: The product of a number and its reciprocal is 1<br />
9. 9. Look for clues/key information:<br /><ul><li> Does the equation contain 0 or 1?
10. 10. What is different about the left and right side of </li></ul> the equation?<br />
11. 11. Example: Name the property illustrated by each equation.<br />