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P1 Real Numbers

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Warm-up How many people: -Are in the class? -Have a brother? -Have a sister? -Have no siblings? Lets make a Venn Diagram of that information.

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Complex Numbers We will worry about them down the road. Pretty much they help us define numbers when we have to take the square root of a negative.

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**Real Numbers Numbers that describe quantities in everyday life.**

They consist of rational numbers and irrational numbers. Ex: 2, π, 2/5, .7, …., 2

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**Rational vs. Irrational Numbers**

A real number that can be written as the ratio p/q of two integers where q≠0 Fractions/Decimals -Terminating: ½ , ¼… -Repeating: 1/3 = … Irrational Numbers that cannot be written as a ratio of two integers Fractions/Decimals -Non-Terminating -Non-Repeating Ex) , etc.

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**Other Subsets… Natural Numbers {1, 2, 3, 4, 5…}**

(Counting Numbers) Whole Numbers {0, 1, 2, 3, 4, 5…} (Natural Numbers including Zero) Integers {…-3, -2, -1, 0, 1, 2, 3…} (Whole Numbers and their Opposites)

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Peardeck Give the most specific set for each type of number.

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Interval Notation [ ] – Including boundary ( ) – Excluding boundary Write each inequality in interval notation & draw on a number line Ex. 1) Ex. 2)

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Writing Inequalities Example 1) x is at least -1 Example 2) y is at most 4 Example 3) z is at least -6 and at most 0

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Given any two numbers… There are 3 possibilities… They are equal One is larger than the other Or the other is larger than the first

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Absolute Value Measures the distance between the number and the origin (magnitude) If a is a real number, then

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Examples 1. Evaluate when: a) x >0 b) x <0

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Examples 2. Evaluate when: a) x > -5 b) x < -5

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**Distance between Two Points**

Properties Distance between Two Points

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**Set up the expression for…**

The distance between x and 5 is 10. b is at most 5 units from a c is at least d units from 7

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**Algebraic Expressions**

Variables (letters) and constants (numbers) with +, -, x, ÷, and exponents Example: Evaluating: Substitute the given value for each of the variables in the expression ~ Evaluate the above expression for x = -5

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Basic Rules of Algebra Let a, b, and c be real numbers, variables, or algebraic expressions Property

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**Properties of Negation**

Let a and b be real numbers, variables, or algebraic expressions Property

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**Properties of Equality**

Let a, b, and c be real numbers, variables, or algebraic expressions

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**Let a and b be real numbers, variables, or algebraic expressions.**

Properties of Zero Let a and b be real numbers, variables, or algebraic expressions.

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**Properties and Operations of Fractions**

Let a, b, c, and d be real numbers, variables, or algebraic expressions such that and

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**Fundamental Theorem of Arithmetic**

Prime Numbers Integer with exactly 2 factors; one and itself Fundamental Theorem of Arithmetic Every positive integer greater than 1 can be written as the product of prime numbers Example)

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