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P1 Real Numbers

Learn about real numbers, rational vs. irrational numbers, subsets like natural, whole, and integers, and fundamental operations in algebra. Understand interval notation, inequalities, absolute value, and prime numbers. Enhance your math skills!

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P1 Real Numbers

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  1. P1 Real Numbers

  2. 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.

  3. 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.

  4. Real Numbers • Numbers that describe quantities in everyday life. • They consist of rational numbers and irrational numbers. • Ex: 2, π, 2/5, .7, .1204123….,

  5. Rational vs. Irrational Numbers Rational 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 = .33333… Irrational Numbers that cannot be written as a ratio of two integers Fractions/Decimals -Non-Terminating -Non-Repeating Ex) , etc.

  6. 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)

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

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

  9. 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

  10. 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

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

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

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

  14. Properties Distance between Two Points

  15. 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

  16. 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

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

  18. Properties of Negation Let a and b be real numbers, variables, or algebraic expressions Property

  19. Properties of Equality Let a, b, and c be real numbers, variables, or algebraic expressions

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

  21. Properties and Operations of Fractions Let a, b, c, and d be real numbers, variables, or algebraic expressions such that and

  22. 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) 36

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