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Review 1.1 to 1.3

Review 1.1 to 1.3. Analyzing Equations and Inequalities. Objectives: - evaluate expressions and formulas using order of operations - understand/use properties & classifications of real numbers - solve equations and inequalities, including those containing absolute value.

Mercy
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Review 1.1 to 1.3

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  1. Review 1.1 to 1.3

  2. Analyzing Equations and Inequalities Objectives: - evaluate expressions and formulas using order of operations - understand/use properties & classifications of real numbers - solve equations and inequalities, including those containing absolute value

  3. Expressions & Formulas ORDER OF OPERATIONS • Parentheses • Exponents • Multiply/Divide from left to right • Add/Subtract from left to right

  4. Order of Operations • Simplify: [9 ÷ (42 - 7)] - 8 • Exponents [9 ÷ (16 - 7)] - 8 • Parentheses [9 ÷ (9)] - 8 • Divide [ 1 ] - 8 • Subtract -7

  5. Expressions and Formulas How do you evaluate expressions and formulas? Replace each variable with a value and then apply the order of operations.

  6. Expressions Evaluate: a[b2(b + a)] if a = 12 and b= 1 • Substitute: 12[12(1 + 12)] • Parentheses: 12[12(13)] • Exponents: 12[1(13)] • Parentheses: 12[13] • Multiply: 156

  7. Properties of Real Numbers The properties of real numbers allow us to manipulate expressions and equations and find the values of a variable.

  8. Naturalnumbers are the counting numbers. Wholenumbers are natural numbers and zero. Integers are whole numbers and their opposites. Rationalnumbers can be written as a fraction. Irrationalnumbers cannot be written as a fraction. All of these numbers are real numbers. Number Classification

  9. Subsets of the Real Numbers Number Classifications Q - Rational Z - Integers I -Irrational W - Whole N - Natural

  10. -1 real, rational, integer real, rational, integer, whole, natural real, irrational real, rational real, rational, integer, whole real, rational Classify each number 6 0 -2.222

  11. Commutative Property Think… commuting to work. Deals with ORDER. It doesn’t matter what order you ADD or MULTIPLY. a+b = b+a 4 • 6 = 6 • 4 Properties of Real Numbers

  12. Associative Property Think…the people you associate with, your group. Deals with grouping when you Add or Multiply. Order does not change. Properties of Real Numbers

  13. Associative Property Properties of Real Numbers • (a + b) + c = a + ( b + c) • (nm)p = n(mp)

  14. Properties of Real Numbers Additive Identity Property • s + 0 = s Multiplicative Identity Property • 1(b) = b

  15. Properties of Real Numbers Distributive Property • a(b + c) = ab + ac • (r + s)9 = 9r + 9s

  16. “Like Terms”

  17. Additive Inverse

  18. Multiplicative Inverse

  19. Solving Equations • To solve an equation, find replacements for the variables to make the equation true. • Each of these replacements is called a solution of the equation. • Equations may have {0, 1, 2 … solutions.

  20. To isolate the variable, perform the inverse or opposite of every operation in the equation on both sides of the equation. Do inverse operations in the reverse order of operations.

  21. 3(2a + 25) - 2(a - 1) = 78

  22. Solve 5(x – 6) = 3x – 18 + 2x.

  23. Solving Equations • Solve: V = πr2h, for h • Solve: de - 4f = 5g, for e

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