Exponents and Order of Operations

Exponents The exponent (little number) indicates how many times the base (big number) appears as a factor.

Order of Operations Parentheses (grouping symbols) Exponents Multiplication/Division Working from left to right in order they appear. Add/Subtract Working from left to right in order they appear.

Arithmetic Mean Fancy way of talking about averages. Mean means average To average: add up all the scores and divide by the number of scores.

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A Return to Algebraic Expressions Term: The number/letter combinations separated by addition signs in an algebraic expression. In my words: The “stuff” being added or subtracted together Example: 3x + 5y + 7: terms are 3x, 5y, and 7

Components of an Algebraic Expression Constant term: fancy name for a number Variable term: terms with letters Example: 3xy – 4z + 17 Variable expression with 3 terms: 3xy, -4z, 17 2 variable terms and 1 constant term

Variable Terms Consist of two parts The variable(letter) part The number part Example: − 2xy has a coefficient of 2 − -6j has a coefficient of –6 − W has a coefficient of 1

Algebraic Expressions Evaluating Algebraic Expressions: Substitute a given value in for the variable and use order of operations to simplify

Translating Verbal Expressions into Variable Expressions Recognize verbal phrases that translate into mathematical operations.

Example of evaluating an expression. Evaluate 3xy – 2x + 7y when x = 2 and y = 3 3(2)(3) – 2(2) + 7(3) 18 – The value of the expression is 35.

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Terms Like terms Terms with the same variable part Same means same letter(s) and power(s) We simplify variable expressions by combining like terms. To combine like terms, work with the coefficients of the like terms

Combining Like Terms 3x + 5 – 9x – 6x b – 7 – 5b -5 – 7 = -12 3b – 5b = -2b Answer: -2b – 12

Simplifying Numerical Expressions Use order of operations. Simplifies to a single number Could also be referred to as evaluating

Simplifying Algebraic Expressions Rewrite using as few symbols as possible Use the distributive property if necessary to remove parentheses. Combine like terms More often than not will have numbers and letters in the final answer.

Opposite of an expression -(4a – 3b + 7c) Change everything on the inside to its opposite -4a + 3b – 7c

Distributive Property This property will be used on a continuous basis throughout this course. a(b + c) = ab + ac − Examples 2(30 + 5) = 2(30) + 2(5) = = 70 3(x – 4) = 3(x) – (3)(4) = 3x – 12 Taking the opposite can be considered distributing -1 -(4a – 3b + 7c) = -1(4a – 3b + 7c)

Simplifying using the distributive property 5x – 9 + 3(2x + 4) 5x – 9 + (3)(2x) + 3(4) 5x – 9 + 6x x + 6x = 11x = 3 Answer: 11x + 3

Distributing a negative -4(y + 2) = (-4)(y) + (-4)(2) = -4y + (-8) = -4y – 8

Using the Distributive Property to Simplify 9t – 5r – 2(3r + 6t) 9t – 5r – 6r – 12t 9t – 12t = -3t -5r – 6r = -11r Answer: -11r – 3t

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