1 2 Algebraic Expressions and Models In this

1. 2 Algebraic Expressions and Models

In this lesson you will: • Evaluate algebraic expressions, • Simplify algebraic expressions by combining like terms, • Solve real life problems using these skills.

A numerical expressions consists of These are numerical expressions: • Numbers • Operations • Grouping symbols These are NOT:

Exponents are used to represent repeated factors in multiplication. Base Exponent 5 factors of 2

To evaluate powers (exponents), notice:

Write the expression using exponents:

To avoid confusion, an order of operations is needed for expression like those shown above • First, do operations that occur within grouping symbols (like parentheses). • Next, evaluate powers. • Then, do multiplications and divisions in order from left to right. • Finally, do additions and subtractions in order from left to right.

Add within parentheses Evaluate power Multiply Add To help you remember the order of operations: PEMDAS (Please Excuse My Dear Aunt Sally: Parentheses, Exponents, Multiplication & Division, Addition & Subtraction.

PEMDAS Evaluate the expression:

A Variable • Is a letter used to represent one or more numbers. • Any number used to replace a variable is a value of the variable. • An expression involving variables is called an algebraic expression.

Evaluate when x = -2.

Evaluate the expression:

Writing and Evaluating a Real-Life Model

Suppose you have $50 and are buying some movies on DVD’s that cost $15 each. Write an expression that shows how much money you have left after buying n movies. Evaluate the expression when n = 2 and n = 3. Verbal Original Model Amount - Price per movie Number of movies bought Original amount = $50 Labels Price per movie = 15 Number of movies bought = n When you buy 2 movies, you have 50 -15(2) = $20 left Algebraic Model 50 -15 n When you buy 3 movies, you have 50 – 15(3) = $ 5 left.

Simplifying Algebraic Expressions

For an expression such as 2 x + 3 The 2 x and 3 are called terms. When a term is the product of a number and a power of a variable such as or The number is the coefficient of the power. and Are like terms because they have the same variable part. The distributive property makes it possible to combine like terms into a single term. Constant terms such as – 4 and 2 are also like terms.

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