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Chapter 6—Expressions and Equations

6-2 Evaluating Algebraic Expressions

 

Procedure

To evaluate an algebraic expression:

  1. Assign a specific numerical values to all of the variables.
  2. Complete the operations

Evaluating Expressions of Addition and Subtraction

Algebraic expressions that use addition and subtraction look like this:

x + 2         y – 4         5 + x         – 8 + w

You can evaluate the expressions by giving each variable a specific numerical value and then completing the addition or subtraction..

fig0801_01.jpg (6391 bytes)

 

Examples:

Examples & Exercises

Evaluating Algebraic Expressions
of Addition and Subtraction

Use these interactive Examples & Exercises to strengthen your understanding and build your skills:

Evaluating Expressions of Multiplication and Division

Algebraic expressions that use multiplication and division look like this:

4a         y/4        

You can evaluate expressions when you are given exact numerical values for the variables.

Examples:

 

Examples & Exercises

Evaluating Algebraic Expressions
of Multiplication and Division

Use these interactive Examples & Exercises to strengthen your understanding and build your skills:

Evaluating Expressions of Addition, Subtraction, Multiplication, and Division

The mastery of effective creative thinking doesn't come from memorizing and recalling endless arrays of procedures. It comes from learning how to read the instructions that are encoded in every problem.

Many algebraic expressions combine all four basic operations: addition, subtraction, multiplication and division. Here are some examples:

2x + 4 4x2 + 3x – 2

 

Recall

Order of Operations
(First to Last)

  1. Evaluate expressions within parentheses (P)
  2. Evaluate exponents (E)
  3. Do multiplication and division, from left to right (MD)
  4. Do addition and subtraction from left to right (AS)

PEMDAS

These expressions might look complicated, but you can think of them as sets of instructions. Once you are given a specific value for the variables, these expressions tell you exactly what to do. Consider this example: 4x2 + 3x – 2. If we let x = 5, the expression looks like this:

4x2 + 3x – 2 = 4(5)2 + 3(5) – 2

Now the expression is purely numerical. Doing the math:

4(5)2 + 3(5) – 2 = 4 • 25 + 15 – 2
4 • 25 + 15 – 2  = 100 + 13
100 + 13 = 113

When x = 5 in the expression, 4x2 + 3x – 2, the expression simplifies to 113.

Examples:

 

Examples & Exercises

Evaluating Algebraic Expressions

Use these interactive Examples & Exercises to strengthen your understanding and build your skills:

 

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