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Evaluation of algebraic expressions

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Lesson Focus

Evaluation of algebraic expressions


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You will evaluate algebraic expressions using substitution.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Evaluate first degree algebraic expressions in one variable by substituting positive integers for the variable and making use of the four basic operations.
  • Evaluate one variable and second degree algebraic expressions involving the four basic operations by substituting positive and negative integers for the variable.
  • Evaluate higher degree algebraic expressions in multiple-variables by substituting positive and negative integers for the variable and making use of the four basic operations as well as exponents.

Everything You'll Have Covered

1. An algebraic expression is a mathematical phrase.

Algebraic expressions contain numbers, operators (add, subtract, multiply, divide), and at least one variable (such as x or y). Algebraic expressions do not have equal signs. A variable is a symbol or letter that stands for the value.


n 2

2. The process of replacing those letters or variables with numerical values and simplifying is known as evaluating an algebraic expression.


3 - (1 - 2 ) Evaluate at x = 2

= 3 - 2(1 - 2 2) Replace x with 2

= 3 - 2(-3)

=3 - (-6)

=3 +6


3. The order of operation is used to evaluate an algebraic expression.

The order of operations refers to the process of performing one arithmetic operation over another while working on a mathematical expression. The rules are as follows:

1. Evaluate expressions inside parentheses.

2. Evaluate all powers.

3. Perform all multiplication and/or division from left to right.

4. Perform all addition and/or subtraction from left to right.


2 + (25 - 4) 20 2

First, do all operations inside parentheses.

2 + (21) 20 2

Perform all multiplication and division, from left to right.

2 + 420 2

2 + 210

Perform all addition and subtraction, from left to right.

If these rules are not rigidly followed, the expression can produce different solutions.

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Students should be familiar with these concepts: evaluating expressions, operations on integers, order of operations, and exponents.
Course Algebra-1
Type of Tutorial Skills Application
Key Vocabulary algebraic expression, substitution,