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ZingPath: Expressions, Equations, and Inequalities

Evaluation of Algebraic Expressions

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Evaluation of Algebraic Expressions

Math Foundations

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You will evaluate algebraic expressions by 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-variable 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 (like x, y). Algebraic expressions do not have equal signs. A variable is a symbol or letter that stands for the value.


n x 2

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

For example,

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

The order of operations refers to the precedence 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 multiplications and/or divisions from left to right.

4. Perform all additions and/or subtractions from left to right.

For example,

2 + (25 - 4) 20 2

First do all operations inside parentheses

2 + (21) 20 2

Perform all multiplications and divisions, from left to right.

2 + 420 2

2 + 210

Perform all additions and subtractions from left to right.

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

The following key vocabulary terms will be used throughout this Activity Object:

algebraic expression - an expression that contains one or more numbers, one or more variables, and one or more arithmetic operations

Examples of algebraic expressions:

evaluate - when a given value is substituted for each variable in an expression and the operations are performed, it is called evaluating the expression

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Learners should be familiar with evaluating expressions, operations on integers, order of operations, and working with exponents.
Course Math Foundations
Type of Tutorial Skills Application
Key Vocabulary algebraic expression, substitution,