Evaluating Algebraic Expressions: Substitution and Simplification, Lecture notes of Mathematics

Instructions on how to evaluate algebraic expressions by substituting variables with their values and simplifying the resulting expression. It covers basic operations, exponents, and the steps to evaluate an expression. Examples are given to illustrate the concepts.

Typology: Lecture notes

2021/2022

Uploaded on 09/27/2022

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1.1: Evaluate Expressions
Goals: *Evaluate algebraic expressions using basic operations
*Evaluate algebraic expressions using exponents
Variable - ____letter_________, or symbol, used to represent one or more ___numbers_____________.
Ex: x, y, z….
Value the __number___________ that replaces a variable.
Ex: If x is the variable and x = 3, the value of the variable is 3.
Expression - __math______ sentence that has ___numbers__________, ___operations___________, and
__variables_____________. (**It does NOT have an _____equals_______ ____sign________!!!)
Ex: 5 + x
Algebraic expression an ____expression_________ that has at least one __variable____________.
Algebraic Expression Meaning Operation
1. 14
𝑦 14 divided by y Division
2. 5 + c 5 plus c Addition
3. 6n 6 times n Multiplication
4. 4 x 4 minus x Subtraction
**Do NOT use __x__ to show multiplication anymore! *It is too easy to get confused with a variable. Use
parenthesis, middle dot, or don’t need anything if it is a number and a variable.
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1.1: Evaluate Expressions

**Goals: *** Evaluate algebraic expressions using basic operations ***** Evaluate algebraic expressions using exponents

Variable - ____ letter _________, or symbol, used to represent one or more ___numbers_____________.

Ex: x , y , z ….

Value – the __number___________ that replaces a variable.

Ex: If x is the variable and x = 3, the value of the variable is 3.

Expression - __math______ sentence that has ___numbers__________, ___operations___________, and

__variables_____________. (**It does NOT have an _____equals_______ ____sign________!!!)

Ex: 5 + x

Algebraic expression – an ____expression_________ that has at least one __variable____________.

Algebraic Expression Meaning Operation

14 𝑦 14 divided by^ y^ Division

2. 5 + c 5 plus c Addition 3. 6 n 6 times n Multiplication 4. 4 – x 4 minus x Subtraction

****** Do NOT use x to show multiplication anymore! *It is too easy to get confused with a variable. Use parenthesis, middle dot, or don’t need anything if it is a number and a variable.

Steps to Evaluate an expression:

1. Write down the ____expression__________. Ex : Evaluate 13 n when n = 3 2. ____Substitute__________, or change the variable to 13(3) 39 its ___value_________. 3. Simplify. (Do the ___math________)

***** Be sure to follow __PEMDAS_________ if there is more than one step.

Evaluate when n = 3.

Ex: n

Ex: n – 1 Ex: n + 8

9 3 3 –^1 3 + 8

3 2 11

Evaluate when y = 2.

Ex: 6 y Ex: y

Ex: y + 4

8 2 2 + 4

12 4 6

Evaluate when c = 4.

Ex: 4 c Ex: 15 + c Ex: 17 – c

4(4) 15 + 4 17 – 4 16 19 13

Ex: The total cost of going to the movies can be represented by the expression a + r where a is the cost of admission and r is the cost of refreshments. Suppose you pay $7.50 for admission and $7.25 for refreshments, find the total cost of going to the movies.

a + r 7.50 + 7.

Ex: The edge of a medium-size storage cube is 14 inches long. Find the volume of the storage cube.

To find volume use the expression s ³ (14)³ 2,744 inches³

Ex: Find the area of a square garden whose side length is 22 feet.

To find area of a square use the expression s ² (22)² 484 ft²