1.4 Evaluating Algebraic Expressions

5 + 84 Numerical 3x + 10 Algebraic Expressions An expression is NOT an equation because it DOES NOT have an equal sign. There are 2 types of expressions. 5 + 84 Numerical 3x + 10 Algebraic Notice there are no equal signs in these expressions so they are not equations!

5 times 3 plus 8 (5•3) + 8 Expressions A numerical expression contains only numbers and symbols and NO LETTERS. 5 times 3 plus 8 (5•3) + 8

An algebraic expression contains only numbers, symbols, and Expressions An algebraic expression contains only numbers, symbols, and variables. It is sometimes referred to as a variable expression. The product of 3 and x 3x The sum of m and 8 m + 8 The difference of r and 2 r - 2

Expressions What is a variable? A variable represents an unknown value. 2) 10 – ? 1) 4 + x 4) 20 3) 5y A variable can be any letter of the alphabet since it represents an unknown.

5 • c or 5c 7 • t or 7t 6 • d or 6d Expressions Word Phrases for multiplication are: The product of 5 and a number c Seven times a number t 6 multiplied by a number d 5 • c or 5c 7 • t or 7t 6 • d or 6d

Always write the variable AFTER the number. Expressions The Placement rule for multiplication is: The product of 5 and a number c Seven times a number t 6 multiplied by a number d 5 • c or 5c Always write the variable AFTER the number. 7 • t or 7t 6 • d or 6d

m = 2 6 + m ? 6 + 2 8 Evaluate means to find the value of an Expressions Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. m = 2 6 + m ? 6 + 2 8

r = 3 7 + r ? 7 + 3 10 Evaluate means to find the value of an Expressions Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. r = 3 7 + r ? 7 + 3 10

Evaluate the variable expression when n = 6. Expressions Evaluate the variable expression when n = 6. 1) 2) Evaluate just means solve by substitution.

Evaluate the variable expression when n = 6. Expressions Evaluate the variable expression when n = 6. 3) 4) Evaluate just means solve by substitution.

Evaluate the algebraic expression when n = 8. Expressions Evaluate the algebraic expression when n = 8. 1) 2)

Evaluate the expression if a = 3 and b = 4. Expressions Evaluate the expression if a = 3 and b = 4. 1) 2)

Evaluate the expression if a = 3 and b = 4. Expressions Evaluate the expression if a = 3 and b = 4. 3) 4)

Evaluate the expression if x = 5 and y = 3. Expressions Evaluate the expression if x = 5 and y = 3. 2) 1)

TYPES OF EXPRESSIONS #1 An expression is NOT an equation because it does not have an equal sign. There are 2 types of expressions. NUMERICAL EXPRESSION: Contains only numbers and symbols. Example: 5 • 3 + 4 ALGEBRAIC EXPRESSION: Contains numbers, symbols, and variables. Also known as a variable expression. Example: m + 8 A VARIABLE is a letter or symbol that represents a number. Example: x

Evaluate means solve. Show the substitution. Circle your answer. #2 Substitute & Evaluate Evaluate if x = 3 and y = 4 Evaluate means solve. Show the substitution. Show your work down. Circle your answer. Show your work one step at a time down. No equal signs!

Model Problems Simplify 7(5² - 2*11) - 3 + 8

5(x³+y) - 25 – y if x= 3 and y= -2

A. express as a formula for the Total Salary. 3.The following table reveals the total salaryand bonus, but not the fixed salary? A. express as a formula for the Total Salary. BONUS(b) $50 $120 $180 $230 Total Salary(S) $340 $410 $470 $520

4. Which of the following makes the algebraic fraction 2x+3 undefined? A.2 B.3 C.-3 D.-2

5. If d is an odd integer and e is an even number, which of the following is an odd integer? A. 2d+e B. 2d+2e C. de + d D. 3e + 3d +1

Practice pages 15-16 odd 1. 6 + 4 · 8 - 3

Evaluate 3. (2·3²)¬(3 4)

5. x[7-2(y)] x=-5 , y=-3

7. 1 + 33 – g +12 g g g - g - + 4 g=3

11. If a≠b, and a and b are prime numbers greater than 2, which of the following expressions must represent an odd integer?