Bell Work: Simplify -3{[(-4 – 1)3] – 5} -3{[(-4 – 1)3] – 5} 2(4 – 7) 2(4 – 7)

Answer: -3{[(-4 – 1)3] – 5} -3{[(-4 – 1)3] – 5} 2(4 – 7) 2(4 – 7) = -3{{(-5)3] – 5} 2(-3) 2(-3) = -3(-15 – 5) = -3(-20) = 60=

{ Lesson 14: Evaluation of Algebraic Expressions

In lesson 4, we said that a number is an idea and that when we wish to write down something to represent this idea, we use a numeral. If we think about the number 7, we could write any of the following: 714/ /

We call each of these notations a numerical expression or just a numeral. Every numerical expression represents only one number and we call this number the value of the expression. Each of the numerical expressions shown before has a value of 7.

Numerical Expression*: a meaningful arrangement of numerals that has a single value.

In algebra we often use letters to represent numbers. Algebraic Expression*: an expression obtained by combining constants and/or variables using the arithmetic operators +, -, x, or /. This can also be called a mathematical expression.

If we write the algebraic expression: 4 + x 4 + x The algebraic expression has a value that depends on the value that we assign to x. if we give x a value of 5, then the algebraic expression has a value of 9 because = = 9

Variable*: The value can be changed or varied. Constant*: A quantity whose value does not change.

In the example 4 + x, 4 is the constant value that stays the same and x is the variable that can be changed.

If an algebraic term is composed of both constant and variable factors, we customarily write the constant factor first.

If we wish to multiply a constant by a variable, we can express it in many different ways. 4s4(s)(4)(s)4 x s(4) x (s)

The notation 4s indicates that 4 is to be multiplied by the value of s. If the value of s was 5 it would be written as 4 x 5 and not like 45.

Example:Solve 4x + mx 4x + mx If x = 3 and m = 5.

Answer: 4(3) + (5)(3) = = 27

While the values assigned to variables may change or be changed, under any set of conditions the value assigned to a particular variable in an algebraic expression is the same value throughout the algebraic expression. Also, when we begin solving equations and working problems we must remember that the value assigned to any particular variable under any set of conditions must be the same value regardless of where the particular variable appears in the equation or the problem.

Practice: Find the value of xmp If x = 4, m = 5, and p = 2

Answer: 4 x 5 x 2 = 40

Practice:Evaluate 4yz – 5 If y = 2 and z = 10

Answer: 4(2)(10) – 5 = 80 – 5 = 75

Practice:Evaluate y – z If y = -2 and z = -6

Answer: (-2) – (-6) = = +4

Practice:Evaluate -a – b – ab If a = -3 and b = -4

Answer: -(-3) – (-4) – (-3)(-4) = – 12 = -5

HW: Lesson 14 #1-30 Due Tomorrow