Evaluating Algebraic Expressions

The terms of an expression are the parts of the expression that are added or subtracted.

• The terms of the expressions 140 + 4x are 140 and 4x.

Create more examples:

In the term 4x, 4 is called the coefficient. A coefficient is the number that is

multiplied by the variable in a algebraic expression.

What is the coefficient of the third term in this expression?

3X + 4Y + 5X

You can use the greatest common factor (GCF) and the Distributive Property to factor numerical expressions.

The greatest common factor (GCF) is the largest common factor of two or more given numbers.

What is the GCF of 12 and 32?

Equivalent expressions are expressions that have the same value for all the values of the variables.

The expressions 15x + 18 and 3(5x + 6) are equivalent expressions because

15x + 18 = 3(5x + 6) for every value of x.

You can evaluate an expression with a variable by substituting a number for the variable.

• Follow the order of operations (PEMDAS).• Substitute the given value for the variable.• Then evaluate.Example: Evaluate a2 + 6 for a = 5Rewrite the expression substituting 5 for “a”

52 + 6 =25 + 6 =31

Formulas are special equations that show relationships among variables.

Common formulas include volume, area, surface area, distance, and velocity.

Example: The formula for Surface Area of a cube is A=6s2

A cube with side lengths of 2in would have SA of A=6(2)2 = 6(4) = 24in2

Example: The formula for Area of a rectangle is A=lw (area = length times width)

w = 4

l = (6 + X) A = 4(6 + X) Evaluate for X = 2A = 4(6) + 4X A =A = 24 + 4X A = A =

6 X

Using the Addition properties to evaluate expressions:

Commutative: The order of two or more addends doesn’t change the sum.

Associative: The way numbers are grouped when adding doesn’t change the sum.

Identity: The sum of an addend and zero is the addend.

Using the Multiplication properties to evaluate expressions:

Commutative: The order of two or more factors doesn’t change the product.

Associative: The way numbers are grouped when multiplying, doesn’t change the product.

Identity: The product of a factor and one is the factor.

• Example: Factor the sum 27 + 39 as a product of the GCF and a sum. 27+39 3.3.3+3.13 Find the GCF of both terms 3.9+3.13 Rewrite each term as a product with

the GCFAn equivalent expression for 27 + 39 is 3(9 + 3) 3(9+13) Apply the distributive property over

addition

Example : Write an equivalent expression for a + a + aThe coefficient of a single variable is 1 a = 1a Identify the coefficient a + a + a = a(1 + 1 + 1) Apply the distributive

property of multiplication

a (1 + 1 + 1) = a . 3 Simplify the expression

a . 3 = 3a Solution

Example: Simplify 10X + 6Y + 4XIdentify the like terms • 10X and 4XUse the commutative property to rewrite the

expression• 10X + 4X + 6YUse the associative property to group like terms• (10X + 4X) + 6Y Use the distributive property of multiplication• (10X + 4X) + 6Y = X(10 + 4) + 6Y Use the commutative property of multiplicationSolution: 14X + 6Y