# Evaluate and Simplify Algebraic Expressions

```Evaluate and Simplify Algebraic Expressions
variable – a letter that represents a number
constant – number that does not change (placed in front of the variable)
algebraic expression – consists of one or more variables, constants, and operations
**Commutative Property – Change the order that terms are added or multiplied
(this does not change the sum or product)
a + b = b + a
or 2 + 3 = 3 + 2
**Associative Property – Change the grouping symbols (not the order of the
numbers or letters)
(a + b) + c = a + (b + c)
or (2 + 3) + 4 = 2 + (3 + 4)
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***Evaluate the following Algebraic Expressions (if you have a number for the variable,
you can evaluate the expression, or get a one number answer). Remember PEMDAS.
**Directions:
Evaluate each expression for m = 7, r = 8, and y = 2
Example 1: 5m - 6
Step 1: Write the original problem:
5m - 6
Step 2: Plug in the numbers for the variables:
5(7) - 6
Step 3: Use Order of Operations to solve:
Step 4: Solution:
35 - 6
29
Example 2: 5y + 2m
Step 1: Write the original problem:
5y + 2m
Step 2: Plug in the numbers for the variables:
5(2) + 2(7)
Step 3: Use Order of Operations to solve:
Step 4: Solution:
10 + 14
24
Example 3: 6r - m
Step 1: Write the original problem:
6r - m
Step 2: Plug in the numbers for the variables:
6(8) - 7
Step 3: Use Order of Operations to solve:
48 - 7
Step 4: Solution:
41
**Directions:
Simplify the following Algebraic Expressions.
Example 1:
Step 1:
8m + 2n + 3 - m
(the m has a 1 in front of it; a variable by itself always has a 1 in front)
Write the original problem:
8m + 2n + 3 - m
Step 2: Find Like terms (same variable); rearrange the terms:
Step 3:
Combine like
Step 4:
Solution:
Example 2:
terms (they have the same variable):
8m – 1m + 2n + 3
7m + 2n + 3
7m + 2n + 3
3x + 3 + 2x
Step 1: Write the original problem:
3x + 3 + 2x
Step 2: Find Like terms (same variable); rearrange the terms:
3x + 2x + 3
Step 3: Combine like
5x + 3
terms (they have the same variable):
Step 4: Solution:
5x + 3
**Distributive Property – Multiply a number by a sum of two terms.
6 (y + 4)
6
y + 6
8 (6 + y)
4
6y + 24
8
6 + 8
y
48 + 8y
Example 3: 8(k - 9)
Step 1: Write the original problem:
8(k - 9)
Step 2: Multiply 8 times k and 8 times 9:
8
Step 3: Combine the terms:
8k - 72
Step 4: Solution:
8k – 72
1k - 8
9
Example 4: 3(4 - w)
Step 1: Write the original problem:
3(4 - w)
Step 2: Multiply 3 times 4 and 3 times w:
3
Step 3: Combine the terms:
12 - 3w
Step 4: Solution:
12 - 3w
4 - 3
1w