advertisement

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) __________________________________________________________________ ***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 (circle answer) 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 (circle answer) 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 (circle answer) **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 (circle answer) 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 (circle answer) 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 (circle answer) (circle answer)