The document discusses order of operations and combining like terms when simplifying algebraic expressions. It covers PEMDAS, combining terms with the same variables, distributing numbers to terms in parentheses, and evaluating expressions by substituting values for variables. Examples are provided to illustrate each concept along with practice problems for the reader. Key steps include distributing, combining like terms, and using order of operations when evaluating expressions.
2. Order of Operations 2/6/13
• PEMDAS
• “Please Excuse My Dear Aunt Sally“
1. Parentheses
2. Exponents
3. Multiply and Divide
(from left to right)
4. Add and Subtract
(from left to right)
5. Combining Like Terms 2/7/13
• What are “like terms”?
▫ Must have the same variable, or
have no variable.
• Terms without a variable are called
“constants.”
• Remember: Variables are letters!
• The number before the letter is called
the coefficient.
6. • Which are like terms?
2x – 6 + 9y + 2 – 6x + 2y
To combine like terms: Add the coefficients!
10. The Distributive Property 2/8/13
• The distributive property tells us how
to simplify expressions like: 2(x – 1)
• We distribute the outside number to
both inside terms.
• Like this:
• Remember: “ab” means “a times b”
19. Evaluating Expressions 2/20/13
• Remember: Variables stand for
numbers.
• Evaluate means to replace each
variable with a number value and
get a number answer.
20. How to Evaluate Expressions:
• Replace each variable (letter) with
the given value (number).
• Always put the new number in ( )!
• Use ORDER OF OPERATIONS to
find the answer.
• Your answer should be a number
with no variables in it!
21. Examples:
• Evaluate each expression.
• 3(x – y); use x = 7 and y = 4
• m – n ÷ 3; use m = 12 and n = 6
22. • qr – 6; use q = 4 and r = 5
• x + y3; use x = 23 and y = 2
23. You Try!
• Evaluate each expression using the
values given.
• ab + b; use a = 4 and b = 2
• 7(x – y); use x = 9 and y = 5
24. Evaluating Expressions with ( )
2/21/13
• Simplify first.
▫ Distribute
▫ Combine Like Terms
• Replace variables with
numbers, then use Order of
Operations.
• Don’t forget ( ) around new
numbers!
25. Examples:
• Simplify each expression. Then
evaluate for the given value.
• 5(x + 3) – 4x; if x = 2
• -4m – (2 – 3m); if m = -3
26. • -2(3k – 1) + 4k + k; if k = -2
• -w + 4 – 2(5w + 7); if w = 1
27. You Try!
• Simplify, then evaluate.
• -(2t – 3) + t – 5; if t = 3
• 2x – 8 + 3(1 – 3x); if x = -2