1-3 algebraic expressions evaluate and simplify algebraic expressions by substituting and using...
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1-3 ALGEBRAIC EXPRESSIONSEvaluate and simplify algebraic expressions by substituting and using order of operations.
How to…• You will need to translate words into mathematical
operations. • What are some words or phrases for:
• Addition Subtraction
• Multiplication Division
Practice
• Ex: The product of 9 and b• 9b
• 26 less than 12 (**when you see “less than” notice that the first number goes last)• 12 - 26
You try:• The quotient of 6 and 3
• 6 more than twice the points
• Two times the sum of a and b
Modeling a Situation• You start with $20 and save $6 each week. What
algebraic expression models the total amount you save?• What do we know?• How can we make an algebraic expression using what we
know?
• 20 + 6w
Evaluate an Algebraic Expression
• Replace variables with values• Use order of operations to simplify• Ex: q + r – 15 if q = 21 and r = 18
• 21 + 18 -15• 39 – 15• 24
Simplifying Expressions• Combine like terms
• Use commutative property• • Combine
• If there is any distributing to be done… distribute FIRST!
1-4 SOLVING EQUATIONSSolve problems by writing equations.
Equation • An equation is a statement that two expressions are
equal.• Equations have an equal sign, expressions do not.
Properties of Equality• Reflexive: a = a
• Ex: 5 = 5
• Symmetric: If a = b, then b = a• Ex: If ½ = 0.5, then 0.5 = ½
• Transitive: If a = b and b = c, then a = c• Ex: If 2.5 = and , then
• Substitution: If a = b, then you can replace a with b and vice versa.• Ex: If a = b and 9 + a = 15, then 9 + b = 15
Solving• A solution of an equation is a value that makes the
equation true.• To find a solution, use inverse operations to “undo” the
equation.• Must be done to BOTH sides of the equation.
• If there is distributing to do, do it first.• Next, undo any addition or subtraction.• Last, undo multiplication or division.• Ex:
• distribute• add 27• subtract 3y• divide by 3
No Solution or Identities• Equations have no solution if all variables cancel and the
statement is false.• Ex: 4 = 5 (there are no variables and we know that 4 5)
• Equations have infinitely many solutions or are identities if all variables cancel and the statement is true.• Ex: 0 = 0 (notice the answer is not zero. We know that it is true that
0 = 0 so the equation is an identity)
Literal Equations• An equation that uses at least 2 different variables.• You solve for a variable “in terms of” the other variables.
• Isolate one of the variables and get all others to the opposite side of the equal sign.
• You Try:• The equation relates temperatures in degrees Fahrenheit
F and degrees Celsius C. What is F in terms of C?• multiply by the reciprocal • add 32
Assignment• Odds p.22 #13-21
p.30 #21-33