Algebraic Expressions - §1.4 - 1.5
Fall 2013 - Math 1010
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Roadmap
For today:
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Identifying parts of algebraic expressions.
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Simplifying algebraic expressions.
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Evaluate algebraic expressions.
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Translate verbal phrases to mathematical expressions (and back).
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Construct mathematical models.
Points 1 to 3 are from §1.4, and points 4 to 5 are from §1.5. Many of
today’s topics are summarized in tips and come with examples. Practice is
very important with these topics.
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Tips on reading algebraic expressions
Terms in an algebraic expression are terms in the sense of addition.
A coefficients of a term is the numerical factor.
Example The expression
−7.12x 2 + x − 8
has three terms: −7.12x 2 , x, and −8. Respectively the coefficients are
−7.12, 1, and −8.
Tips:
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Terms such as x, y , and the like, have coefficent 1. Their opposites
are written −x, −y , and so on, and have coefficient −1.
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Terms with equivalent variable factors are called like terms.
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Simplify - Combine like terms
Combining like terms is one of serveral steps in simplifying algebraic
expressions.
Example Perimeter of a rectangle is the total distance around the
rectangle. Find the perimeter of the rectangle below:
b
1.6b + 2
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Simplify - Combine like terms
Combining like terms is one of serveral steps in simplifying algebraic
expressions.
Example Perimeter of a rectangle is the total distance around the
rectangle. Find the perimeter of the rectangle below:
b
1.6b + 2
2(b) + 2(1.6b + 2) = 2b + 3.2b + 4 = 5.2b + 4
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Tips on evaluating algebraic expressions
Example Evaluate y 2 + 3x − 7 when x = 1 and y = −1.
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Tips on evaluating algebraic expressions
Example Evaluate y 2 + 3x − 7 when x = 1 and y = −1.
(−1)2 + 3(1) − 7 = 1 + 3 − 7 = −3
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Avoid confusing subtraction with negative numbers by substuting
numbers inside parantheses.
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Values for every variable must be known to evaluate an expression.
E.g., can 5y − 2x + 1 be evaluated knowing x = 3?
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Simplifying an algebraic expression and evaluating an algebraic
expression are different. How?
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Translating Phrases
Verbal expressions such as, ”twenty-eight percent of six million dollars,”
link real-life numerical problems to mathematical models.
Discuss examples of key words or phrases to describe algebraic expressions.
Start with a list of three key words or phrases for each of:
Addition
Subtraction
Multiplication (the example above works)
Division
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Translating Phrases
Examples Translate the verbal descriptions to their algebraic expressions.
a. The sum of x and 2, all times 4.
b. Seven less than 3 times n.
c. The quotient of y and 9.
d. x times the sum of y and 1.
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Translating Phrases
Examples Translate the verbal descriptions to their algebraic expressions.
a. The sum of x and 2, all times 4.
b. Seven less than 3 times n.
c. The quotient of y and 9.
d. x times the sum of y and 1.
a. (x + 2)(4).
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b. 3n − 7.
c.
y
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M 1010 §1.4 - 1.5
d. x(y + 1).
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Constructing Mathematical Models
Tip: Rely on past experiences and the physical nature of problems to
identify which operation is hidden in the problem statement.
1. Construct a verbal model that represents the problem situation.
2. Assign labels to all quantities in the verbal model.
3. Construct a mathematical mdoel (algebraic expressions).
Use unit analysis to check if units of measurement are correct. For step
one, treat each number as an unknown, and in step two replace each
unknown with either a variable or a specific value.
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Assignment
Assignment:
For Monday:
1. Read sections 2.1 and 2.2.
2. Exercises from §1.4 - 1.5 due Monday, September 9
Vocabulary: terms (and like terms), coefficients, algebraic expression,
evaulate, key words for verbal phrases (p 41), mathematical model
Understand: Identify terms in an expression, and identify coefficients of
terms. Combine like terms. Substitute a number in all places for an
unknown in an algebraic expression (evaluate). Convert key phrases into
mathematical expressions, and vice versa.
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