to understand how each term of an expression works and how changing the value of variables impacts the resulting quantity 112 Interpreting Complicated Expressions 1 Key Concepts If a situation is described verbally it is often necessary to ID: 717255
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IntroductionAlgebraic expressions, used to describe various situations, contain variables. It is important to understand how each term of an expression works and how changing the value of variables impacts the resulting quantity.
1.1.2: Interpreting Complicated Expressions
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Key ConceptsIf a situation is described verbally, it is often necessary to first translate each expression into an algebraic expression. This will allow you to see mathematically how each term
interacts with the other terms.
As
variables change, it is important to understand that constants will always remain the same. The change in the variable will not change the value of a given constant.
1.1.2: Interpreting Complicated Expressions
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Key Concepts, continuedSimilarly, changing the value of a constant will not change terms containing variables.
It is also important to follow the order of operations, as this will help guide your awareness and
understanding of each term.
1.1.2: Interpreting Complicated Expressions
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Common Errors/Misconceptionsincorrectly translating given verbal expressions
1.1.2: Interpreting Complicated Expressions
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Guided PracticeExample 2To calculate the perimeter of an isosceles triangle, the expression 2s + b is used, where s represents the length of the two congruent sides and
b represents the length of the base. What effect, if any, does increasing the length of the congruent sides have on the expression?
1.1.2: Interpreting Complicated Expressions
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Guided Practice: Example 2, continued
Refer
to the expression given: 2
s + b
.Changing only the length of the congruent sides,
s
, will not impact the length of base
b
since
b
is a separate term.
1.1.2: Interpreting Complicated Expressions
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Guided Practice: Example 2, continuedIf
the value of the congruent sides, s,
is
increased, the product of 2s will
also increase. Likewise, if the value of
s
is decreased, the value
of 2
s
will
also decrease.
1.1.2: Interpreting Complicated Expressions
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Guided Practice: Example 2, continuedIf the value of
s is changed, the result of the change in the terms is a doubling of the change in s
while the value of
b remains the same.
1.1.2: Interpreting Complicated Expressions
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Guided Practice: Example 2, continued
1.1.2: Interpreting Complicated Expressions
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Guided PracticeExample 3Money deposited in a bank account earns interest on the initial amount deposited as well as any interest earned as time passes. This compound interest can be described by the expression P(1 + r)n
, where P represents the initial amount deposited, r represents the interest rate, and n represents the number of months that pass. How does a change in each variable affect the value of the expression?
1.1.2: Interpreting Complicated Expressions
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Guided Practice: Example 3, continuedRefer
to the given expression: P(1 + r
)
n.
Notice the expression is made up of one term containing the factors
P
and (1 +
r
)
n
.
1.1.2: Interpreting Complicated Expressions
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Guided Practice: Example 3, continuedChanging
the value of P does not change the value of the
factor (
1 + r)n
, but it will change the value of the expression by a factor of P.
In
other words, the change in
P
will multiply by the result of (1 +
r
)
n
.
1.1.2: Interpreting Complicated Expressions
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Guided Practice: Example 3, continuedSimilarly, changing
r changes the base of the exponent, but
does not change the value of
P. (
The base
is the number that will be multiplied by itself.) This change
in
r
will affect the value of the overall expression.
1.1.2: Interpreting Complicated Expressions
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Guided Practice: Example 3, continuedChanging
n changes the number of times (1 +
r
) will be multiplied by itself
, but does not change the value of P.
This change will affect the value of the overall expression.
1.1.2: Interpreting Complicated Expressions
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✔Slide15
Guided Practice: Example 3, continued
1.1.2: Interpreting Complicated Expressions
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