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Introduction Algebraic 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 1

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Key Concepts If 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 2

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Key Concepts, continued Similarly, 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 3

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Common Errors/Misconceptions incorrectly translating given verbal expressions 1.1.2: Interpreting Complicated Expressions 4

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Guided Practice Example 2 To 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 5

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Guided Practice: Example 2, continued 1.Refer to the expression given: 2s + 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 6

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Guided Practice: Example 2, continued 2.If 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 2s will also decrease. 1.1.2: Interpreting Complicated Expressions 7

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Guided Practice: Example 2, continued 3.If 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 8 ✔

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Guided Practice: Example 2, continued 1.1.2: Interpreting Complicated Expressions 9

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Guided Practice Example 3 Money 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 10

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Guided Practice: Example 3, continued 1.Refer 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 11

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Guided Practice: Example 3, continued 2.Changing 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 12

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Guided Practice: Example 3, continued 3.Similarly, 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 13

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Guided Practice: Example 3, continued 4.Changing 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 14 ✔

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Guided Practice: Example 3, continued 1.1.2: Interpreting Complicated Expressions 15

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The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

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