Questions and Answers
Write a verbal expression for the algebraic expression c + 2d.
c plus the product of 2 and d.
What is the verbal expression for 4 - 5h?
Difference of 4 and 5 times h.
What is the verbal expression for 2b?
Product of 2 and the square of b.
Write a verbal expression for 7x - 1.
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What is the algebraic expression for 6 more than twice m?
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Write an algebraic expression for 8 increased by three times a number.
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What is the expression for the difference of 17 and 5 times a number?
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What is the value of the expression 4(3 + 5) - 5 * 4?
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Evaluate 22/11 * 9 - 3.
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What is the result of 6 + 3 * 7 - 9?
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Evaluate 3[10 - (27/9)].
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What is the evaluation of 2[5{2} + (36/6)]?
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What is 162 / [6(7 - 4){2}]?
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If a = 12, b = 9, c = 4, what is the value of 2c(a + b)?
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What is the result of (a/4b) + c when a = 12, b = 9, c = 4?
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Define a variable and write an expression to represent the total cost of renting a car for Frank.
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How much will it cost Frank to rent the car for 300 miles?
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Identify the property used in the equation: 5 + x = x + 5.
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Identify the property used in the equation: (2 * 3) * 6 = 2 * (3 * 6).
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Identify the property in the equation: 2 + 0 = 2.
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Identify the property: 2 * (1/2) = 1.
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Identify the properties used in the steps of the equation: 4 + 3[49 - (3 + 4) * 2] to 4 + 0.
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Study Notes
Algebraic Expressions and Verbal Expressions
- Algebraic expressions can be converted into verbal expressions, emphasizing the operations involved.
- Examples include:
- c + 2d translates to "c plus the product of 2 and d".
- 4 - 5h means "the difference of 4 and 5 times h".
- 2b represents "the product of 2 and the square of b".
- 7x - 1 stands for "7 multiplied by x to the power of 3 minus 1".
Creating Algebraic Expressions from Verbal Statements
- Understanding how to formulate algebraic expressions from verbal cues is essential.
- For instance:
- “6 more than twice m” can be expressed as 6 + 2m.
- “8 increased by three times a number” translates to 8 + 3x.
- “The difference of 17 and 5 times a number” is written as 17 - 5x.
Evaluating Expressions
- Different expressions can be evaluated to find numerical answers:
- 4(3 + 5) - 5 * 4 evaluates to 12.
- 22/11 * 9 - 3 gives 9 upon solving.
- 6 + 3 * 7 - 9 results in 48.
- More complex evaluations like 3[10 - (27/9)] equal 21.
Substituting Variables to Evaluate Expressions
- Expressions can be evaluated using defined variables:
- For 2c(a + b), when a = 12, b = 9, c = 4, the result is 168.
- Evaluating (a/4b) + c results in 8 using the same variable values.
Cost Function for Car Rental
- Frank's car rental costs can be expressed mathematically:
- Total cost is represented as 100 + 3x, where x is the number of miles driven.
- For a distance of 300 miles, the total cost computes to $1000.
Identifying Mathematical Properties
- Various properties are utilized in equations:
- Commutative Property of Addition: 5 + x = x + 5.
- Associative Property of Multiplication: (2 * 3) * 6 = 2 * (3 * 6).
- Identity Property of Addition: 2 + 0 = 2 shows the identity element.
- Inverse Property of Multiplication: 2 * (1/2) = 1 demonstrates the inverse relationship.
Steps in Property Identification
- Each step in an equation can represent a specific property:
- Use of substitution in transformations.
- Application of the Inverse Property of Addition.
- Multiplication property of zero contributes to simplification.
Summary Points
- Understanding both verbal and algebraic expressions is crucial in algebra.
- Evaluating expressions demands knowledge of arithmetic operations and properties.
- Identifying properties promotes proficiency in algebraic manipulation and problem-solving skills.
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Description
This quiz guide covers key concepts from Chapter 1 of Advanced Algebra, focusing on verbal expressions for algebraic equations. Students will enhance their understanding of translating algebraic terms into verbal phrases through practical examples. Ideal for preparing for exams and reinforcing foundational algebra skills.
