Questions and Answers
Write an algebraic expression that models the word phrase 'four more than a number b.'
4 + b
Write an algebraic expression that models the word phrase 'the product of 8 and the sum of a number x and 3.'
8(x + 3)
Write an algebraic expression that models the situation 'the piggy bank contained $25, and $1.50 is added each day.' Use d to represent the number of days.
25 + 1.5d
Write an algebraic expression that models the situation 'you had 250 minutes left on your cell phone, and you talk an hour a week.' Use w to represent the number of weeks.
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Evaluate the expression for the given values of the variables: 4a + 7b + 3a - 2b + 2a; a = -5 and b = 3.
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Evaluate the expression for the given values of the variables: 4(2m - n) - 3(2m - n); m = -15 and n = -18.
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The expression 16t^2 models the distance, in feet, that an object falls during the first t seconds after being dropped. Find the distance the object falls in 2 seconds.
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In the expression 4(2m - n), determine which of the following best describes the role of 2.
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In the expression 4(2m - n), determine which of the following best describes the role of (2m - n).
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In the expression 4(2m - n), determine which of the following best describes the role of 2m.
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In the expression 4b + 32xz, determine which of the following best describes the role of 32xz. Choose any of the following which apply.
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In the expression 4b + 32xz, determine which of the following best describes the role of 4. Choose any of the following which apply.
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Study Notes
Algebraic Expressions Study Notes
- Algebraic expressions represent mathematical phrases combining numbers and variables.
- "Four more than a number b" converts to the expression 4 + b.
- "The product of 8 and the sum of a number x and 3" translates to 8(x + 3).
- Savings situation of "$25 with an addition of $1.50 daily" is modeled as 25 + 1.5d, with d as days.
- A cell phone usage scenario of "250 minutes left and 60 minutes used weekly" is expressed as 250 - 60w, where w represents weeks.
Evaluating Expressions
- The expression 4a + 7b + 3a - 2b + 2a simplifies to -30 for values a = -5 and b = 3.
- For the expression 4(2m - n) - 3(2m - n), substituting m = -15 and n = -18 yields -12.
Application of Expressions
- The expression 16t² indicates the distance an object falls in feet after t seconds; after 2 seconds, it falls 64 feet.
- In the expression 4(2m - n), 2 functions as a coefficient, illustrating its role in multiplication.
- The subexpression (2m - n) is categorized as a factor since it is multiplied by 4.
- Within 4(2m - n), 2m is designated as a term, representing a component of the overall expression.
Further Breakdown of Terms
- In 4b + 32xz, 32xz is identified as both a product and a term, indicating multiple variables multiplied together.
- The number 4 in the expression is regarded as both a factor and a coefficient, impacting the value of b.
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Description
This quiz focuses on algebraic expressions, testing your ability to translate word phrases into mathematical expressions. You'll encounter phrases involving addition, multiplication, and real-world scenarios that require you to formulate equations. Prepare to strengthen your skills in algebraic modeling!
