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Questions and Answers
Which algebraic expression represents 'eight less than the product of three and a number'?
Which algebraic expression represents 'eight less than the product of three and a number'?
- 3(x - 8)
- 8 - 3x
- 8 < 3x
- 3x - 8 (correct)
Translate the following sentence into an algebraic equation: 'The quotient of a number and four is equal to the sum of the number and one.'
Translate the following sentence into an algebraic equation: 'The quotient of a number and four is equal to the sum of the number and one.'
- $x/4 = x - 1$
- $4/x = x + 1$
- $4/x = x - 1$
- $x/4 = x + 1$ (correct)
If 'n' represents an integer, how would you represent the sum of three consecutive integers?
If 'n' represents an integer, how would you represent the sum of three consecutive integers?
- $n + (n + 1)$
- $3n + 3$
- $n + (n + 1) + (n + 2)$ (correct)
- $n + (n + 1) + (n + 3)$
Evaluate the expression $5x - 3y + 2$ when $x = 4$ and $y = -2$.
Evaluate the expression $5x - 3y + 2$ when $x = 4$ and $y = -2$.
Simplify and evaluate the expression $2(a + b) - c$, given $a = 5$, $b = -1$, and $c = 3$.
Simplify and evaluate the expression $2(a + b) - c$, given $a = 5$, $b = -1$, and $c = 3$.
What is the value of the expression $\frac{x + y}{z}$, if $x = 10$, $y = 6$, and $z = 2$?
What is the value of the expression $\frac{x + y}{z}$, if $x = 10$, $y = 6$, and $z = 2$?
Evaluate the expression $|3x - 7|$ when $x = 2$.
Evaluate the expression $|3x - 7|$ when $x = 2$.
Simplify and then evaluate: $4a + 2b - a + 3b$ when $a = 3$ and $b = 1$.
Simplify and then evaluate: $4a + 2b - a + 3b$ when $a = 3$ and $b = 1$.
What is the result of evaluating $5[3(n - 1) + 2m]$ when $n = 4$ and $m = -2$?
What is the result of evaluating $5[3(n - 1) + 2m]$ when $n = 4$ and $m = -2$?
Evaluate $-x^2 + 4x$ if $x = 5$.
Evaluate $-x^2 + 4x$ if $x = 5$.
Which expression correctly translates 'five less than twice a number is fifteen'?
Which expression correctly translates 'five less than twice a number is fifteen'?
If 'k' represents a number, how do you express 'the sum of a number and its square'?
If 'k' represents a number, how do you express 'the sum of a number and its square'?
Evaluate $a^2 - 3ab + b^2$ when $a = -2$ and $b = 3$.
Evaluate $a^2 - 3ab + b^2$ when $a = -2$ and $b = 3$.
What is the simplified value of $2[4(x + y) - 2x]$ when $x = 1$ and $y = -1$?
What is the simplified value of $2[4(x + y) - 2x]$ when $x = 1$ and $y = -1$?
If $y = -2$, what is the value of $\frac{3y + 6}{y - 1}$?
If $y = -2$, what is the value of $\frac{3y + 6}{y - 1}$?
Which of the following represents 'seven less than half of a number'?
Which of the following represents 'seven less than half of a number'?
Given the expression $x^3 - 2x^2 + x - 5$, evaluate when $x = -1$.
Given the expression $x^3 - 2x^2 + x - 5$, evaluate when $x = -1$.
The total cost $C$ of an item after a discount of $d$ percent is given by $C = P(1 - \frac{d}{100})$, where $P$ is the original price. What is the cost if the original price is $200 and the discount is 25%?
The total cost $C$ of an item after a discount of $d$ percent is given by $C = P(1 - \frac{d}{100})$, where $P$ is the original price. What is the cost if the original price is $200 and the discount is 25%?
What is the value of $\frac{|-4x + 8|}{2}$ when $x = -1$?
What is the value of $\frac{|-4x + 8|}{2}$ when $x = -1$?
Flashcards
Translating Algebraic Expressions
Translating Algebraic Expressions
Converting verbal phrases or sentences into algebraic expressions or equations.
Variable
Variable
A value that represents an unknown quantity.
Sum
Sum
The sum of numbers or expressions.
Difference
Difference
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Product
Product
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Quotient
Quotient
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Consecutive Integers
Consecutive Integers
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Evaluating Algebraic Expressions
Evaluating Algebraic Expressions
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Order of Operations
Order of Operations
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Absolute Value
Absolute Value
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Like Terms
Like Terms
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Nested Parentheses/Brackets
Nested Parentheses/Brackets
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Integer Operations
Integer Operations
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Study Notes
- Algebraic expressions involve variables, constants, and mathematical operations
- They represent mathematical relationships and can be translated from verbal phrases and evaluated for specific values of variables.
Translating Algebraic Expressions
- Translation involves converting verbal phrases or sentences into algebraic expressions or equations.
- Identify key words and phrases that indicate mathematical operations.
- Addition: "sum," "plus," "increased by," "more than," "total"
- Subtraction: "difference," "minus," "decreased by," "less than," "fewer than"
- Multiplication: "product," "times," "multiplied by," "of," "twice," "double," "triple"
- Division: "quotient," "divided by," "ratio," "per"
- Choose variables to represent unknown quantities.
- Example: Let 'x' represent an unknown number.
- Write the algebraic expression using the chosen variables and the appropriate mathematical symbols.
- "A number increased by five" translates to x + 5
- "The product of two and a number" translates to 2x
- "Three less than a number" translates to x - 3
- Common phrases and their translations:
- "The sum of a number and 7": x + 7
- "The difference between a number and 4": x - 4
- "The product of 6 and a number": 6x
- "A number divided by 3": x / 3
- "Twice a number": 2x
- "Five more than twice a number": 2x + 5
- "Seven less than three times a number": 3x - 7
- Translating sentences into equations involves recognizing equality.
- Use the equals sign (=) to show the relationship between expressions.
- "The sum of a number and 3 is 10" translates to x + 3 = 10
- "Twice a number equals 14" translates to 2x = 14
- Consecutive integers can be represented algebraically.
- If 'n' is an integer, the next consecutive integer is 'n + 1', and the one after that is 'n + 2', and so on.
- "The sum of two consecutive integers is 25" translates to n + (n + 1) = 25
- Pay attention to order when translating subtraction and division
- "Less than" and "fewer than" indicate that the order is reversed
- "The quotient of a number and 5" translates to x / 5
- "The quotient of 5 and a number" translates to 5 / x
Evaluating Algebraic Expressions
- Evaluation involves substituting given values for variables and simplifying the expression.
- Given an expression like 3x + 5, and a value x = 2, substitute 2 for x.
- 3(2) + 5 is the result of the substitution
- Use the order of operations (PEMDAS/BODMAS) to simplify the expression.
- Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
- 3(2) + 5 simplifies to 6 + 5 = 11
- Consider the expression 2(x + y) - z, where x = 3, y = 4, and z = 1.
- Substitute the values: 2(3 + 4) - 1
- Simplify inside the parentheses: 2(7) - 1
- Perform multiplication: 14 - 1
- Perform subtraction: 13
- When evaluating expressions with exponents, remember to apply the exponent before other operations.
- Evaluate x^2 + 3x - 2, where x = 4.
- Substitute the value: 4^2 + 3(4) - 2
- Evaluate the exponent: 16 + 3(4) - 2
- Perform multiplication: 16 + 12 - 2
- Perform addition and subtraction from left to right: 28 - 2 = 26
- Evaluate x^2 + 3x - 2, where x = 4.
- If the expression contains fractions, simplify the numerator and denominator separately before dividing.
- Evaluate (x + 5) / (y - 2), where x = 7 and y = 6.
- Substitute the values: (7 + 5) / (6 - 2)
- Simplify the numerator: 12 / (6 - 2)
- Simplify the denominator: 12 / 4
- Perform division: 3
- Evaluate (x + 5) / (y - 2), where x = 7 and y = 6.
- Absolute value symbols indicate the distance from zero, so the value inside the absolute value is always non-negative.
- Evaluate |2x - 5|, where x = 1.
- Substitute the value: |2(1) - 5|
- Simplify inside the absolute value: |2 - 5|
- Simplify further: |-3|
- Take the absolute value: 3
- Evaluate |2x - 5|, where x = 1.
- Combine like terms before substituting values if possible, to simplify the expression.
- 2x + 3x + 4y - y can be simplified to 5x + 3y
- For expressions with multiple operations and nested parentheses/brackets, work from the innermost parentheses outwards.
- Evaluate 3[2(x + 1) - y], where x = 2 and y = 4.
- Substitute the values: 3[2(2 + 1) - 4]
- Simplify inside the inner parentheses: 3[2(3) - 4]
- Perform multiplication inside the brackets: 3[6 - 4]
- Perform subtraction inside the brackets: 3[2]
- Perform multiplication: 6
- Evaluate 3[2(x + 1) - y], where x = 2 and y = 4.
- When evaluating expressions with negative numbers, pay attention to the signs and follow the rules for integer operations.
- Evaluate x - 2y, where x = -3 and y = -1.
- Substitute the values: -3 - 2(-1)
- Perform multiplication: -3 - (-2)
- Simplify the subtraction: -3 + 2 = -1
- Evaluate x - 2y, where x = -3 and y = -1.
- Be careful when dealing with exponents and negative signs.
- Evaluate -x^2, where x = 3.
- Substitute the value: -(3)^2
- Evaluate the exponent: -(9)
- Apply the negative sign: -9
- Evaluate (-x)^2, where x = 3.
- Substitute the value: (-3)^2
- Evaluate the exponent: 9
- Evaluate -x^2, where x = 3.
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