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Questions and Answers
Which phrase represents the algebraic expression $\frac{1}{4}d + 7$?
Which phrase represents the algebraic expression $\frac{1}{4}d + 7$?
- One-fourth of a number plus seven (correct)
- Four times a number plus seven
- Seven divided by a quarter of a number
- Seven minus one-fourth of a number
Which phrase represents the algebraic expression $\frac{3p + 6}{7p - 9}$?
Which phrase represents the algebraic expression $\frac{3p + 6}{7p - 9}$?
- Seven times a number minus nine, divided by three times a number plus six (correct)
- The product of three times a number and six divided by seven times a number minus nine
- Three times a number plus six, all multiplied by seven times a number minus nine
- The sum of three times a number and six, divided by seven times a number minus nine
Which algebraic expression represents the phrase 'two times the quantity of a number minus 12'?
Which algebraic expression represents the phrase 'two times the quantity of a number minus 12'?
- 2n + 12
- n - 12 + 2
- 2n - 12
- 2(n - 12) (correct)
Which property of real numbers is shown? $-6 + 6 = 0$
Which property of real numbers is shown? $-6 + 6 = 0$
Which of the following sets is closed under division?
Which of the following sets is closed under division?
Given $4c + 5 = 0$ and C is a real number, what is the multiplicative inverse?
Given $4c + 5 = 0$ and C is a real number, what is the multiplicative inverse?
Which number is an irrational number?
Which number is an irrational number?
Which represents four times a number?
Which represents four times a number?
Which represents the solution set of $5(x + 5)$?
Which represents the solution set of $5(x + 5)$?
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Study Notes
Real Numbers and Inequalities
- The expression -6(4x + 5) = -24x - 30 exemplifies the Distributive Property of real numbers.
- The algebraic expression 1/4 d + 7 can be represented with the phrase: "one fourth of d added to seven."
- The algebraic expression for 3p + (6/7)p - 9 can be expressed as: "three times p plus six-sevenths of p minus nine."
- The phrase "two times the quantity of a number minus 12" translates to the algebraic expression: "2(n - 12)."
- The equation -6 + 6 = 0 demonstrates the Additive Inverse Property of real numbers.
- The set of Non-Zero Rational Numbers is closed under division, indicating that dividing two non-zero rational numbers yields another non-zero rational number.
- For the equation 4c + 5 = 0, the multiplicative inverse of c can be expressed as: "the reciprocal of c."
- An example of an irrational number is -√3, which cannot be expressed as a fraction of integers.
- The phrase representing "four times a number" can be formulated as: "4n," where n is the number.
- The solution set for the expression 5(x + 5) can be framed as: "the values of x that satisfy the equation."
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