Question 1

Simplify.
-$6(-21)+2(-9)$
A) 144
B) -144
C) 1242
D) 38

Accepted Answer

The expression simplifies as follows: $6(-21) + 2(-9) = -126 - 18 = -144$.

Question 2

Simplify.
-$(-19-8)(-19-18)$
A) -999
B) 11
C) -11
D) 999

Accepted Answer

The expression simplifies to $27 \times 37 = 999$.

Question 3

Simplify.
-$3+4^{2}(13)-(-24)$
A) 44
B) 67
C) 235
D) 271

Accepted Answer

The answer of Simplify.
-$3+4^{2}(13)-(-24)$
A) 44
B) 67
C) 235
D) 271...

Question 4

Simplify.
-$(-7-8)[6+(6+3)]$
A) -225
B) 30
C) 26
D) -99

Accepted Answer

First, simplify inside the brackets: $6 + 3 = 9$. Then, the expression becomes $(-7-8)[6+9]$. Simplify $-7-8$ to get $-15$. Now, multiply $-15$ by $15$ (since $6+9=15$): $-15 \times 15 = -225$.

Question 5

Simplify.
-$\frac{8 \cdot(6+2)+8 \cdot 3}{8 \cdot(3-1)}$
A) $5 \frac{1}{2}$
B) $3 \frac{19}{23}$
C) 2
D) $7 \frac{13}{23}$

Accepted Answer

First, simplify the expression inside the parentheses and then apply the distributive property: $\frac{8 \cdot 8 + 8 \cdot 3}{8 \cdot 2} = \frac{64 + 24}{16} = \frac{88}{16} = 5 \frac{1}{2}$.

Question 6

Simplify.
--| - 20| - | - 21 - $11 \mid$
A) 12
B) -52
C) -12
D) 52

Accepted Answer

The answer of Simplify.
--| - 20| - | - 21...

Question 7

Simplify.
-$\frac{12-4^{2}}{2^{2}+4^{2}}$
A) $-\frac{1}{5}$
B) $-\frac{2}{3}$
C) $\frac{16}{5}$
D) $\frac{4}{3}$

Accepted Answer

The expression simplifies as follows: $\frac{12-4^{2}}{2^{2}+4^{2}} = \frac{12-16}{4+16} = \frac{-4}{20} = -\frac{1}{5}$.

Question 8

Simplify.
-$\frac{125-4 \cdot 5}{2^{3} \div 2^{2}-(-2)^{2}}$
A) $-\frac{105}{2}$
B) 3
C) -1
D) $\frac{35}{2}$

Accepted Answer

The expression simplifies as follows: $\frac{125-4 \cdot 5}{2^{3} \div 2^{2}-(-2)^{2}} = \frac{125-20}{8 \div 4 - 4} = \frac{105}{2 \div 4 - 4} = \frac{105}{0.5 - 4} = \frac{105}{-3.5} = -\frac{105}{2}$.

Question 9

Provide an appropriate response.
-Choose the expression that is equivalent to the following: $0+5 b$
A) 0
B) $5+b$
C) $5 \mathrm{~b}$
D) $-5 b$

Accepted Answer

The expression $0+5b$ simplifies to $5b$ because adding 0 to any term does not change its value.

Question 10

Provide an appropriate response.
-Choose the expression that is equivalent to the following: $3(4 a)+3(7 b)$
A) $6(4 a+7 b)$
B) $3(4 a+7 b)$
C) $3(11 \mathrm{ab})$
D) $6(11 \mathrm{ab})$

Accepted Answer

Distributing the 3 into both terms inside the parentheses gives $3(4a) + 3(7b) = 3(4a + 7b)$, which matches choice B.

Question 11

Provide an appropriate response.
-Choose the expression that is equivalent to the following: $15 x+5 y$
A) $5(3 x+y)$
B) $5(10 x+y)$
C) $20 x y$
D) $5(3 x+5 y)$

Accepted Answer

Factoring out the common factor of 5 from both terms in the expression $15x + 5y$ gives $5(3x + y)$.

Question 12

Provide an appropriate response.
-Choose the expression that is equivalent to the following: $(5 x+3 y)(4 y+8 x)$
A) $13 x+7 y$
B) $(5 x+3 y)(8 y+4 x)$
C) $(5 x+3 y)(8 x+4 y)$
D) $(5 x+8 x)(3 y+4 y)$

Accepted Answer

The correct expression is obtained by distributing each term in the first parenthesis with each term in the second parenthesis, which results in $20x^2 + 40xy + 12xy + 24y^2$, simplifying to $20x^2 + 52xy + 24y^2$, which is not directly listed as an option. However, option C, when simplified, matches the structure of the original expression, indicating a typographical error in the question or answer choices.

Question 13

Provide an appropriate response.
-Choose the expression that is equivalent to the following: $(8 x+5 y)\left(2 y^{3}\right)$
A) $(8 x)+(5 y)\left(2 y^{3}\right)$
B) $\left(8 x+2 y^{3}\right)(5 y)$
C) $\left(2 y^{3}\right)(8 x+5 y)$
D) $8 x+\left(5 y+2 y^{3}\right)$

Accepted Answer

The expression $(8 x+5 y)\left(2 y^{3}\right)$ is equivalent to multiplying the entire expression $(8 x+5 y)$ by $2 y^{3}$, which is exactly what option C represents, showing the commutative property of multiplication.

Question 14

Write the word or phrase that best completes each statement or answers the question.
-Is this statement true or false? Why?
$(9-9)-9=9-(9-9)$

Accepted Answer

The left side simplifies to $-9$ while the right side simplifies to $9$, so they are not equal.

Question 15

Choose the one alternative that best completes the statement or answers the question.
-According to the rules for the order of operations, what should be the first step when simplifying the expression $[-6+(-11+3)]+(-3+8)$ ?
A) find the sum of 3 and -3
B) find the sum of -6 and -3
C) find the sum of -11 and 3
D) find the sum of -6 and -11

Accepted Answer

According to the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), the first step is to simplify expressions inside parentheses. In the given expression, the first operation to perform is finding the sum of -11 and 3, which are inside the innermost parentheses.

Question 16

Choose the one alternative that best completes the statement or answers the question.
-Choose the expression that is equivalent to the following: $1\left(6 y^{3}\right)$
A) 1
B) $6 y^{4}$
C) $7 y^{3}$
D) $6 y^{3}$

Accepted Answer

The expression $1(6y^3)$ simplifies directly to $6y^3$ because multiplying by 1 does not change the value of the expression.

Quiz 1: Introduction to Real Numbers and Algebraic Expressions

Simplify. - $6(-21) +2(-9)$

Simplify. - $(-19-8) (-19-18)$

Simplify. - $3+4^{2}(13) -(-24)$

Simplify. - $(-7-8) [6+(6+3) ]$

Simplify. - $\frac{8 \cdot(6+2) +8 \cdot 3}{8 \cdot(3-1) }$

Simplify. --| - 20| - | - 21 - $11 \mid$

Simplify. - $\frac{12-4^{2}}{2^{2}+4^{2}}$

Simplify. - $\frac{125-4 \cdot 5}{2^{3} \div 2^{2}-(-2) ^{2}}$

Provide an appropriate response. -Choose the expression that is equivalent to the following: $0+5 b$

Provide an appropriate response. -Choose the expression that is equivalent to the following: $3(4 a) +3(7 b)$

Provide an appropriate response. -Choose the expression that is equivalent to the following: $15 x+5 y$

Provide an appropriate response. -Choose the expression that is equivalent to the following: $(5 x+3 y) (4 y+8 x)$

Provide an appropriate response. -Choose the expression that is equivalent to the following: $(8 x+5 y) \left(2 y^{3}\right)$

Write the word or phrase that best completes each statement or answers the question. -Is this statement true or false? Why? $(9-9)-9=9-(9-9)$

Choose the one alternative that best completes the statement or answers the question. -According to the rules for the order of operations, what should be the first step when simplifying the expression $[-6+(-11+3) ]+(-3+8)$ ?

Choose the one alternative that best completes the statement or answers the question. -Choose the expression that is equivalent to the following: $1\left(6 y^{3}\right)$

Quiz 1: Introduction to Real Numbers and Algebraic Expressions

Simplify. - 6(−21) +2(−9) 6(-21) +2(-9) 6(−21) +2(−9)

Simplify. - (−19−8) (−19−18) (-19-8) (-19-18) (−19−8) (−19−18)

Simplify. - 3+42(13) −(−24) 3+4^{2}(13) -(-24) 3+42(13) −(−24)

Simplify. - (−7−8) [6+(6+3) ](-7-8) [6+(6+3) ](−7−8) [6+(6+3) ]

Simplify. - 8⋅(6+2) +8⋅38⋅(3−1) \frac{8 \cdot(6+2) +8 \cdot 3}{8 \cdot(3-1) }8⋅(3−1) 8⋅(6+2) +8⋅3​

Simplify. --| - 20| - | - 21 - 11∣11 \mid11∣

Simplify. - 12−4222+42\frac{12-4^{2}}{2^{2}+4^{2}}22+4212−42​

Simplify. - 125−4⋅523÷22−(−2) 2\frac{125-4 \cdot 5}{2^{3} \div 2^{2}-(-2) ^{2}}23÷22−(−2) 2125−4⋅5​

Provide an appropriate response. -Choose the expression that is equivalent to the following: 0+5b0+5 b0+5b

Provide an appropriate response. -Choose the expression that is equivalent to the following: 3(4a) +3(7b) 3(4 a) +3(7 b) 3(4a) +3(7b)

Provide an appropriate response. -Choose the expression that is equivalent to the following: 15x+5y15 x+5 y15x+5y

Provide an appropriate response. -Choose the expression that is equivalent to the following: (5x+3y) (4y+8x) (5 x+3 y) (4 y+8 x) (5x+3y) (4y+8x)

Provide an appropriate response. -Choose the expression that is equivalent to the following: (8x+5y) (2y3) (8 x+5 y) \left(2 y^{3}\right) (8x+5y) (2y3)

Write the word or phrase that best completes each statement or answers the question. -Is this statement true or false? Why? (9−9)−9=9−(9−9)(9-9)-9=9-(9-9)(9−9)−9=9−(9−9)

Choose the one alternative that best completes the statement or answers the question. -According to the rules for the order of operations, what should be the first step when simplifying the expression [−6+(−11+3) ]+(−3+8) [-6+(-11+3) ]+(-3+8) [−6+(−11+3) ]+(−3+8) ?

Choose the one alternative that best completes the statement or answers the question. -Choose the expression that is equivalent to the following: 1(6y3) 1\left(6 y^{3}\right) 1(6y3)