Question 1

State whether the inequality is true or false. $- \frac { 1 } { 10 } > - \frac { 1 } { 100 }$

Accepted Answer

When comparing negative fractions, the one with the smaller absolute value is greater, so $-\frac{1}{10}$ is actually less than $-\frac{1}{100}$.

Question 2

Perform the indicated operation. $\frac { 1 } { 4 } + \frac { 1 } { 12 }$
A) $\frac { 1 } { 16 }$
B) $\frac { 1 } { 48 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 3 }$
E) $3$

Accepted Answer

To add two fractions, we need a common denominator. The lowest common multiple of 4 and 12 is 12. Therefore, we can rewrite the given fractions as $\frac{3}{12}+\frac{1}{12}=\frac{4}{12}=\frac{1}{3}$. Option D is the only answer choice that matches.

Question 3

Write the following statement in terms of inequalities. $Z$ is greater than or equal to $- 1$ .
A) $z \leq - 1$
B) $z \geq - 1$
C) $z < - 1$
D) $z > - 1$
E) $z = 0$

Accepted Answer

The statement "Z is greater than or equal to -1" can be written as "Z is at least -1" which can be represented as the inequality "Z ≥ -1", making option B the correct choice. Option A is incorrect because it is the opposite inequality. Option C and D are incorrect because they use only "less than" or "greater than" symbols respectively, without including the equal sign. Option E is incorrect because it is a specific value and not an inequality.

Question 4

Perform the indicated operation. $\frac { 1 } { 6 } \div \frac { 2 } { 3 }$
A) $- \frac { 1 } { 2 }$
B) $\frac { 2 } { 18 }$
C) $\frac { 1 } { 18 }$
D) $\frac { 1 } { 3 }$
E) $\frac { 1 } { 4 }$

Accepted Answer

The answer of Perform the indicated operation. \(\frac { 1...

Question 5

Perform the indicated operations. $\frac { \frac { 2 } { 5 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }$

Accepted Answer

The answer of Perform the indicated operations. \(\frac { \frac...

Question 6

State whether the inequality is true or false. $\frac { 22 } { 7 } > \pi$

Accepted Answer

The fraction 22/7 is an approximation of pi, and is slightly greater than pi. Therefore, the inequality is true.

Question 7

Write the following statement in terms of inequalities. $x$ is negative.
A) $x > 0$
B) $x < 0$
C) $x \geq 0$
D) $x \leq 0$
E) $x = 0$

Accepted Answer

If $x$ is negative, it cannot be greater than or equal to 0 (choices A and C), nor can it be equal to 0 (choice E). The only option that fits is that $x$ is less than 0, which is choice B.

Question 8

Use properties of real numbers to write $- r ( s - 2 )$ without parentheses.
A) $- 2 r + 2 s$
B) $- r S + 2$
C) $rs + 2 r$
D) $- r s + 2 r$
E) $- rs- 2 r$

Accepted Answer

We can use the distributive property to write the expression as:
$-r(s-2) = -r \cdot s + r \cdot 2$
Then, using the commutative property, we can write:
$-r \cdot s + r \cdot 2 = 2r - rs$
Therefore, the correct choice is D.

Question 9

Perform the indicated operations. $\frac { \frac { 1 } { 10 } } { \frac { 1 } { 3 } - \frac { 1 } { 5 } }$

Accepted Answer

The answer of Perform the indicated operations. \(\frac { \frac...

Question 10

Use the properties of real numbers to write the expression without parentheses. $2 x \left( a - b - 2 c + \frac { d } { 2 } \right)$
A) $x a - x b - 2 x c + x d$
B) $2 x a - 2 x b - x c + 4 x d$
C) $x a - 2 x b - 4 x c + x d$
D) $2 x a - 2 x b - 4 x c + x d$
E) $2 x a - x b - 2 x c + 2 x d$

Accepted Answer

Using the distributive property, each term inside the parentheses is multiplied by $2x$, resulting in $2xa - 2xb - 4xc + xd$.

Question 11

State the property of real numbers being used. $$x + 4 = 4 + x$$
A) Commutative Property for addition
B) Commutative Property for multiplication
C) Associative Property for addition
D) Associative Property for multiplication
E) Distributive Property

Accepted Answer

The equation is an example of the Commutative Property for addition, which states that changing the order of the addends does not change the sum. In this case, we can rearrange the equation to be written as 4 + x = x + 4, and it still holds true.

Question 12

State the property of real numbers being used. $$2 ( x + 5 y ) = 2 x + 10 y$$
A) Commutative Property for addition
B) Commutative Property for multiplication
C) Associative Property for addition
D) Associative Property for multiplication
E) Distributive Property

Accepted Answer

This equation is using the Distributive Property, which states that for any real numbers a, b, and c, a(b+c) = ab + ac. In this case, we have 2 multiplied by the sum of x and 5y, which can be rewritten as 2x + 2(5y) using the Distributive Property. Therefore, the answer is E, Distributive Property.

Question 13

Perform the indicated operations. $\frac { \frac { 2 } { 3 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }$

Accepted Answer

The answer of Perform the indicated operations. \(\frac { \frac...

Question 14

State whether the inequality is true or false. $- \sqrt { 2 } < - 1.41$

Accepted Answer

Both -√2 and -1.41 represent negative square roots of 2. However, -√2 is slightly less than -1.41 (approximately -1.414), so the inequality is true.

Question 15

Perform the indicated operations. $\frac { \frac { 1 } { 12 } } { \frac { 1 } { 8 } - \frac { 1 } { 12 } }$

Accepted Answer

The answer of Perform the indicated operations. \(\frac { \frac...

Question 16

Perform the indicated operation(s) and simplify. $\frac { 1 } { 5 } \div \left[ \frac { 1 } { 4 } \left( \frac { 1 } { 2 } + \frac { 1 } { 3 } \right) \right]$
A) $\frac { 3 } { 2 }$
B) $\frac { 25 } { 24 }$
C) $1$
D) $\frac { 2 } { 3 }$
E) $\frac { 24 } { 25 }$

Accepted Answer

First, simplify inside the brackets: $\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$. Then, multiply by $\frac{1}{4}$: $\frac{1}{4} \times \frac{5}{6} = \frac{5}{24}$. Finally, divide $\frac{1}{5}$ by $\frac{5}{24}$, which is the same as multiplying $\frac{1}{5}$ by the reciprocal of $\frac{5}{24}$, resulting in $\frac{1}{5} \times \frac{24}{5} = \frac{24}{25}$.

Question 17

Use properties of real numbers to write $12 ( z / 4 )$ without parentheses.
A) $\frac { 1 } { 4 } Z$
B) $\frac { 1 } { 12 } z$
C) $48 z$
D) $12 z$
E) $3 z$

Accepted Answer

Using the distributive property, $12 ( z / 4 )$ simplifies to $12z/4$, which further simplifies to $3z$.

Question 18

Use properties of real numbers to write $3 ( 2 a + b )$ without parentheses.
A) $6 a + 6 b$
B) $3 + 2 a b$
C) $6 a - b$
D) $6 a + 3 b$
E) $6 a - 3 b$

Accepted Answer

Distributive property states that a(b+c) = ab + ac. Therefore, applying it here, we get 3(2a+b) = 3(2a) + 3(b) = 6a + 3b, which is option D.

Question 19

State the property of real numbers being used. $$3 x y = y x 3$$
A) Commutative Property for addition
B) Commutative Property for multiplication
C) Associative Property for addition
D) Associative Property for multiplication
E) Distributive Property

Accepted Answer

The given equation shows the commutative property of multiplication, which states that the order of factors can be changed without changing the product. In this case, 3xy and yx3 are equal due to the commutative property of multiplication.

Question 20

Perform the indicated operation(s) and simplify. $\frac { 1 } { 4 } + 5 \left( \frac { 1 } { 4 } \cdot \frac { 1 } { 5 } \right) - \frac { 3 } { 4 }$
A) $- \frac { 3 } { 4 }$
B) $\frac { 3 } { 4 }$
C) $\frac { 1 } { 25 }$
D) $- \frac { 1 } { 4 }$
E) $\frac { 1 } { 4 }$

Accepted Answer

The answer of Perform the indicated operation(s) and simplify. \(\frac...

Quiz 1: Fundamentals

State whether the inequality is true or false. $- \frac { 1 } { 10 } > - \frac { 1 } { 100 }$

Perform the indicated operation. $\frac { 1 } { 4 } + \frac { 1 } { 12 }$

Write the following statement in terms of inequalities. $Z$ is greater than or equal to $- 1$ .

Perform the indicated operation. $\frac { 1 } { 6 } \div \frac { 2 } { 3 }$

Perform the indicated operations. $\frac { \frac { 2 } { 5 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }$

State whether the inequality is true or false. $\frac { 22 } { 7 } > \pi$

Write the following statement in terms of inequalities. $x$ is negative.

Use properties of real numbers to write $- r ( s - 2 )$ without parentheses.

Perform the indicated operations. $\frac { \frac { 1 } { 10 } } { \frac { 1 } { 3 } - \frac { 1 } { 5 } }$

Use the properties of real numbers to write the expression without parentheses. $2 x \left( a - b - 2 c + \frac { d } { 2 } \right)$

State the property of real numbers being used. $x + 4 = 4 + x$

State the property of real numbers being used. $2 ( x + 5 y ) = 2 x + 10 y$

Perform the indicated operations. $\frac { \frac { 2 } { 3 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }$

State whether the inequality is true or false. $- \sqrt { 2 } < - 1.41$

Perform the indicated operations. $\frac { \frac { 1 } { 12 } } { \frac { 1 } { 8 } - \frac { 1 } { 12 } }$

Perform the indicated operation(s) and simplify. $\frac { 1 } { 5 } \div \left[ \frac { 1 } { 4 } \left( \frac { 1 } { 2 } + \frac { 1 } { 3 } \right) \right]$

Use properties of real numbers to write $12 ( z / 4 )$ without parentheses.

Use properties of real numbers to write $3 ( 2 a + b )$ without parentheses.

State the property of real numbers being used. $3 x y = y x 3$

Perform the indicated operation(s) and simplify. $\frac { 1 } { 4 } + 5 \left( \frac { 1 } { 4 } \cdot \frac { 1 } { 5 } \right) - \frac { 3 } { 4 }$

Quiz 1: Fundamentals

State whether the inequality is true or false. −110>−1100- \frac { 1 } { 10 } > - \frac { 1 } { 100 }−101​>−1001​

Perform the indicated operation. 14+112\frac { 1 } { 4 } + \frac { 1 } { 12 }41​+121​

Write the following statement in terms of inequalities. ZZZ is greater than or equal to −1- 1−1 .

Perform the indicated operation. 16÷23\frac { 1 } { 6 } \div \frac { 2 } { 3 }61​÷32​

Perform the indicated operations. 25+12110+35\frac { \frac { 2 } { 5 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }101​+53​52​+21​​

State whether the inequality is true or false. 227>π\frac { 22 } { 7 } > \pi722​>π

Write the following statement in terms of inequalities. xxx is negative.

Use properties of real numbers to write −r(s−2) - r ( s - 2 ) −r(s−2) without parentheses.

Perform the indicated operations. 11013−15\frac { \frac { 1 } { 10 } } { \frac { 1 } { 3 } - \frac { 1 } { 5 } }31​−51​101​​

Use the properties of real numbers to write the expression without parentheses. 2x(a−b−2c+d2) 2 x \left( a - b - 2 c + \frac { d } { 2 } \right) 2x(a−b−2c+2d​)

State the property of real numbers being used. x+4=4+xx + 4 = 4 + xx+4=4+x

State the property of real numbers being used. 2(x+5y) =2x+10y2 ( x + 5 y ) = 2 x + 10 y2(x+5y) =2x+10y

Perform the indicated operations. 23+12110+35\frac { \frac { 2 } { 3 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }101​+53​32​+21​​

State whether the inequality is true or false. −2<−1.41- \sqrt { 2 } < - 1.41−2​<−1.41

Perform the indicated operations. 11218−112\frac { \frac { 1 } { 12 } } { \frac { 1 } { 8 } - \frac { 1 } { 12 } }81​−121​121​​

Perform the indicated operation(s) and simplify. 15÷[14(12+13) ]\frac { 1 } { 5 } \div \left[ \frac { 1 } { 4 } \left( \frac { 1 } { 2 } + \frac { 1 } { 3 } \right) \right]51​÷[41​(21​+31​) ]

Use properties of real numbers to write 12(z/4) 12 ( z / 4 ) 12(z/4) without parentheses.

Use properties of real numbers to write 3(2a+b) 3 ( 2 a + b ) 3(2a+b) without parentheses.

State the property of real numbers being used. 3xy=yx33 x y = y x 33xy=yx3

Perform the indicated operation(s) and simplify. 14+5(14⋅15) −34\frac { 1 } { 4 } + 5 \left( \frac { 1 } { 4 } \cdot \frac { 1 } { 5 } \right) - \frac { 3 } { 4 }41​+5(41​⋅51​) −43​

State whether the inequality is true or false. $- \frac { 1 } { 10 } > - \frac { 1 } { 100 }$

Perform the indicated operation. $\frac { 1 } { 4 } + \frac { 1 } { 12 }$

Write the following statement in terms of inequalities. $Z$ is greater than or equal to $- 1$ .

Perform the indicated operation. $\frac { 1 } { 6 } \div \frac { 2 } { 3 }$

Perform the indicated operations. $\frac { \frac { 2 } { 5 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }$

State whether the inequality is true or false. $\frac { 22 } { 7 } > \pi$

Write the following statement in terms of inequalities. $x$ is negative.

Use properties of real numbers to write $- r ( s - 2 )$ without parentheses.

Perform the indicated operations. $\frac { \frac { 1 } { 10 } } { \frac { 1 } { 3 } - \frac { 1 } { 5 } }$

Use the properties of real numbers to write the expression without parentheses. $2 x \left( a - b - 2 c + \frac { d } { 2 } \right)$

State the property of real numbers being used. $x + 4 = 4 + x$

State the property of real numbers being used. $2 ( x + 5 y ) = 2 x + 10 y$

Perform the indicated operations. $\frac { \frac { 2 } { 3 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }$

State whether the inequality is true or false. $- \sqrt { 2 } < - 1.41$

Perform the indicated operations. $\frac { \frac { 1 } { 12 } } { \frac { 1 } { 8 } - \frac { 1 } { 12 } }$

Perform the indicated operation(s) and simplify. $\frac { 1 } { 5 } \div \left[ \frac { 1 } { 4 } \left( \frac { 1 } { 2 } + \frac { 1 } { 3 } \right) \right]$

Use properties of real numbers to write $12 ( z / 4 )$ without parentheses.

Use properties of real numbers to write $3 ( 2 a + b )$ without parentheses.

State the property of real numbers being used. $3 x y = y x 3$

Perform the indicated operation(s) and simplify. $\frac { 1 } { 4 } + 5 \left( \frac { 1 } { 4 } \cdot \frac { 1 } { 5 } \right) - \frac { 3 } { 4 }$