Question 1

Find the LCM.
-500, 300, 150

Accepted Answer

A) 1500 
B) 500 
C) 750 
D) 300 
A) 1500 
B) 500 
C) 750 
D) 300

Question 2

Solve.
-The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 5 cm on a side is 375 g, find the weight of the liquid in a cubical container 4 cm on a side.

Accepted Answer

A) 64 g 
B) 192 g 
C) 12 g 
D) 44 g 
A) 64 g 
B) 192 g 
C) 12 g 
D) 44 g

Question 3

Find the LCM.
-$10 x y , 25 x ^ { 2 }$

Accepted Answer

A)  $50 x y ^ { 2 }$ 
B)  $50 x ^ { 2 } y$ 
C)  $50 x ^ { 3 } y$ 
D)  $50 \mathrm { xy } ^ { 3 }$ 
A)  $50 x y ^ { 2 }$ 
B)  $50 x ^ { 2 } y$ 
C)  $50 x ^ { 3 } y$ 
D)  $50 \mathrm { xy } ^ { 3 }$

Question 4

Multiply and, if possible, simplify.
-$\frac { 2 x ^ { 2 } } { 5 } \cdot \frac { 30 } { x ^ { 3 } }$

Accepted Answer

A)  $\frac { x ^ { 5 } } { 75 }$ 
B)  $\frac { x } { 75 }$ 
C)  $\frac { 12 } { x }$ 
D)  $\frac { 12 x ^ { 2 } } { x ^ { 3 } }$ 
A)  $\frac { x ^ { 5 } } { 75 }$ 
B)  $\frac { x } { 75 }$ 
C)  $\frac { 12 } { x }$ 
D)  $\frac { 12 x ^ { 2 } } { x ^ { 3 } }$

Question 5

Find all numbers for which the rational expression is not defined.
-$$\frac { 2 } { a - 5 }$$

Accepted Answer

A) None 
B) a = 0 
C) a = -5 
D) a = 5 
A) None 
B) a = 0 
C) a = -5 
D) a = 5

Question 6

Divide and simplify.
-$$\frac { z ^ { 2 } + 9 z + 14 } { z ^ { 2 } + 16 z + 63 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 2 z - 63 }$$

Accepted Answer

A)  $\frac { z - 7 } { z ^ { 2 } + 9 z }$ 
B)  $z - 7$ 
C)  $\frac { z - 7 } { z }$ 
D)  $\frac { z } { z ^ { 2 } + 16 z + 63 }$ 
A)  $\frac { z - 7 } { z ^ { 2 } + 9 z }$ 
B)  $z - 7$ 
C)  $\frac { z - 7 } { z }$ 
D)  $\frac { z } { z ^ { 2 } + 16 z + 63 }$

Question 7

Solve the problem.
-A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?

Accepted Answer

A) Bike: 12 mph 
B) Bike: 11.5 mph 
C) Bike: 14.5 mph 
D) Bike: 13 mph Hike: 2 mph Hike: 1.5 mph Hike: 4.5 mph Hike: 3 mph 
A) Bike: 12 mph 
B) Bike: 11.5 mph 
C) Bike: 14.5 mph 
D) Bike: 13 mph Hike: 2 mph Hike: 1.5 mph Hike: 4.5 mph Hike: 3 mph

Question 8

Subtract. Simplify, if possible.
-$$\frac { 4 x - 24 } { x ^ { 2 } - 36 } - \frac { 4 x - 24 } { 36 - x ^ { 2 } }$$

Accepted Answer

A)  8 
B)  $\frac { 8 } { x + 6 }$ 
C)  0 
D)  $\frac { 8 } { x - 6 }$ 
A)  8 
B)  $\frac { 8 } { x + 6 }$ 
C)  0 
D)  $\frac { 8 } { x - 6 }$

Question 9

Find an equation of variation in which y varies inversely as x and the following is true.
-$$y = 5.25 , \text { when } x = 0.24$$

Accepted Answer

A)  $y = \frac { 21.88 } { x }$ 
B)  $y = \frac { 1.26 } { x }$ 
C)  $y = \frac { 1.66 } { x }$ 
D)  $y = 21.88 x$ 
A)  $y = \frac { 21.88 } { x }$ 
B)  $y = \frac { 1.26 } { x }$ 
C)  $y = \frac { 1.66 } { x }$ 
D)  $y = 21.88 x$

Question 10

Answer the question.
-Describe two ways in which multiplying by 1 is used in adding or subtracting using fractional notation.

Accepted Answer

Multiplying by 1 is used to wr

Question 11

Solve the problem.
-Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 330 miles in the same time that Dana travels 300 miles. If Chuck's rate of travel is 5 mph more than Dana's, and they travel the same length of time, at What speed does Chuck travel?

Accepted Answer

A) 49 mph 
B) 50 mph 
C) 61 mph 
D) 55 mph 
A) 49 mph 
B) 50 mph 
C) 61 mph 
D) 55 mph

Question 12

Add. Simplify, if possible.
-$$\frac { 4 } { 8 } + \frac { 6 } { 8 }$$

Accepted Answer

A)  $\frac { 5 } { 2 }$ 
B)  5 
C)  $\frac { 4 } { 5 }$ 
D)  $\frac { 5 } { 4 }$ 
A)  $\frac { 5 } { 2 }$ 
B)  5 
C)  $\frac { 4 } { 5 }$ 
D)  $\frac { 5 } { 4 }$

Question 13

Add. Simplify, if possible.
-$$\frac { 4 } { 5 - m } + \frac { 6 } { m - 5 }$$

Accepted Answer

A)  $\frac { 24 } { 5 - m }$ 
B)  $\frac { 10 } { 5 - m }$ 
C)  $\frac { - 2 } { 5 - m }$ 
D)  $\frac { 2 } { 5 - m }$ 
A)  $\frac { 24 } { 5 - m }$ 
B)  $\frac { 10 } { 5 - m }$ 
C)  $\frac { - 2 } { 5 - m }$ 
D)  $\frac { 2 } { 5 - m }$

Question 14

Subtract. Simplify, if possible.
-$$\frac { - 6 } { y - 2 } - \frac { 3 } { 2 - y }$$

Accepted Answer

A)  $\frac { 9 } { y - 2 }$ 
B)  $\frac { - 9 } { y - 2 }$ 
C)  $\frac { - 3 } { y - 2 }$ 
D)  $\frac { - 18 } { y - 2 }$ 
A)  $\frac { 9 } { y - 2 }$ 
B)  $\frac { - 9 } { y - 2 }$ 
C)  $\frac { - 3 } { y - 2 }$ 
D)  $\frac { - 18 } { y - 2 }$

Question 15

Find an equation of variation in which the following are true.
-$x$ varies inversely as $y ^ { 2 }$, and $x = 10$ when $y = 16$.

Accepted Answer

A)  $x = \frac { 1 } { - 6 y ^ { 2 } }$ 
B)  $x = 2560 y ^ { 2 }$ 
C)  $x = \frac { 1 } { 2560 y ^ { 2 } }$ 
D)  $x = \frac { 2560 } { y ^ { 2 } }$ 
A)  $x = \frac { 1 } { - 6 y ^ { 2 } }$ 
B)  $x = 2560 y ^ { 2 }$ 
C)  $x = \frac { 1 } { 2560 y ^ { 2 } }$ 
D)  $x = \frac { 2560 } { y ^ { 2 } }$

Question 16

Find the LCM.
-$50x ^5 y , 60 x ^ { 4 } y ^ { 3 } , 30 x ^ { 2 } y ^ { 4 }$

Accepted Answer

A)  $150 x ^ { 20 } y ^ { 12 }$ 
B)  $300 x ^ { 5 } y ^ { 4 }$ 
C)  $100 x ^ { 5 } y ^ { 4 }$ 
D)  $60 x ^ { 5 } y$ 
A)  $150 x ^ { 20 } y ^ { 12 }$ 
B)  $300 x ^ { 5 } y ^ { 4 }$ 
C)  $100 x ^ { 5 } y ^ { 4 }$ 
D)  $60 x ^ { 5 } y$

Question 17

Solve the equation.
-$$\frac { x } { x + 2 } - \frac { 2 } { x - 2 } = \frac { x ^ { 2 } + 4 } { x ^ { 2 } - 4 }$$

Accepted Answer

A)  $- 2,2$ 
B)  $- 2$ 
C)  2 
D)  No solution 
A)  $- 2,2$ 
B)  $- 2$ 
C)  2 
D)  No solution

Question 18

Simplify.
-$$\frac { x + 6 + \frac { 9 } { x } } { x + 8 + \frac { 15 } { x } }$$

Accepted Answer

A)  $\frac { ( x + 3 ) ^ { 2 } } { x + 5 }$ 
B)  $\frac { x ^ { 2 } + 6 x + 9 } { x ^ { 2 } + 8 x + 15 }$ 
C)  $\frac { x + 3 } { x + 5 }$ 
D)  $\frac { x + 3 } { x ^ { 2 } + 5 x }$ 
A)  $\frac { ( x + 3 ) ^ { 2 } } { x + 5 }$ 
B)  $\frac { x ^ { 2 } + 6 x + 9 } { x ^ { 2 } + 8 x + 15 }$ 
C)  $\frac { x + 3 } { x + 5 }$ 
D)  $\frac { x + 3 } { x ^ { 2 } + 5 x }$

Question 19

Find an equation of variation in which y varies inversely as x and the following is true.
-$y = 21$, when $x = 48$

Accepted Answer

A)  $\mathrm { y } = \frac { 0.44 } { \mathrm { x } }$ 
B)  $y = 1008 x$ 
C)  $\mathrm { y } = 0.44 \mathrm { x }$ 
D)  $\mathrm { y } = \frac { 1008 } { \mathrm { x } }$ 
A)  $\mathrm { y } = \frac { 0.44 } { \mathrm { x } }$ 
B)  $y = 1008 x$ 
C)  $\mathrm { y } = 0.44 \mathrm { x }$ 
D)  $\mathrm { y } = \frac { 1008 } { \mathrm { x } }$

Question 20

Solve.
-The weight of a body above the surface of the earth varies inversely as the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 2?

Accepted Answer

A) The weight is multiplied by 2. 
B) The weight is divided by 4. 
C) The weight is divided by 2. 
D) The weight is multiplied by 4. 
A) The weight is multiplied by 2. 
B) The weight is divided by 4. 
C) The weight is divided by 2. 
D) The weight is multiplied by 4.

Find the LCM. -500, 300, 150

Solve. -The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 5 cm on a side is 375 g, find the weight of the liquid in a cubical container 4 cm on a side.

Find the LCM. - $10 x y , 25 x ^ { 2 }$

Multiply and, if possible, simplify. - $\frac { 2 x ^ { 2 } } { 5 } \cdot \frac { 30 } { x ^ { 3 } }$

Find all numbers for which the rational expression is not defined. - $\frac { 2 } { a - 5 }$

Divide and simplify. - $\frac { z ^ { 2 } + 9 z + 14 } { z ^ { 2 } + 16 z + 63 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 2 z - 63 }$

Solve the problem. -A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?

Subtract. Simplify, if possible. - $\frac { 4 x - 24 } { x ^ { 2 } - 36 } - \frac { 4 x - 24 } { 36 - x ^ { 2 } }$

Find an equation of variation in which y varies inversely as x and the following is true. - $y = 5.25 , \text { when } x = 0.24$

Answer the question. -Describe two ways in which multiplying by 1 is used in adding or subtracting using fractional notation.

Solve the problem. -Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 330 miles in the same time that Dana travels 300 miles. If Chuck's rate of travel is 5 mph more than Dana's, and they travel the same length of time, at What speed does Chuck travel?

Add. Simplify, if possible. - $\frac { 4 } { 8 } + \frac { 6 } { 8 }$

Add. Simplify, if possible. - $\frac { 4 } { 5 - m } + \frac { 6 } { m - 5 }$

Subtract. Simplify, if possible. - $\frac { - 6 } { y - 2 } - \frac { 3 } { 2 - y }$

Find an equation of variation in which the following are true. - $x$ varies inversely as $y ^ { 2 }$ , and $x = 10$ when $y = 16$ .

Find the LCM. - $50x ^5 y , 60 x ^ { 4 } y ^ { 3 } , 30 x ^ { 2 } y ^ { 4 }$

Solve the equation. - $\frac { x } { x + 2 } - \frac { 2 } { x - 2 } = \frac { x ^ { 2 } + 4 } { x ^ { 2 } - 4 }$

Simplify. - $\frac { x + 6 + \frac { 9 } { x } } { x + 8 + \frac { 15 } { x } }$

Find an equation of variation in which y varies inversely as x and the following is true. - $y = 21$ , when $x = 48$

Solve. -The weight of a body above the surface of the earth varies inversely as the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 2?

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

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Exam 6: Rational Expressions and Equations

Find the LCM. -500, 300, 150

Solve. -The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 5 cm on a side is 375 g, find the weight of the liquid in a cubical container 4 cm on a side.

Find the LCM. - 10xy,25x210 x y , 25 x ^ { 2 }10xy,25x2

Multiply and, if possible, simplify. - 2x25⋅30x3\frac { 2 x ^ { 2 } } { 5 } \cdot \frac { 30 } { x ^ { 3 } }52x2​⋅x330​

Find all numbers for which the rational expression is not defined. - 2a−5\frac { 2 } { a - 5 }a−52​

Divide and simplify. - z2+9z+14z2+16z+63÷z2+2zz2+2z−63\frac { z ^ { 2 } + 9 z + 14 } { z ^ { 2 } + 16 z + 63 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 2 z - 63 }z2+16z+63z2+9z+14​÷z2+2z−63z2+2z​