Deck 9: Rational Expressions
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Deck 9: Rational Expressions
1
Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches 5. 
A) Y approaches
from the left and
from the right.
B) Y approaches
from the left and
from the right.
C) Y approaches
from the left and
from the right.
D) Y approaches
from the left and
from the right.
E) Y approaches
from the left and
from the right.

A) Y approaches


B) Y approaches


C) Y approaches


D) Y approaches


E) Y approaches


Y approaches
from the left and
from the right.


2
List 5 possible widths and lengths of rectangles with area of 36 square inches. Calculate the perimeter for each rectangle. Which is not true?
A) The product of the length and width is constant.
B) A rectangle with length of 14.4 inches and width of 2.5 inches has an area of 36 square inches.
C) The sum of the length and width is constant.
D) As the measures of the length and width get closer together, the perimeter gets smaller.
E) The smallest perimeter is when the length and width are equal.
A) The product of the length and width is constant.
B) A rectangle with length of 14.4 inches and width of 2.5 inches has an area of 36 square inches.
C) The sum of the length and width is constant.
D) As the measures of the length and width get closer together, the perimeter gets smaller.
E) The smallest perimeter is when the length and width are equal.
The sum of the length and width is constant.
3
Find the missing number or expression in each pair of equivalent fractions. Assume there is no zero denominators. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)


4
A potential landfill site contains 1,000,000 cubic yards of space. If a city with a population of 100,000 produces 400 cubic yards of garbage each day, how many years will the landfill last? Assume there are 365 days in a year. Please round your answer to nearest tenth.
A) 7.6 years
B) 6.8 years
C) 7.4 years
D) 6.4 years
E) 6.6 years
A) 7.6 years
B) 6.8 years
C) 7.4 years
D) 6.4 years
E) 6.6 years
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5
Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches 8. 
A) Y approaches
from the left and
from the right.
B) Y approaches
from the left and
from the right.
C) Y approaches
from the left and
from the right.
D) Y approaches
from the left and
from the right.
E) Y approaches 8.

A) Y approaches


B) Y approaches


C) Y approaches


D) Y approaches


E) Y approaches 8.
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6
Find the missing number or expression in the pair of equivalent fractions. Assume that all denominators are nonzero. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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7
What inputs are defined for the expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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8
What inputs are defined for the expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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9
Simplify: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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10
What inputs are defined for the expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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11
What inputs are defined for the expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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12
Estimated crude oil reserves in a certain year was about 1,100 billion barrels. If the average consumption of crude oil is x barrels per day, what equation describes how many days the oil reserves will last?
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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13
What inputs are defined for the expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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14
A potential landfill site contains 1,400,000 cubic yards of space. If the average fill per day is x cubic yards, what equation describes how many days the landfill site may be used?
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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15
Simplify. 
A) 5 ft
B) 500 foot-pounds
C) 1600 foot-pounds
D) 2 ft
E) 5 foot-pounds

A) 5 ft
B) 500 foot-pounds
C) 1600 foot-pounds
D) 2 ft
E) 5 foot-pounds
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16
Simplify 
A) 3 in2
B) 66 in2
C) 21 in2
D) 23 in.
E) 23 in2

A) 3 in2
B) 66 in2
C) 21 in2
D) 23 in.
E) 23 in2
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17
Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches -7. 
A) Y approaches
from the left and
from the right.
B) Y approaches
from the left and
from the right.
C) Y approaches
from the left and
from the right.
D) Y approaches
from the left and
from the right.
E) Y approaches
from the left and
from the right.

A) Y approaches


B) Y approaches


C) Y approaches


D) Y approaches


E) Y approaches


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18
Find the missing number or expression in each pair of equivalent fraction. Assume there is no zero denominators. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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19
Simplify the expression. Assume the denominator is nonzero. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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20
Suppose you have 6 miles to travel on a sometimes congested freeway. How long would it take you to travel that distance at the speed of 10 miles per hour?
A) 100 minutes
B) 40 minutes
C) 36 minutes
D) 30 minutes
E) 24 minutes
A) 100 minutes
B) 40 minutes
C) 36 minutes
D) 30 minutes
E) 24 minutes
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21
What may be concluded about these fractions? 
A) They are equal.
B) They are not equal.

A) They are equal.
B) They are not equal.
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22
Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. 
A) 5.92 seconds
B) 4.42 seconds
C) 5.02 seconds
D) 4.92 seconds
E) 4.87 seconds

A) 5.92 seconds
B) 4.42 seconds
C) 5.02 seconds
D) 4.92 seconds
E) 4.87 seconds
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23
The current, I, in an electrical circuit is found by dividing the voltage, V, by the resistance, R. Suppose the voltage and resistance vary with time as in the following equations.
Assume there are no zero denominators. Find a formula in terms of t that gives the current, I.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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24
Simplify. Assume there are no zero denominators. 
A)
B) x = 3
C) x = 2
D) 3
E) Does not simplify.

A)

B) x = 3
C) x = 2
D) 3
E) Does not simplify.
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25
Multiply: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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26
Simplify the fraction. 
A) 1
B) -1
C) -3
D) 4
E) -4

A) 1
B) -1
C) -3
D) 4
E) -4
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27
Use the properties of fractions to simplify the expression. 
A) kilometers
B)
C) second
D)
E) kilometers2

A) kilometers
B)

C) second
D)

E) kilometers2
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28
Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. 
A) 0.16 page/min
B) 0.16 min/page
C) 0.21 min/page
D) 6.15 min
E) 0.21 page/min

A) 0.16 page/min
B) 0.16 min/page
C) 0.21 min/page
D) 6.15 min
E) 0.21 page/min
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29
Multiply: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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30
Simplify. Assume there are no zero denominators. 
A)
B) x = 3
C) x = 2
D) 3
E) Does not simplify.

A)

B) x = 3
C) x = 2
D) 3
E) Does not simplify.
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31
In economics, total quantity sold is the product of the price and the demand. Find the total quantity, Q.
Assume there are no zero denominators.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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32
Simplify. Assume there are no zero denominators. 
A)
B) 3
C)
D)
E) Does not simplify.

A)

B) 3
C)

D)

E) Does not simplify.
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33
Multiply and divide the two fractions. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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34
Multiply and divide fractions. Assume all denominators are nonzero. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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35
Indicate whether the statement is true or false.
A fraction can have the same variables in the numerator and denominator and be unsimplifiable.
A fraction can have the same variables in the numerator and denominator and be unsimplifiable.
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36
Divide: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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37
Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. 
A) 2.5 gal/hr
B) 2.5 hr/gal
C) 2 hr/gal
D) 5 gal
E) 3.5 gal/hr

A) 2.5 gal/hr
B) 2.5 hr/gal
C) 2 hr/gal
D) 5 gal
E) 3.5 gal/hr
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38
Divide: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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39
Use the properties of fractions to simplify the expression. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places if necessary. 
A) 3.85 sec
B) 4.35 feet
C) 2.65 sec
D) 2.65 feet/sec
E) 0.26 feet

A) 3.85 sec
B) 4.35 feet
C) 2.65 sec
D) 2.65 feet/sec
E) 0.26 feet
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40
Divide: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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41
Simplify: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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42
Find the least common denominator for the equation. 
A) 4
B) 80
C) 40
D) 8
E) 10

A) 4
B) 80
C) 40
D) 8
E) 10
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43
Simplify: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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44
Simplify: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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45
Add the fractions on the right side of the equals sign to obtain a single fraction for the application formula. Assume there are no zero denominators. Resistors in parallel in an electrical circuit: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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46
Simplify: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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47
Find the slope of the line connecting the points. Simplify to eliminate fractions from the numerators and denominators. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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48
What is the result of the operation? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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49
Add the rational expressions. Assume there are no zero denominators. 
A) 1
B) 3
C) 6
D)
E)

A) 1
B) 3
C) 6
D)

E)

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50
Multiply the expressions, and simplify the results. Assume there are no zero denominators. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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51
Simplify: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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52
Find the slope of the line segment connecting the points. Simplify. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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53
Simplify the complex fraction to eliminate fractions from the numerators and denominators. Assume there are no zero denominators. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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54
What is the least common denominator for the set of rational expressions? 
A) 15
B) 270
C) 135
D) 27
E) 150

A) 15
B) 270
C) 135
D) 27
E) 150
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55
Simplify: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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56
Multiply the expressions, and simplify the results. Assume there are no zero denominators. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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57
Find the least common denominator for the equation. 
A) 6
B) 90
C) 30
D) 30x
E) 6x

A) 6
B) 90
C) 30
D) 30x
E) 6x
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58
Find the least common denominator for the equation. 
A)
B)
C) 24
D) 8
E)

A)

B)

C) 24
D) 8
E)

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59
Simplify: 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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60
Solve: 
A)
B)
C) 22
D) -23
E) 23

A)

B)

C) 22
D) -23
E) 23
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61
Set up and solve an equation. Round to the nearest tenth. One door can clear a theater in 6 minutes. A second door can clear a theater in 9 minutes. How fast can the theater be cleared if both doors are available?
A) 15 min
B) 0.3 min
C) 4.6 min
D) 3.6 min
E) 14 min
A) 15 min
B) 0.3 min
C) 4.6 min
D) 3.6 min
E) 14 min
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62
Set up and solve an equation. Round to the nearest tenth. One farmer bales her hay in 15 days. A second farmer does it in 6 days. How many days will it take them working together?
A) 4.3 days
B) 0.2 day
C) 3.3 days
D) 21 days
E) 20 days
A) 4.3 days
B) 0.2 day
C) 3.3 days
D) 21 days
E) 20 days
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63
Set up and solve an equation. Round to the nearest tenth. A
-inch garden hose fills a child's pool in 1 hour. A
-inch garden hose fills a child's pool in 1.2 hours. How long will it take to fill the pool if both hoses are used at once?
A) 0.4 hr
B) 0.5 hr
C) 1.8 hr
D) 5.5 hr
E) 4.5 hr


A) 0.4 hr
B) 0.5 hr
C) 1.8 hr
D) 5.5 hr
E) 4.5 hr
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64
Indicate any inputs that must be excluded and then solve the equation. Factoring of the quadratic equation may be helpful. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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65
Indicate any inputs that must be excluded and then solve the equation. Factoring of the quadratic equation may be helpful. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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66
Indicate any inputs that must be excluded and then solve the equation. Factoring of the quadratic equation may be helpful. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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