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Deck 6: Rational Expressions and Equations; Ratio and Proportion
Full screen (f)
Question
Simplify this rational expression. Assume the denominator never equals zero. 
A)
B)
C)
D)
E) Does not simplify further.
A)
B)
C)
D)
E) Does not simplify further.
Question
Determine the domain of the given function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Simplify the rational expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the indicated operation and simplify. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the indicated operation and simplify. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the division. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the indicated operation and simplify. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the indicated division and express your answer in simplest form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify this rational expression. Assume the denominator never equals zero. 
A) 1
B) 2 a - 8 x
C) 8 x - 2 a
D) -1
E) Does not simplify further.
A) 1
B) 2 a - 8 x
C) 8 x - 2 a
D) -1
E) Does not simplify further.
Question
Perform the indicated operation and simplify. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine the domain of the given function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Perform the indicated operation and simplify. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find any real numbers x which make 
undefined.
A)
B)
C)
D) defined for all real numbers
undefined.A)
B)
C)
D) defined for all real numbers
Question
Which value of x makes the rational expression 
undefined?
A)
B)
C)
D)
E) none
undefined?A)
B)
C)
D)
E) none
Question
Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero. 
A)
B)
C)
D)
E) in lowest terms
A)
B)
C)
D)
E) in lowest terms
Question
Perform the indicated operation and simplify. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Perform the indicated operation and simplify. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the expression. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Determine the domain of the given function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero. 
A)
B)
C)
D)
E) in lowest terms
A)
B)
C)
D)
E) in lowest terms
Question
Simplify the complex fraction. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the indicated operation. Simplify the answer if possible. 
Question
Perform the indicated operation and simplify. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the indicated operation and simplify. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Perform the indicated operation. 
Question
Perform the operation. Simplify the answer, if possible. 
Question
Add the rational expressions. Be sure to express your answer in simplest form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the operations. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the operation. Simplify the answer, if possible. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the indicated operation and express your answer in simplest form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the indicated division and express your answer in simplest form. 
Question
Add or subtract the rational expressions. Be sure to express your answer in simplest form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the complex fraction. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the indicated operation and simplify. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the indicated operations involving rational numbers. Express the final answer in reduced form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Subtract as indicated and express your answer in simplest form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Two denominators are given. Find the LCD. t 2 
7 t 
8, t 2 
64
7 t 8, t 2 64 Question
Perform the indicated operation and express your answer in simplest form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the complex fraction. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Add the rational expressions. Be sure to express your answer in simplest form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Find the unit price. They charged 
for 
minutes.
A)
per min
B)
per min
C)
per min
D)
per min
E)
per min
for minutes.A)
per minB)
per minC)
per minD)
per minE)
per min Question
Question
Write the rate as a unit rate. 
presents for 
children
A)
presents per child
B)
presents per child
C)
presents per child
D)
presents per child
E)
presents per child
presents for childrenA)
presents per childB)
presents per childC)
presents per childD)
presents per childE)
presents per child Question
Solve for the variable in the proportion. 
Question
Find the unit price. 
barrels cost $ 
.
A) $
per barrel
B) $
per barrel
C) $
per barrel
D) $
per barrel
E) $
per barrel
barrels cost $ .A) $
per barrelB) $
per barrelC) $
per barrelD) $
per barrelE) $
per barrel Question
Write the ratio as a fraction in simplest form. 2 to 16
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the proportion for the variable. 
A) 15
B) 17
C) 14
D) 12
E) no solution
A) 15
B) 17
C) 14
D) 12
E) no solution
Question
Question
Simplify the complex fraction. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Question
Write the rate as a unit rate. 
trips every 
months
A)
trips per month
B)
trips per month
C)
trips per month
D)
trips per month
E)
trips per month
trips every monthsA)
trips per monthB)
trips per monthC)
trips per monthD)
trips per monthE)
trips per month Question
Find the unit price. For 
dozen, you will pay $ 
.
A) $
per dozen
B) $
per dozen
C) $
per dozen
D) $
per dozen
E) $
per dozen
dozen, you will pay $ .A) $
per dozenB) $
per dozenC) $
per dozenD) $
per dozenE) $
per dozen Question
Simplify the complex fraction. 
A)
B)
C)
D)
E) none of these
A)
B)
C)
D)
E) none of these
Question
Simplify the complex fraction. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the proportion for the variable. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Write each rate as a unit rate. 
people living in 
square
A)
people per square mi
B)
people per square mi
C)
people per square mi
D)
people per square mi
E)
people per square mi
people living in squareA)
people per square miB)
people per square miC)
people per square miD)
people per square miE)
people per square mi Question
Write the ratio as a fraction in simplest form. 7 to 28
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the ratio as a fraction in simplest form. 0.09 to 0.72.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Is the expression a proportion? 
Question
Is the expression a proportion? 
Question
Use similar triangles to help solve the problem. A man places a mirror on the ground and sees the reflection of the top of a flagpole as shown in the figure below. The two triangles in the figure are similar. Find the height h of the flagpole. 
a = 11, b = 5, c = 25
A)
ft
B)
ft
C)
D)
a = 11, b = 5, c = 25A)
ftB)
ftC)
D)
Question
Is the expression a proportion? 
Question
Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree. 
A) h = 27 ft
B) h = 42 ft
C) h = 30 ft
D) h = 35 ft
E) h = 22 ft
A) h = 27 ft
B) h = 42 ft
C) h = 30 ft
D) h = 35 ft
E) h = 22 ft
Question
Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.) Round your answer to the nearest integer. 
A) x = 870 ft
B) x = 813 ft
C) x = 845 ft
D) x = 885 ft
E) x = 833 ft
A) x = 870 ft
B) x = 813 ft
C) x = 845 ft
D) x = 885 ft
E) x = 833 ft
Question
A recipe for chocolate chip cookies calls for 
cups of flour and 1 cup of sugar. The recipe will make 
dozen cookies. How many cups of flour will be needed to make 
dozen cookies? Round your answer to the nearest fourth of a cup.
A)
cups
B)
cups
C)
cups
D)
cups
E)
cups
cups of flour and 1 cup of sugar. The recipe will make dozen cookies. How many cups of flour will be needed to make dozen cookies? Round your answer to the nearest fourth of a cup.A)
cupsB)
cupsC)
cupsD)
cupsE)
cups
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Full screen (f)
Deck 6: Rational Expressions and Equations; Ratio and Proportion
1
Simplify this rational expression. Assume the denominator never equals zero.
A)
B)
C)
D)
E) Does not simplify further.
A)
B)
C)
D)
E) Does not simplify further.
2
Determine the domain of the given function.
A)
B)
C)
D)
A)
B)
C)
D)
3
Simplify the rational expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Perform the indicated operation and simplify.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
Perform the indicated operation and simplify.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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6
Perform the division.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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7
Perform the indicated operation and simplify.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
Perform the indicated division and express your answer in simplest form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
Simplify this rational expression. Assume the denominator never equals zero.
A) 1
B) 2 a - 8 x
C) 8 x - 2 a
D) -1
E) Does not simplify further.
A) 1
B) 2 a - 8 x
C) 8 x - 2 a
D) -1
E) Does not simplify further.
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10
Perform the indicated operation and simplify.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Determine the domain of the given function.
A)
B)
C)
D)
A)
B)
C)
D)
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12
Perform the indicated operation and simplify.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
Find any real numbers x which make undefined.
A)
B)
C)
D) defined for all real numbers
undefined.A)
B)
C)
D) defined for all real numbers
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14
Which value of x makes the rational expression undefined?
A)
B)
C)
D)
E) none
undefined?A)
B)
C)
D)
E) none
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15
Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero.
A)
B)
C)
D)
E) in lowest terms
A)
B)
C)
D)
E) in lowest terms
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16
Perform the indicated operation and simplify.
A)
B)
C)
D)
A)
B)
C)
D)
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17
Perform the indicated operation and simplify.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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18
Solve the expression.
A)
B)
C)
D)
A)
B)
C)
D)
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19
Determine the domain of the given function.
A)
B)
C)
D)
A)
B)
C)
D)
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20
Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero.
A)
B)
C)
D)
E) in lowest terms
A)
B)
C)
D)
E) in lowest terms
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21
Simplify the complex fraction.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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22
Perform the indicated operation. Simplify the answer if possible.
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23
Perform the indicated operation and simplify.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
Perform the indicated operation and simplify.
A)
B)
C)
D)
A)
B)
C)
D)
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25
Perform the indicated operation.
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26
Perform the operation. Simplify the answer, if possible.
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27
Add the rational expressions. Be sure to express your answer in simplest form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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28
Perform the operations.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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29
Perform the operation. Simplify the answer, if possible.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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30
Perform the indicated operation and express your answer in simplest form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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31
Perform the indicated division and express your answer in simplest form.
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32
Add or subtract the rational expressions. Be sure to express your answer in simplest form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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33
Simplify the complex fraction.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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34
Perform the indicated operation and simplify.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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35
Perform the indicated operations involving rational numbers. Express the final answer in reduced form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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36
Subtract as indicated and express your answer in simplest form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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37
Two denominators are given. Find the LCD. t 2 7 t 8, t 2 64
7 t 8, t 2 64 Unlock Deck
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38
Perform the indicated operation and express your answer in simplest form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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39
Simplify the complex fraction.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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40
Add the rational expressions. Be sure to express your answer in simplest form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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41
The real estate taxes on a summer home assessed at $72,900 were $3,645. Find the tax rate as a percent.
A) 0.6%
B) 6%
C) 50%
D) 5%
E) 0.06%
A) 0.6%
B) 6%
C) 50%
D) 5%
E) 0.06%
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42
Find the unit price. They charged for minutes.
A) per min
B) per min
C) per min
D) per min
E) per min
for minutes.A)
per minB)
per minC)
per minD)
per minE)
per min Unlock Deck
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k this deck
43
Ricardo worked for 9 hours to help insulate a hockey arena. For his work, he received $337.50. Find his hourly rate of pay.
A) $37.35/hr
B) $37.50/hr
C) $0.03/hr
D) $37.55/hr
E) $37.40/hr
A) $37.35/hr
B) $37.50/hr
C) $0.03/hr
D) $37.55/hr
E) $37.40/hr
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44
Write the rate as a unit rate. presents for children
A) presents per child
B) presents per child
C) presents per child
D) presents per child
E) presents per child
presents for childrenA)
presents per childB)
presents per childC)
presents per childD)
presents per childE)
presents per child Unlock Deck
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45
Solve for the variable in the proportion.
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46
Find the unit price. barrels cost $ .
A) $ per barrel
B) $ per barrel
C) $ per barrel
D) $ per barrel
E) $ per barrel
barrels cost $ .A) $
per barrelB) $
per barrelC) $
per barrelD) $
per barrelE) $
per barrel Unlock Deck
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47
Write the ratio as a fraction in simplest form. 2 to 16
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
Solve the proportion for the variable.
A) 15
B) 17
C) 14
D) 12
E) no solution
A) 15
B) 17
C) 14
D) 12
E) no solution
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49
An airplane travels from one town to another town, a distance of 1,821 miles, in 3 hours. Find the rate of speed of the plane.
A) 58 mph
B) 617 mph
C) 15 mph
D) 628 mph
E) 63 mph
A) 58 mph
B) 617 mph
C) 15 mph
D) 628 mph
E) 63 mph
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50
Simplify the complex fraction.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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51
If shirts are on sale at two for $25, how much will 7 shirts cost?
A) $87.50
B) $98.50
C) $78.50
D) $95.50
E) $77.50
A) $87.50
B) $98.50
C) $78.50
D) $95.50
E) $77.50
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52
A school board has determined that there should be 4 teachers for every 60 students. How many teachers are needed for an enrollment of 3,180 students?
A) 187 teachers
B) 223 teachers
C) 212 teachers
D) 196 teachers
E) 155 teachers
A) 187 teachers
B) 223 teachers
C) 212 teachers
D) 196 teachers
E) 155 teachers
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53
Write the rate as a unit rate. trips every months
A) trips per month
B) trips per month
C) trips per month
D) trips per month
E) trips per month
trips every monthsA)
trips per monthB)
trips per monthC)
trips per monthD)
trips per monthE)
trips per month Unlock Deck
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54
Find the unit price. For dozen, you will pay $ .
A) $ per dozen
B) $ per dozen
C) $ per dozen
D) $ per dozen
E) $ per dozen
dozen, you will pay $ .A) $
per dozenB) $
per dozenC) $
per dozenD) $
per dozenE) $
per dozen Unlock Deck
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55
Simplify the complex fraction.
A)
B)
C)
D)
E) none of these
A)
B)
C)
D)
E) none of these
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56
Simplify the complex fraction.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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57
Solve the proportion for the variable.
A)
B)
C)
D)
A)
B)
C)
D)
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58
Write each rate as a unit rate. people living in square
A) people per square mi
B) people per square mi
C) people per square mi
D) people per square mi
E) people per square mi
people living in squareA)
people per square miB)
people per square miC)
people per square miD)
people per square miE)
people per square mi Unlock Deck
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59
Write the ratio as a fraction in simplest form. 7 to 28
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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60
Write the ratio as a fraction in simplest form. 0.09 to 0.72.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
61
Is the expression a proportion?
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62
Is the expression a proportion?
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63
Use similar triangles to help solve the problem. A man places a mirror on the ground and sees the reflection of the top of a flagpole as shown in the figure below. The two triangles in the figure are similar. Find the height h of the flagpole. a = 11, b = 5, c = 25
A) ft
B) ft
C)
D)
a = 11, b = 5, c = 25A)
ftB)
ftC)
D)
Unlock Deck
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Unlock Deck
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64
Is the expression a proportion?
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65
Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.
A) h = 27 ft
B) h = 42 ft
C) h = 30 ft
D) h = 35 ft
E) h = 22 ft
A) h = 27 ft
B) h = 42 ft
C) h = 30 ft
D) h = 35 ft
E) h = 22 ft
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Unlock for access to all 67 flashcards in this deck.
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k this deck
66
Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.) Round your answer to the nearest integer.
A) x = 870 ft
B) x = 813 ft
C) x = 845 ft
D) x = 885 ft
E) x = 833 ft
A) x = 870 ft
B) x = 813 ft
C) x = 845 ft
D) x = 885 ft
E) x = 833 ft
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67
A recipe for chocolate chip cookies calls for cups of flour and 1 cup of sugar. The recipe will make dozen cookies. How many cups of flour will be needed to make dozen cookies? Round your answer to the nearest fourth of a cup.
A) cups
B) cups
C) cups
D) cups
E) cups
cups of flour and 1 cup of sugar. The recipe will make dozen cookies. How many cups of flour will be needed to make dozen cookies? Round your answer to the nearest fourth of a cup.A)
cupsB)
cupsC)
cupsD)
cupsE)
cups Unlock Deck
Unlock for access to all 67 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 67 flashcards in this deck.
