Deck 6: Reducing Rational Expressions to Lowest Terms

Question 1

In 1897 a large Ferris wheel was built in Vienna; it is still in operation today. Known as The Great Wheel , it has a circumference of 618 feet. If one trip around the circumference of the wheel took 15 minutes, find the average speed of a rider in feet per minute.

A) 42.9 feet / minute
B) 41.2 feet / minute
C) 45.5 feet / minute
D) 39.5 feet / minute
E) 43.7 feet / minute

Answer 1

B

Question 2

Reduce the following rational expression to lowest terms, if possible.

A)
B)
C)
D)
E)

Answer 2

D

Question 3

Reduce the following rational expression to lowest terms, if possible.

A)
B)
C)
D)
E)

Answer 3

C

Question 4

To reduce the following rational expression to lowest terms, you will have to use factoring by grouping. Be sure to factor each numerator and denominator completely before dividing out any common factors. (Remember, factoring by grouping takes two steps.)

A)
B)
C)
D)
E)

Question 5

Write the ratio as a fraction in lowest terms. to

A)
B)
C)
D)
E)

Question 6

Reduce the following rational expression to lowest terms, if possible.

A)
B)
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D)
E)

Question 7

Reduce the following rational expression to lowest terms, if possible. Also, specify any restrictions on the variable.

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B)
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D)
E)

Question 8

Reduce the following rational expression to lowest terms, if possible.

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B)
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D)
E)

Question 9

Reduce the following rational expression to lowest terms, if possible. Also, specify any restrictions on the variable.

A)
B)
C)
D)
E)

Question 10

An economy car travels 264 miles on 5.5 gallons of gas. Give the average fuel consumption of the car in miles per gallon.

A) 42 miles / gallon
B) 50 miles / gallon
C) 48 miles / gallon
D) 58 miles / gallon
E) 40 miles / gallon

Question 11

You know that . Compare these expressions by completing the following table. (Be careful - not all the rows have equal entries.)

A)
B)
C)
D)

Question 12

If a bank charges $6.00 per month and $0.12 per check for one of its checking accounts, then the total monthly cost to write x checks is , and the average cost of each of the x checks written is Compare these two formulas by filling in the following table. Round to the nearest cent.

A)
B)
C)
D)

Question 13

Reduce the following rational expression to lowest terms, if possible.

A)
B)
C)
D)
E)

Question 14

To reduce the following rational expression to lowest terms, you will have to use factoring by grouping. Be sure to factor each numerator and denominator completely before dividing out any common factors. (Remember, factoring by grouping takes two steps.)

A)
B)
C)
D)
E)

Question 15

Complete the following table.

A)
B)
C)
D)

Question 16

Reduce the following rational expression to lowest terms, if possible.

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D)
E)

Question 17

In 1897 a large Ferris wheel was built in Vienna; it is still in operation today. Known as The Great Wheel , it has a circumference of 618 feet. If one trip around the circumference of the wheel took 15 minutes, find the average speed of a rider in feet per minute. __________ feet / minute

Question 18

Reduce the following rational expression to lowest terms, if possible.

A)
B)
C)
D)
E)

Question 19

Reduce the following rational expression to lowest terms, if possible.

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D)
E)

Question 20

Write the ratio as a fraction in lowest terms. to

A)
B)
C)
D)
E)

Question 21

Reduce the following rational expression to lowest terms.

Question 22

Write the ratio as a fraction in lowest terms. to

Question 23

Reduce the following rational expression to lowest terms.

Question 24

To reduce the following rational expression to lowest terms, you will have to use factoring by grouping. Be sure to factor each numerator and denominator completely before dividing out any common factors. (Remember, factoring by grouping takes two steps.)

Question 25

Perform the indicated operation. Reduce your answer to lowest terms.

A)
B)
C)
D)
E)

Question 26

A Ferris wheel called Colossus was built in St. Louis in 1986. It has a circumference of 518 feet. If one trip around the wheel takes 40 seconds, find the average speed of a rider on this wheel in miles per hour.

A) 77.44 miles per hour
B) 774.4 miles per hour
C) 7.74 miles per hour
D) 8.8 miles per hour
E) 88 miles per hour

Question 27

A jogger covers a distance of 1 mile in 24 minutes. Find the average speed of the jogger in miles per hour.

A) 2.5 miles per hour
B) 2.4 miles per hour
C) 4.00 miles per hour
D) 25 miles per hour
E) 0.40 miles per hour

Question 28

Write the ratio as a fraction in lowest terms. to

Question 29

Reduce the following rational expression to lowest terms.

Question 30

An economy car travels 189 miles on 4.5 gallons of gas. Give the average fuel consumption of the car in miles per gallon. __________ miles / gallon

Question 31

Perform the indicated operation. Reduce your answer to lowest terms.

A)
B)
C)
D)
E)

Question 32

Reduce the following rational expression to lowest terms.

Question 33

Perform the indicated operation. Reduce your answer to lowest terms.

A)
B)
C)
D)
E)

Question 34

To reduce the following rational expression to lowest terms, you will have to use factoring by grouping. Be sure to factor each numerator and denominator completely before dividing out any common factors. (Remember, factoring by grouping takes two steps.)

Question 35

Perform the indicated operation. Reduce your answer to lowest terms.

A)
B)
C)
D)
E)

Question 36

Reduce the following rational expressions to lowest terms.

Question 37

Reduce the following rational expression to lowest terms.

Question 38

Perform the indicated operation. Reduce your answer to lowest terms.

A)
B)
C)
D)
E)

Question 39

Reduce the following rational expression to lowest terms.

Question 40

Reduce the following rational expression to lowest terms.

Question 41

Perform the indicated operation. Reduce your answer to lowest terms.

A)
B)
C)
D)
E)

Question 42

Simplify the expression. Work inside parentheses first, and then divide out common factors.

A)
B)
C)
D)
E)

Question 43

The following problem involves some factoring by grouping. Remember, before you can divide out factors common to the numerator and denominator of a product, you must factor completely.

A)
B)
C)
D)
E)

Question 44

The first Ferris wheel was designed and built by George Ferris in 1893. It was a large wheel with a circumference of 785 feet. If one trip around the wheel takes 20 minutes, find the average speed of a rider on this wheel in miles per hour. Give the answer to two decimal places, if necessary. __________ miles per hour

Question 45

Simplify the expression. Work inside parentheses first, and then divide out common factors.

A)
B)
C)
D)
E)

Question 46

A jogger covers a distance of 2 miles in 24 minutes. Find the average speed of the jogger in miles per hour. Give the answer to one decimal place, if necessary. __________ miles per hour

Question 47

Multiply the expressions.

A)
B)
C)
D)
E)

Question 48

Perform the indicated operation. Reduce your answer to lowest terms.

Question 49

Perform the indicated operation. Reduce your answer to lowest terms.

Question 50

The following problem involves some factoring by grouping. Remember, before you can divide out factors common to the numerator and denominator of a product, you must factor completely.

Question 51

Perform the indicated operation. Reduce your answer to lowest terms.

A)
B)
C)
D)
E)

Question 52

Perform the indicated operation. Reduce your answer to lowest terms.

Question 53

Multiply the expressions.

A)
B)
C)
D)
E)

Question 54

Perform the indicated operation. Reduce your answer to lowest terms.

A)
B)
C)
D)
E)

Question 55

The following problem involves some factoring by grouping. Remember, before you can divide out factors common to the numerator and denominator of a product, you must factor completely.

A)
B)
C)
D)
E)

Question 56

The following problem involves some factoring by grouping. Remember, before you can divide out factors common to the numerator and denominator of a product, you must factor completely.

A)
B)
C)
D)
E)

Question 57

Perform the indicated operation. Reduce your answer to lowest terms.

Question 58

Perform the indicated operation. Reduce your answer to lowest terms.

A)
B)
C)
D)
E)

Question 59

Perform the indicated operation. Reduce your answer to lowest terms.

A)
B)
C)
D)
E)

Question 60

The following problem involves some factoring by grouping. Remember, before you can divide out factors common to the numerator and denominator of a product, you must factor completely.

Question 61

Perform the indicated operation. Reduce your answer to lowest terms.

Question 62

The following problem involves some factoring by grouping. Remember, before you can divide out factors common to the numerator and denominator of a product, you must factor completely.

Question 63

Perform the indicated operation. Reduce your answer to lowest terms.

Question 64

Perform the indicated operation. Reduce your answer to lowest terms.

Question 65

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 66

Perform the indicated operation. Reduce your answer to lowest terms.

Question 67

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 68

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 69

Simplify the expression. Work inside parentheses first, and then divide out common factors.

Question 70

Multiply the expressions.

Question 71

Perform the indicated operation. Reduce your answer to lowest terms.

Question 72

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 73

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 74

Multiply the expressions.

Question 75

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 76

Perform the indicated operation.

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B)
C)
D)
E)

Question 77

Perform the indicated operation.

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B)
C)
D)
E)

Question 78

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 79

Simplify the expression. Work inside parentheses first, and then divide out common factors.

Question 80

Perform the indicated operation. Reduce your answer to lowest terms.