Deck 7: Rational Expressions

Question 1

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)

Answer 1

Question 2

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

A)
B)
C)
D)
E)

Answer 2

Question 3

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

A)
B)
C)
D)
E)

Answer 3

Question 4

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 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)
C)
D)
E)

Question 7

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

A)
B)
C)
D)
E)

Question 8

An economy car travels 261 miles on 4.5 gallons of gas. Give the average fuel consumption of the car in miles per gallon.

A)48 miles \ gallon
B)58 miles \ gallon
C)50 miles \ gallon
D)42 miles \ gallon
E)56 miles \ gallon

Question 9

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

A)
B)
C)
D)
E)

Question 10

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 11

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

A)
B)
C)
D)
E)

Question 12

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 13

Complete the following table.

A)
B)
C)
D)

Question 14

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

A)
B)
C)
D)
E)

Question 15

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

A)
B)
C)
D)
E)

Question 16

Write the ratio as a fraction in lowest terms. to

A)
B)
C)
D)
E)

Question 17

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

A)
B)
C)
D)
E)

Question 18

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

A)
B)
C)
D)
E)

Question 19

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

Question 20

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 21

An economy car travels 234 miles on 4.5 gallons of gas. Give the average fuel consumption of the car in miles per gallon. __________ miles \ gallon

Question 22

Reduce the following rational expression to lowest terms.

Question 23

A jogger covers a distance of 2 miles in 24 minutes. Find the average speed of the jogger in miles per hour.

A)2.00 miles per hour
B)0.20 miles per hour
C)5 miles per hour
D)4.9 miles per hour
E)50 miles per hour

Question 24

Reduce the following rational expression to lowest terms.

Question 25

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

A)
B)
C)
D)
E)

Question 26

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

A)
B)
C)
D)
E)

Question 27

Reduce the following rational expression to lowest terms.

Question 28

Reduce the following rational expression to lowest terms.

Question 29

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)88 miles per hour
C)8.8 miles per hour
D)7.74 miles per hour
E)774.4 miles per hour

Question 30

Write the ratio as a fraction in lowest terms. to

Question 31

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 32

Write the ratio as a fraction in lowest terms. to

Question 33

Reduce the following rational expression to lowest terms.

Question 34

Reduce the following rational expression to lowest terms.

Question 35

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 36

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

A)
B)
C)
D)
E)

Question 37

Reduce the following rational expressions to lowest terms.

Question 38

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

A)
B)
C)
D)
E)

Question 39

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

A)
B)
C)
D)
E)

Question 40

Reduce the following rational expression to lowest terms.

Question 41

A jogger covers a distance of 1 mile in 40 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 42

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

Question 43

Multiply the expressions.

A)
B)
C)
D)
E)

Question 44

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 45

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 46

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

A)
B)
C)
D)
E)

Question 47

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 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

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

A)
B)
C)
D)
E)

Question 51

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 52

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

A)
B)
C)
D)
E)

Question 53

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

Question 54

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 55

Multiply the expressions.

A)
B)
C)
D)
E)

Question 56

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

A)
B)
C)
D)
E)

Question 57

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

A)
B)
C)
D)
E)

Question 58

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 59

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

A)
B)
C)
D)
E)

Question 60

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

A)
B)
C)
D)
E)

Question 61

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

Question 62

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

Question 63

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 64

Perform the indicated operation.

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B)
C)
D)
E)

Question 65

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

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

Multiply the expressions.

Question 69

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 70

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 71

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 72

Multiply the expressions.

Question 73

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 74

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

Question 75

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

Question 76

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 77

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

Question 78

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

Question 79

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 80

Perform the indicated operation.

A)
B)
C)
D)
E)