Deck 7: Rational Expressions

Question 1

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

A)
B)
C)
D)
E)

Answer 1

Question 2

Complete the following table; then show why the table turns out as it does.

A)
B)
C)
D)

Answer 2

Question 3

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

Answer 3

Question 4

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

A)
B)
C)
D)
E)

Question 5

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

A)
B)
C)
D)
E)

Question 6

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

A)
B)
C)
D)
E)

Question 7

Write the ratio as a fraction in lowest terms. to

A)
B)
C)
D)
E)

Question 8

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

A)
B)
C)
D)
E)

Question 9

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 10

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 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

An economy car travels 231 miles on 5.5 gallons of gas. Give the average fuel consumption of the car in miles per gallon.

A) 56 miles / gallon
B) 54 miles / gallon
C) 46 miles / gallon
D) 44 miles / gallon
E) 42 miles / gallon

Question 13

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 circumference of the wheel took 20 minutes, find the average speed of a rider in feet per minute.

Average speed = __________ feet / minute

Question 14

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

Question 15

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

A)
B)
C)
D)
E)

Question 16

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

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. Also, specify any restrictions on the variable.

A)
B)
C)
D)
E)

Question 19

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

A)
B)
C)
D)
E)

Question 20

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

Question 21

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

A)
B)
C)
D)
E)

Question 22

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 23

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

Question 24

Multiply the expressions.

A)
B)
C)
D)
E)

Question 25

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

A)
B)
C)
D)
E)

Question 26

Write the ratio as a fraction in lowest terms. to

Question 27

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

A)
B)
C)
D)
E)

Question 28

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

A) 1
B)
C)
D)
E)

Question 29

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

A)
B)
C)
D)
E)

Question 30

Multiply the expressions.

A)
B)
C)
D)
E)

Question 31

Multiply the expressions.

A)
B)
C)
D)
E)

Question 32

Write the ratio as a fraction in lowest terms. to

Question 33

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

A)
B)
C)
D)
E)

Question 34

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

A)
B)
C)
D)
E)

Question 35

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

Question 36

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 37

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 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

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

A)
B)
C)
D)
E)

Question 41

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 42

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 43

Perform the indicated operation.

A)
B)
C) x
D)
E)

Question 44

Perform the indicated operation.

A)
B)
C)
D)
E) y

Question 45

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 46

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 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.

A)
B)
C)
D)
E)

Question 48

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

Question 49

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 50

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

A)
B)
C)
D)
E)

Question 51

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 52

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 53

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 54

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 55

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 56

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 57

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 58

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 59

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 60

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

A)
B)
C)
D)
E)

Question 61

Perform the indicated operation.

Question 62

Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable.

A)
B)
C)
D)
E) no solution

Question 63

Perform the indicated operation.

Question 64

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 65

Perform the indicated operation.

Question 66

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 67

Complete the following table.

A)
B)
C)
D)

Question 68

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 69

Perform the indicated operation.

Question 70

Perform the indicated operation.

A)
B)
C)
D)
E)

Question 71

Perform the indicated operation.

Question 72

Perform the indicated operation.

Question 73

Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable.

A)
B)
C)
D)
E) no solution

Question 74

Perform the indicated operation.

Question 75

Perform the indicated operation.

Question 76

Perform the indicated operation.

Question 77

Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable.

A)
B) no solution
C)
D)
E)

Question 78

Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable.

A)
B)
C)
D)
E) no solution

Question 79

Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable.

A)
B)
C) no solution
D)
E)

Question 80

Perform the indicated operation.