Deck 6: Section 2: Rational Expressions

Question 1

Reduce the expression to lowest terms.

Answer 1

Question 2

Reduce the expression to lowest terms.

Answer 2

Question 3

Reduce the given expression to lowest terms.

Answer 3

w - 1

Question 4

Simplify.

Question 5

Jimbo biked 50 miles at x mph. He then increased his speed by 5 mph and biked another 40 miles. Write a rational expression for Jimbo's total travel time.

Question 6

Build the rational expression into an equivalent rational expression with the indicated denominator.

Question 7

Marta averaged miles per hour for the x hours in which she drove home. Later, she drove another hour at the same rate to her parents' home. How many miles did she drive to her parents' house?

Question 8

Reduce the given expression to lowest terms.

Question 9

Solve the equation. Watch for extraneous solutions.

Question 10

Hugo empties his piggy bank onto his kitchen table. After the coins come to rest, one-fourth of the nickels are heads up, two-thirds of the dimes are heads up, and one-half of the quarters are heads up. The figure below shows the composition of the coins that were in the piggy bank. Use the figure and the given information to determine the percentage of coins that are heads up.

Question 11

David hires a septic system contractor to dig trenches for his new septic tank. The cost to hire the contractor is a fixed cost of $250 plus an additional $80 per hour. Write an expression which describes the average cost of an x-hour job.

Question 12

Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator.

Question 13

Perform the indicated operations and write your result in lowest terms.

Question 14

Find the least common multiple of the given terms.
q² + 7q - 30, q² + 20q + 100

Question 15

Perform the indicated operations and write your result in lowest terms.

Question 16

Find the indicated value for the given rational expression.

Question 17

Among 100 college students, 40 said they study 11 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 11 hours per week to those that do not?

Question 18

For the given ratio, find and equivalent ratio of integers in lowest terms.

Question 19

Solve the equation.

Question 20

Perform the indicated operations and write your result in lowest terms.

Question 21

Solve the equation for y.

Question 22

Chris prepares a 10-pound mixture of cashews and peanuts. He paid $18 for the cashews and $14 for the peanuts. If cashews cost three times more than peanuts, then how many pounds of cashews did he use?

Question 23

Solve the given equation.

Question 24

Cora can paddle her canoe 8 miles in the same time that Susan's motorboat covers 28 miles. If Susan's boat travels 10 mph faster than Cora's canoe, then how fast is Susan's boat?

Question 25

A large pump can fill a 78,000 gallon reservoir in 8 hours. Working together, the large pump and a smaller one can fill the reservoir in 6 hours. How long would it take the smaller pump to fill the reservoir by itself?