Exam 6: Reducing Rational Expressions to Lowest Terms

The scale on a map indicates that 1 inch on the map corresponds to an actual distance of 95 miles. Two cities are 7.5 inches apart on the map. What is the actual distance between the two cities? __________ miles

A map is drawn so that every 3.5 inches on the map corresponds to an actual distance of 100 miles. If the actual distance between the two cities is 220 miles, how far apart are they on the map?

A solution contains 12 milliliters of alcohol and 16 milliliters of water. If another solution is to have the same concentration of alcohol in water but is to contain 32 milliliters of water, how much alcohol must it contain?

Perform the indicated operation.

A basketball player makes 6 of 9 free throws in the first game of the season. If she shoots with the same accuracy in the second game, how many of the 21 free throws she attempts will she make?

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

Solve the following proportion.

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.

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

Solve the following equation. If impossible, answer no solution . Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable. x = __________

A bathtub can be filled by the cold water faucet in 17 minutes and by the hot water faucet in 18 minutes. The drain can empty the tub in 14 minutes. Can the tub be filled if both faucets and the drain are open?

Perform the indicated operation.

Travis paddles his kayak in the harbor at Morro Bay, California, where the incoming tide has caused a current in the water. From the point where he enters the water, he paddles 2 miles against the current, then turns around and paddles 2 miles back to where he started. His average speed when paddling with the current is 2 miles per hour faster than his speed against the current. If the complete trip (out and back) takes him 1.5 hours, find his average speed when he paddles against the current.

A man drives his car 123 miles in 3 hours. At this rate, how far will he travel in 11 hours? __________ miles

Solve the following equation. If impossible, answer no solution . Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable. x = __________

Simplify the complex fraction.

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

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.

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.

Simplify inside the parentheses first, then multiply.