Mastering Adding & Simplifying Rational Expressions

A recipe requires 3/4 cup of sugar for 2 servings. How much sugar is needed for 5 servings? Simplify your answer as a rational expression.

• 15/8

• 1/2

• 1 cup

• 2/3

A car travels 1/2 of a mile in 1/4 hour. What is the car's speed in miles per hour? Express your answer as a simplified rational expression.

• 4

• 1

• 2

• 3

Two friends are sharing a pizza. One friend eats 2/3 of the pizza and the other eats 1/4. How much pizza is left? Add the fractions and simplify the result.

• 1/6

• 1/8

• 1/4

• 1/12

A gardener has 3/5 of a bag of soil. If he uses 1/10 of the bag for a plant, how much soil does he have left? Express your answer as a simplified rational expression.

• 1/2

• 3/10

• 2/5

• 27/50

A tank can be filled by a pipe in 1/3 hour and emptied by another pipe in 1/6 hour. How long will it take to fill the tank if both pipes are open? Add the rates and simplify the expression.

• The tank will take 1 hour to fill.

• The tank will take 1/2 hour to fill.

• The tank cannot be filled.

• The tank will overflow in 1/4 hour.

A recipe calls for 1/2 cup of oil and 1/3 cup of vinegar. How much liquid is needed in total? Add the fractions and simplify your answer as a rational expression.

• 5/6

• 1/2

• 2/3

• 3/4

A cyclist travels 3/4 of a mile in 1/2 hour. What is the cyclist's speed in miles per hour? Express your answer as a simplified rational expression.

• 3/2

• 3/4

• 2

• 1

A school has 2/5 of its budget allocated for sports and 1/3 for arts. How much of the budget is allocated for both? Add the fractions and simplify the result.

• 7/15

• 11/15

• 1/2

• 3/5

A baker uses 1/4 of a cup of flour for each cookie. If he makes 12 cookies, how much flour does he use in total? Express your answer as a rational expression and simplify.

• 3

• 2

• 5

• 4

A tank can be filled in 2/3 hour and emptied in 1/4 hour. If both actions happen simultaneously, how long will it take to fill the tank? Add the rates and simplify the expression.

• The tank will never fill.

• The tank will fill in 15 minutes.

• The tank will fill in 30 minutes.

• The tank will fill in 1 hour.