Unit Rates With Complex Fractions

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as a quantity of one. For example, if a car travels 300 miles in 5 hours, the unit rate is 60 miles per hour.

Front

How do you find a unit rate from a complex fraction?

Back

To find a unit rate from a complex fraction, divide the numerator by the denominator to simplify the fraction, then interpret the result as a rate per one unit.

Front

If Jaycee read 1/10 of a novel in 1/2 hour, how do you calculate the time to read 1 novel?

Back

To find the time to read 1 novel, set up a proportion: (1/10 novel)/(1/2 hour) = (1 novel)/(x hours). Cross-multiply and solve for x to find that it takes 5 hours.

Front

How many 1/3 cup servings are in 18 3/4 cups of ice cream?

Back

Convert 18 3/4 to an improper fraction (75/4). Then divide by 1/3: (75/4) ÷ (1/3) = (75/4) * (3/1) = 225/4 = 56 servings.

Front

What is the rate of water leaking from a pool if it leaks 7/8 gallon in 1/2 hour?

Back

To find the leak rate, divide 7/8 gallon by 1/2 hour: (7/8) ÷ (1/2) = (7/8) * (2/1) = 14/8 = 7/4 gallons per hour.

Front

If Paige mows 1/6 of an acre in 1/4 hour, how do you find her mowing rate per hour?

Back

Set up a proportion: (1/6 acre)/(1/4 hour) = (x acres)/(1 hour). Cross-multiply to find x = 2/3 acres per hour.

Front

How much sugar is needed for 1 batch of brownies if 2/3 cup is needed for 1/3 batch?

Back

To find the amount for 1 batch, set up a proportion: (2/3 cup)/(1/3 batch) = (x cups)/(1 batch). Cross-multiply to find x = 2 cups.

Front

What is a complex fraction?

Back

A complex fraction is a fraction where the numerator, the denominator, or both are also fractions. For example, (1/2)/(3/4) is a complex fraction.

Front

How do you simplify a complex fraction?

Back

To simplify a complex fraction, multiply the numerator and the denominator by the least common denominator (LCD) of the fractions involved.

Front

What is the relationship between unit rates and proportions?

Back

Unit rates can be expressed as proportions, where one quantity is compared to one unit of another quantity.