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 calculate a unit rate from a complex fraction?

Back

To calculate a unit rate from a complex fraction, divide the numerator by the denominator. For example, if you have 3/4 of a mile in 1/2 hour, the unit rate is (3/4) ÷ (1/2) = 3/4 * 2/1 = 3/2 miles per hour.

Front

What is the formula for speed?

Back

Speed is calculated using the formula: Speed = Distance ÷ Time.

Front

How do you convert a mixed number to an improper fraction?

Back

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place that sum over the original denominator. For example, 3 2/5 = (3*5 + 2)/5 = 17/5.

Front

What is the first step in solving a problem involving unit rates?

Back

The first step is to identify the quantities involved and determine the total distance or amount and the total time or number of items.

Front

How do you compare two unit rates?

Back

To compare two unit rates, calculate each unit rate and then compare the values. The larger value indicates the better rate.

Front

What is the unit rate for 1/6 acre mowed in 1/4 hour?

Back

The unit rate is (1/6) ÷ (1/4) = (1/6) * (4/1) = 4/6 = 2/3 acres per hour.

Front

How do you find the unit rate when given a fraction of a quantity?

Back

To find the unit rate, divide the fraction by the time or quantity it corresponds to. For example, if Hannah reads 5/8 page in 2/3 minute, the unit rate is (5/8) ÷ (2/3) = (5/8) * (3/2) = 15/16 pages per minute.

Front

What is the significance of unit rates in real-life situations?

Back

Unit rates help compare prices, speeds, and efficiencies, making it easier to make informed decisions, such as choosing the best deal or understanding travel times.

Front

How do you convert a fraction to a decimal?

Back

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.