Unit Rates with Fractions

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It expresses how much of one quantity corresponds to one unit of another quantity.

Front

How do you calculate a unit rate from a total cost and quantity?

Back

To calculate a unit rate, divide the total cost by the quantity. For example, if the total cost is $3.75 for 3 pounds, the unit rate is $3.75 ÷ 3 = $1.25 per pound.

Front

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

Back

To find the rate in acres per hour, first find how many 1/4 hours are in an hour (4), then multiply the amount mowed (1/6) by 4. So, 1/6 * 4 = 2/3 acres per hour.

Front

What is the formula to find speed in miles per hour?

Back

Speed (in mph) = Distance (in miles) ÷ Time (in hours).

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 over the original denominator.

Front

If Joe runs 3 2/5 miles in 7/8 of an hour, how do you calculate his speed?

Back

Convert 3 2/5 to an improper fraction (17/5), then divide by 7/8. Speed = (17/5) ÷ (7/8) = (17/5) * (8/7) = 3 31/35 mph.

Front

What does it mean to find how many items can be completed in a unit of time?

Back

It means to determine the rate at which an activity is performed, such as how many pies Kyle can eat in one minute.

Front

How do you find the rate of pies eaten per minute if Kyle eats 1/2 of a pie in 1/5 of a minute?

Back

To find the rate, calculate how many pies can be eaten in one minute: (1/2) ÷ (1/5) = 2 and 1/2 pies per minute.

Front

What is the relationship between distance, speed, and time?

Back

The relationship is defined by the formula: Distance = Speed × Time.

Front

If Tony walked 3 1/2 miles in 7/8 of an hour, how do you find how far he can walk in one hour?

Back

To find the distance in one hour, set up a proportion: (3 1/2 miles) / (7/8 hour) = x / 1 hour. Solve for x to find that he can walk 4 miles in one hour.