A “ratio” is any comparison of two numerical measurements. Each measurement is called a “term. " A “rate” is a ratio in which the two terms are measured in different units. All rates are ratios, but not all rations are rates. A “unit rate” is a rate in which the second term equals “1. " When calculating a unit rate, you need to determine how much of the first term exists for every one unit of the second term.
Common examples include: speed (miles/kilometers per hour), unit price (cost per item), and wage (earnings per hour/week). [2] X Research source If you aren’t sure about whether or not you’re being asked for the unit rate, look for the word “per” somewhere in the description. Some unit rate problems won’t include “per,” but many do. Example: A certain bakery can bake 40 loaves of bread in an 8 hour work day. How many loaves of bread can that same bakery make in one hour? In other words, how many loaves of bread are typically baked per hour?
Example: You must calculate loaves of bread per unit of time (in this case, the unit of time is an hour). The total loaves of bread will become the numerator, and the total hours will become the denominator, giving you: 40 loaves / 8 hours
Example: Divide the total number of loaves by the total number of hours: 40 loaves / 8 hours = 5 loaves/hours
Make sure that you include both units in your answer. You can either separate the units with the fraction sign (/) or with the word “per. " Example: This bakery can bake 5 loaves/hour. Alternatively, you could write, “This bakery can bake 5 loaves per hour. ”
In other words, you are calculating the cost per item. Example: Jennifer purchased 7 boxes of cereal for a total cost of $16. 38 (without tax). Assuming each box of cereal cost the same amount of money, calculate the unit price on the cereal Jennifer purchased.
Example: The total cost, $16. 38, should be set as the numerator. The number of items, 7, should be set as the denominator. In other words, the cereal costs: $16. 38 / 7 boxes Treat the fraction as a division problem and solve: $16. 38 / 7 boxes = $2. 34 / box
Make sure that you include both units labels in your answer. Example: The price per box of cereal is $2. 34. Another way of writing this answer would be: The cost of the cereal is $2. 34 / box.
Essentially, you calculating the cost per unit of time. Note that the unit of time will vary depending on the circumstances. In many cases, the unit of time used will be the “hour. ” In some cases, though, you may need to use “day,” “week,” “month,” or “year. ” Example: Robert worked 40 hours this week and earned $630. 00 before taxes. Calculate Robert’s wage as an expression of how much money Robert earns per hour.
Example: Set the total pay, $630, as the numerator. Set the total number of hours, 40, as the denominator. You should have: $630 / 40 hours Divide the fraction accordingly: $630 / 40 hours = $15. 75 / hour
You must include both units labels in your answer. Example: Robert’s earns a wage of $15. 75 per hour.
In essence, you are calculating the distance per unit of time. The units will vary depending on the circumstance, but one unit must express distance (mile, kilometre, feet, meters, etc. ) and the other unit must express time (hours, minutes, seconds, etc. ). Example: The Smith family travelled 150 miles in 3 hours. If they drove the same speed during the entire trip, how fast did the Smith family car drive as an expression of miles per hour?
Example: Set the total number of miles, 150, as the numerator. Set the total number of hours, 3, as the denominator. This should give you a fraction of 150 miles / 3 hours Treat the fraction as a division problem: 150 miles / 3 hours = 50 miles / hour
Make sure that both unit labels are included in your final answer. Example: The Smith family drove their car at a speed of 50 miles per hour (miles/hour).
This means that you’ll be calculating the distance per volume of gasoline. The units may vary based on circumstance, but one must express distance (usually miles or kilometres) and the other must express volume (usually gallons or litres). Example: The Smith family’s car needed 4. 2 gallons of gasoline to drive a distance of 150 miles. Based on this information, determine the average gas mileage their vehicle is capable of as an expression of miles per gallon.
Example: The number of miles, 150, should be the numerator and the number of gallons, 4. 2, should be the denominator. This means that: 150 miles / 4. 2 gallons Treat the fraction as a division problem and solve: 150 miles / 4. 2 gallons = 35. 7 miles / gallon
Both unit labels must be included in the final answer. Example: The Smith family’s car gets average gas mileage of 35. 7 miles/gallon (miles per gallon).
