A couple of words about unit rate definition
Of course, you’re impatiently waiting for a clear unit rate definition. In simple words, it can be defined as a comparison of any two separate, but quite related measurements, when the second of them is diminished to a value of one. We can’t do without the use of division when it comes to computing the unit rate.
In the world of math, rates as well as unit rates are employed to tackle many real world issues. For instance, it takes you thirty minutes for a tap to fill just one bucket. We’re eager to know how much time it will take to fill up to six buckets. We can find the answer by means the unit rate. So, as you see, it makes sense to keep studying the unit rate definition.
As for the example with buckets, here we can say that our unit rate to fill those buckets will be precisely 1/0.5 bucket an hour, so it’s two buckets an hour. Therefore, in order to fill six buckets, it will take 3 hours (six divided by two). However, problems of this type can be successfully solved with the help of proportions, though unit rates appear to be far more convenient for this purpose due to their simplified form and the denominator one.
Calculating the unite rate
Perhaps, the best way to grasp the very essence of the unit rate definition is to do it in the process of calculation. First, we should get back to the unit rate definition once again. The unit rate or UR for short, is a special type of ration, where the two separate measurements get compared and then expressed as a quantity of one solid thing. Let’s make it clearer:
- A rate can be defined as a ratio, where the two terms get measured in different units. In fact, all rates are rations, however, not all rations can be regarded as true rates.
- As for ration, it could be any comparison of two numerical measurements, and every measurement is dubbed term.
- Finally, the unit rate definition states that it’s a rate, which suggests that the second term is equal to one. So, when computing this stuff, you require determining how much of the first terms is true for each one unit of the second term.
Secondly, examine the data very attentively. The problem should come with two terms. You are expected to determine how much of one term is true per unit of another.
- In common examples, you’ll find unit price (cost per item), speed (miles per hour) and wage (earnings per week or hour).
- If you don’t know for sure whether you’re being asked exactly for the unit rate or not, just seek the word «per» in the description. That’s a typical distinctive feature of unit rates, though some of them come without this attribute. Let’s assume that this particular bakery is capable of baking up to 40 bread loaves for 8 hours. We’re eager to learn how many loaves could be baked in one hour or in to be exact per hour.
We keep learning the unit rate definition, and the next stage suggests rewriting the data as a sort of division problem. The very first term in the issue is the mound we’re trying to compute per unit. Let’s dub it the numerator or the top number. As for the second term, it’s the unit, we’ll call it the denominator or the bottom number. For instance, you’ve just been assigned to compute bread loaves per a certain unit of time. Well, in this case this unit would be an hour. So, the total number of loaves is the numerator, while the total hours should be regarded as the denominator. Therefore, if you divide 40 loaves by 8 hours you’ll obtain 5 loaves per hour.
Then, you’re welcome to divide both values by the denominator. In order to spot the unit rate, you require solving the newly written division issue. Thus, you’ll reduce your denominator to one.
Finally, you should write the solid solution. That would be your final answer.
Ensure you’ve just included both units in your answer. You’re free to separate them by means of the fraction sign or the word «per». For instance, this particular baker is capable of baking five loaves/hour or per hour.
Unit price
Here, you require examining the problem. In order to compute the unit price of any product, you should know for sure how much money it’s going to cost to purchase a certain amount of the product. Utilize this information to compute how many bucks or any other unit of currency it’s going to cost to buy one unit of the product, in other words – the cost per item.
For example, you bought seven boxes of cereal for $16.38. Let’s assume every box of cereal cost the same sum, compute the unit price on the cereal purchased by you. You should divide the overall cost by the total amount. In this particular case, you require dividing $16/38 by seven boxes. You’ll obtain $2.34 / box. So, the cost of the cereal is $2.34 per box.
A persuasive practical example – wage
In order to calculate wage, you should know how much money will be made during a certain period of time. It’s possible to utilize that information to find out how many bucks are going to be earned per one unit of time.
By the way, depending on the circumstances, the unit of time will greatly vary. In most cases, the unit of time employed will be an hour, though nothing prevents you to make use of a day, week, month and so on.
For instance, this week, Robert worked forty hours and earned up to$630.00 before taxes. You need to compute his wage or to be exact how much money he earns per hour. You require dividing the total pay by the overall time. You should rewrite your data as a fraction. In this case, the total pay would be your numerator, while the total amount of time would be the denominator. You require dividing your numerator by the dominator. So, $630 divided by 40 hours will give $15.75 per hour. The final answer: Robert’s wage per hour is $15.75.
Let’s calculate speed
We keep pursuing the unit rate definition, and now let’s see how unit rates could be useful when it comes to computing speed.
If you need to calculate the speed of a moving object, you should know the distance traveled within a certain period of time. Using the data, you should figure out the distance traveled per hour.
It’s clear that depending on the circumstances, the units will vary, though one unit should express distance, while another should express time.
For example, one family traveled 150 miles for 3 hours. Let’s assume, they drive the same speed all the trip. Determine their speed as an expression of miles/hour and it will help you to better understand the unit rate definition.
Your require writing the data as a fraction. In this case, the distance would be the numerator, while the amount of time would be the denominator. You require dividing the distance by the time. For instance, let 150 miles be your numerator, and three hours designate as the denominator. You’ll get a fraction, where 150 miles are divided by 3 hours. The answer will be 50 miles per hour. So the family drove their vehicle at a speed of fifty miles per hour.
Calculating gas mileage
We’ve just learnt enough and even almost grasped the unit rate definition. Just a couple of nuances are left to consider, and one of them is calculating gas mileage. In order to compute the gas mileage of a car, you should know the distance the car could overcome on a certain amount of fuel. Employ this date to compute how many miles can be past per gallon of gas.
For example, a particular family’s vehicle needs up to 4.2 gallons of gas to drive 150 miles. Being aware of this, we can figure out the average gas mileage of their car, expressed as miles per gallon.
As in the previous examples, you should also rewrite the available data in the form of a fraction. Here, your numerator would be the distance, while the overall volume of gas would act as the denominator. Having divided the numerator by the denominator, you’ll obtain gas mileage. So, divided 150 miles by 4.2 gallons and you’ll obtain 35.7 miles per gallon. So, the family’s vehicle boasts an average gas mileage 35.7 miles per gallon.
That’s how unit rates are utilized. Probably, you no longer have any question regarding the unit rate definition.
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