The Unit Rate is only one part of the bigger concept of rates. Rates as a concept are one of the most practical mathematics philosophies that humans implement almost daily. It is even as popular as the simple computations of Addition, subtractions, multiplication and division. You must have used the word rate when discussing prices and negotiating certain terms in many instances. For example, a freelance Voice creator could stipulate his/her price in terms of the number of words of voice-over service needed.
The freelancer could state that his price rate is $100 for a 1500 words voice-over. In this particular instance, the concept of rate has been used. This is because there is a comparison between two related and yet different quantities, which in this instance are the price and the number of words. To fully understand the compared quantities, they need to be expressed as ratios. A ratio is like a division between two quantities and can show how one quantity differs from the other. It is expressed in the form of a fraction i.e. Number of words/price.
Typically, the quantities that make up a ratio can be interchanged. That is, they could be expressed as
or as
However, it is most preferred that the numerator has the largest quantity in terms of numbers while the denominator has the fewer quantities. It is important to note that this is not a condition that must be followed as convenience of division and the context in which comparison is being made must be observed. Based on the above description, a rate is simply a ratio of two compared quantities. On the other hand, A Unit rate is a ratio whose denominator has been reduced to one. This means in context that one of the quantities has been expressed in its basic form with respect to the other quantity. For example, since the freelancer would perform a voice over of 1500 words for $100, then the price rate per word would be
the $0.06 is the unit rate for the job because if expressed as a ratio will be $0.06/1
which is literally $0.06
This article will explain the concept of Unit rate and what mathematicians should expect when calculating it.
Unit Rate Definition
Unit Rate is a ratio of two related distinct quantities where the denominator quantity is simplified to one.
Mathematically, the unit rate is expressed as;
The above expression is the Unit Rate formula.
How to Calculate the Unit Rate?
Step 1: Express the Quantities in ratios
Step 2: Divide until the denominator becomes 1
Note: If the problem is actually in the form of a word problem, then it must first be fully understood before it is expressed as a form of a ratio.
What Does Unit Rate Mean?
The example considered in our example is actually what a Unit rate is about. However, it is important to know that the example is simply basic. The unit rate can be a bit complicated when there are surrounding complex factors concerning its calculation. For example, the concept could come in the form of Word Problem, which is the case for accountants and Human Resources Professionals who have to make important decisions that could affect employment and relieving of staff. Also, the concept can be applied in pretty much every industry, including military, logistics and judging performance of tolls and humans in the simplest way.
The Unit Rate can even make the statistician or mathematician provide insight into what a company can do to get the best out of the product. From the result, the statistician may decide to employ further analysis like the empirical rule for better insight.
We will now consider some major examples of Rates and how they can be applied.
Example 1
If a 25-litre fuel tank costs $200, how much will a driver spend for just a litre?
Solution
The best solution to use in this case is the Unit Rate. We will now follow the steps for solving the unit rate.
Step 1: Express the Quantities in ratios
Since 25 litres cost $200, it can be expressed as
Step 2: Divide until the denominator becomes 1
Just like the first example, this means that it will take $8 to buy a liter of fuel.
This example is pretty straightforward. However, unit rate is more helpful in a situation where there is a level of complexity and there is a need for a very good level of clarity. The Unit rate can easily help break down the confoundedness in such situations and make it very easy for people or companies to determine if they are making profits or not.
The next example will consider a bit of a complex example to explain what we are driving at.
Example 2
A manufacturing company employed a statistician to help identify whether a particular staff is being overpaid for his production services. The statistician was given details concerning the production output of the staff for the last year. According to the report, the staff was found to produce 10,000 products for an annual salary of $100,000.
To get more information about the staff, the statistician asked the manufacturing company how much was the production cost and other related costs for the entire 10,000 products. Also, he asked for the entire revenue generated for the same products. The 10,000 units were found to attract a cost of $200,000 and revenue of $500,000.
The statistician decides to use unit rate to identify whether the staff was productive or not?
Solution
The Staff production capacity = 10,000 units
The staff salary = $100,000
The production revenue = $500,000
The production cost = $200,000
The statistician’s aim is to calculate whether the staff salary for each product is lesser or higher than the profit made from each day. To do this, the statistician will need to find the unit rates of the staff salary, production revenue and the production cost.
After that, he will also need to subtract the unit cost from the unit revenue and compare it to the unit salary of the staff.
Step 1: Express the Quantities in ratios
Production capacity rate:
Production Revenue Rate:
Production Cost Rate:
Step 2: Divide until the denominator becomes 1
Production capacity unit rate:
This means that the staff salary for each produced product is $10
Production Revenue unit rate:
This means that the revenue derived from each product that the staff produced is $50
Production Cost unit Rate:
The cost for each product is $20
Obviously, the Unit rates for all of the products have been computed, but that is not where it stops. The statistician will have to analyse whether the staff salary for each product is worth it. To do this, the staff Unit salary must be significantly lesser than the unit profit made from each product.
Unit profit per product = Production Revenue unit rate – Production Cost Unit Rate
Unit profit per product = $50 – $20 = $30.
Now the staff unit salary is $10.
Unit profit per product – unit salary = $30 – $10 = $20
This means that for every $10 paid to the staff, the company makes a profit of $20. As such it can be said that the staff is productive.
However, how productive the staff is would be judged by the Human Resource specialist depending on the expected performance that the company requires from the staff. Based on expected work ethics, it is considered that the optimal profit a company can make hiring an employee should be 10 multiplied by the employee’s salary. So why $20 is quite commendable. Makin $100 from the employee would be considered the optimal option for the company.
However, as already stated, it would depend on the human resource specialist and the company to determine if they are satisfied with the employee commitment or if it is the product they need to work on.
Conclusion
As can be seen from the examples, the unit rate calculation is very simple as expressing ratios does not require a lot. Also, the second example showed that the Unit rate could be very useful for analysing the performance and ability of staff. For simple comparisons, it can help a company know the most efficient staff in its employment portfolio. In the same vein, Unit rate can be employed to production machines and determine whether a machine is defective by comparing its defective products to others and ascertaining if its defective products are due to randomness or poor performance.
Unit rate can be expressed as simple calculations and can help resolve bogus and certain complex situations. All you need to do is to know how to use it and determine the instances where it can be implemented. This is because certain problems will not provide answers and trying to use them may not lead to the required solution you want.
You can continue to solve other examples by following the steps and examples shown in this article.
