This Unit Rate Calculator will help you calculate the unit rate for a given fraction. This article will introduce you to the definition of the unit rate, formulas, graphical display, and many other exciting things related to the unit rate through the article. 

What is a unit rate? Unit rate definition

It is necessary to say a few introductory and basic information about the unit rate itself. The name unit rate refers to the specific type of ratio that bears the name and the rate with one unit. This way, you can compare one unit of a quantity to many different units of different quantities. It is the rate type in which the lowest number is the number 1. You can also look for an explanation from the mathematical aspect, where the rate is the ratio with which you can compare two different quantities with different units. 

Simply, you can compare the second quantity with the number 1. For example, one minute has 60 seconds, so you can express the unit speed as 60 seconds per minute, where part of the phrase “per minute” actually refers to one minute. This type of rate can make the process of comparing data values more accessible for you. Different unit rates are known and used worldwide, such as miles per hour, kilometers per hour, price per unit, number of revolutions per minute, and many others.

Ratio and Unit Rate
Ratio and Unit Rate

Unit Rate Equation

You can use Unit Rate Calculator to calculate the unit rate and the process is straightforward. Given the fact that the rate is the ratio of two different quantities to different units, you can therefore derive a formula accordingly. Examples of unit rates are miles per hour or dollars per ounce. You can use the word “per” to explain the relationship between quantity and unit. If you replace the word “per” with the symbol “/”, the quantity by “a” and the unit by “b”,  the formula for calculating the unit rate looks like this:

U_{r} = \frac{a}{b}

Following the given formula, you can conclude that you always express the unit rate as quantity 1. So it would look like this below:

\frac{a}{b} = \frac{c}{1} \Rightarrow \frac{a}{b} = c

where c is a value that satisfies a given equation and a solution for the ratio of two numbers.

Ratios and rates

If you want to compare two values, in that case, you would very likely use a ratio. In many cases, you can represent this as a fraction, using a fractional line or a colon. For example, if the test result is 82% and the grade point average is 55%. You can calculate the ratio by comparing the result with the grade point average, which would look like 82/55.

The result obtained would represent a mean value which, if it is greater than 1, your result achieved in the exam is above average. While on the other hand, a rate is a unit that tells you how much the value of the first number corresponds to the second number. For example, if you have a cat and give it occasional treats as a reward.

If your cat eats 15 treats in seven days, then the rate of treats eaten will be 15 treats in 7 days. The table below shows several differences between these two terms:

RateRatio
Different units are taken into comparison.Same units are taken into comparison.
Rate of two quantities are expressed using the word “per” or the symbol “/”.Ratio of two numbers are expressed using the word “to” or the symbol “:”.
Example: 100 miles per hour, or 100 miles/hourExample: 3 apples to 2 cups of milk, or 3:2 apples to cups of milk.
Difference between rate and ration

Rate constant units

Let’s start first with the reaction rate, which decreases with time due to the decrease in the concentration of reactants. The reverse situation with increasing speed also applies to the reaction speed. Rate laws are also linked here. They are math descriptions of confidential data, which you can write from different perspectives. You can use the reaction rate law for reaction rate, representing the relationship between reaction rate and species concentration.

You can also present the law of reaction speed as a change in the concentration of reactants or products per unit time, which you can express as M / s. The rate constant marked k represents the proportionality constant of the reaction rate and the reactant concentration, with the unit of reciprocal second (s-1). The unit of this measure depends on the law of velocity for a particular reaction. The concentration increases to a specific exponent, showing the degree to which the reaction rate depends on the reactant concentration.

Unit rate problems

Below we will solve one example of unit rate problems:

Let’s say you are in a situation where you pay a particular company $ 90 every six months to host your website. What amount of money do you allocate monthly for hosting, and what is that amount for ten months?

Solution: 

Using our calculator, you can get the rate value. First, you need to write the rate as follows:

Cost / time = $ 90/6 months

The second step involves using a fraction line to find the cost per month value, which looks like this:

\frac{90}{6} = 15

That is equal to $ 15/1 or $ 15 per month.

In the third step, you can answer the question of how much money you would earn in 10 months:

\frac{15}{1} = \frac{x}{10} \Rightarrow x = 150

Answer: 

The conclusion is that you pay $ 15 each month and $ 150 for ten months of hosting your site.

Unit rate graph

The following example will explain how you can represent the rate value on a graph.

Take, for example, the case where a car consumes five liters of fuel for every 60 kilometers traveled. By plotting values on a graph, you get the following:

Unit rate graph
Unit rate graph

If the car has 20 liters of fuel in the tank, it will cover 240 kilometers. You can read from the chart that after 180 kilometers, the car consumes 15 liters of fuel. By connecting the dots, you get a straight line. According to all data from the text, the unit rate in this case is:

\frac{60}{5} = 12

This means that the car covers 12 kilometers for 1 liter of fuel.

Example – How to find the unit rate? Unit rate example

Take, for example, the situation where a chocolate shop offers you 25 chocolates for $ 10. How much is the price of one chocolate?

This example shows you how our unit rate calculator works. You can see the unit rate steps after entering the value. The value of “a” equals the price of $ 10, while the value of “b” equals 25 chocolates. You can obtain the unit cost of chocolate by comparing the cost of chocolate with the number of chocolates, so the unit cost is $ 0.4.

FAQ?

1. What is the formula for unit rate?

You can calculate the unit rate by creating a fraction ratio, where you will need to divide the numerator by the denominator. Following this, the formula has the following appearance: unit rate = a / b

2. What is a unit rate in math?

The name of the unit rate observed from the field of math science means the rate for one unit of something. You can write this by putting a denominator 1 to the ratio. If you ran 50 yards for 10 seconds, the unit rate is 5 yards per second.

3. How to find the unit rate with fractions?

For example, we will take that Miley rides 11/4 miles per 3/4 hours. What is the rate of miles per hour? Using the basic formula, you can get the amount of value, as below:
(11/4) / (3/4) = (11/4) x (4/3) = 44/12 = 3,66 …
The answer is that Miley rides 3.67 miles per hour.