Introduction
Finding a balance is all it is about and the world around us is no stranger to it. There are many contexts where we need to strike a relation between two quantities to find ‘just the right amount’ for everything. This might be for some jolly and cheerful baking or some serious accounting homework, ratios and rates are used literally in almost every field. Although both of them involve finding a relationship between two quantities by division, they lie miles apart in their fundamentals. Let's take a closer look at how:
Rate vs. Ratio
The main difference between rate and ratio lies in their features. The rate can have one or more dimensions whereas the ratio is a dimensionless element. This is because ratio defines the relationship between two values of the same unit. On the other hand, rate defines how a quantity changes concerning another, thus it has dimensions.
Difference Between Rate and Ratio in Tabular Form
| Parameters of Comparison | Rate | Ratio |
| Fundamentals | Describes the frequency of the occurrence of a certain event. | Describes the relationship between any two quantities of the same unit. |
| Dimension | Rate can be one or more dimensions. | The ratio is a dimensionless quantity. |
| The fraction form | Rate is easier to calculate and demonstrate when the denominator has a unit value i.e., 1, while the numerator can vary. | When the ratio is fixed, the numerator changes if the denominator varies and vice versa. |
| Need of similar units | Rate is not measured between quantities of the same units. | The ratio is calculated for quantities of the same units. |
| Representation | Rate is usually measured and referred to with the keyword ‘per’ and represented with ‘/’. | Ratio is calculated and represented with the symbol ‘:’. |
| Example | Kilometers per hour(km/h), rupees per month, bits per second(b/s) | 6:5, 7:12, 8:3 |
What is Rate?
The rate can be described with many variations, depending on the context it speaks about. A few ways we can use to define rate are:
- The frequency of one quantity with respect to another quantity. This can also be put as how many times one quantity can occur for every unit occurrence of the second quantity.
- How one measurement can change with respect to another measurement.
- Rate can also be defined as the value of one quantity for every bit of the other quantity.
From the above definitions, it is clear that rate involves two quantities of different units and calculates the frequency of occurrence of either of the quantities. But how is a rate represented?
How is a rate represented?
We have learned that rate involves the calculation between two quantities. Thus, the end product must have a certain unit representation when multiple units are involved. How is this done?
- Amongst the two quantities involved, we choose the quantity whose frequency is being calculated, divided by the frequency against which the frequency is being calculated.
- We can simplify it further and refer to it as the quantity we take in the numerator and the units of the quantity in the denominator, taken in fraction form., i.eThey are divided.
- Any similar units get canceled off approximately and the remnant units are represented as units along with the final value.
- The short form representation is done by using ‘/’ and the long-form representation by using ‘per, both between the remnant units.
For example, when we calculate the speed of a vehicle, we calculate the distance against the time taken to travel that certain distance.
Thus, we write- Speed=DistanceTime=KilometersHours=kmh
When written in a simpler form, km/h can also be referred to as kmph. We can also use the long-form representation and call it ‘kilometers per hour. These units are used right beside the final measurement of the rate.
Although here we do not have any cancellable terms, rates, when calculated in terms of chemistry concepts, have several units that can be canceled while calculation. Thus, one must always be careful while representing because we wouldn't want that ‘-1’ for wrong units on the test now, do we? :)
We have been talking a lot about this ‘final value’, but how exactly does this calculation proceed?
How is it calculated?
Rate is simply calculated by dividing one quantity against the other. But the tricky part arrives when people often get confused as to which quantity to divide against the other. Easily put, when a question is framed in a way that says, “How many liters does the tap fill per hour?”, it indicates that the quantity describing the measurement of the liquid i.e., liters must be divided against the quantity that describes time i.e., hours.
It is always easier to explain with an example so let us consider a problem statement that states: A general store sells 1800 cans of soda, 360 tubes of cream, and 432 containers of dog food. Calculate how many of each are sold per hour?
Since there are 24 hours in a day, we will need to divide each of these quantities by 24 hours.
The number of soda cans= 180024=75
This is described as 75 cans of soda per hour.
Number of cream tubes= 36024=15
This is described as 15 tubes of cream per hour.
Number of dog food containers= 43224=18
This is described as 18 containers of dog food per hour.
Where do we use rates in daily life?
There are many times of rates and the most common one of them all is the kind of rate that is measured with respect to time. This time can be taken as:
- seconds or hours when considering the speed of automobiles
- Minutes when calculating heartbeat or rhythm
- Months or years when calculating finance-related matters such as interest.
Rates are used in many technical areas that require the frequency of sampling a signal:
- Bitrate, sampling rate, and symbol rate are very important considerations while studying the subject of Information Theory and Coding in Electronics.
- Radioactive decay is another topic vital to students attempting competitive exams where the rate of decay is calculated.
As previously mentioned, finance uses a lot of rate concepts since numbers are all they’re made of!:
- Exchange rate
- Interest rate
- Tax rate
- Wage rate
- Inflation rate, etc.
Other contexts where the rate is calculated to include that of a census:
- Birth rate/ mortality rate
- Literacy rate, etc.
What is Ratio?
Unlike rate, the ratio can be explained in a much simpler way. The ratio describes the relationship between two quantities that have the same units. When a ratio is calculated between two units, you also infer what proportion one quantity is of the other. It is important to know that one must be careful while evaluating ratios as they might confuse the quantities since they are dimensionless. Thus there must be clarity in the order in which the ratio is measured.
How is the ratio represented?
We have seen that a ratio involves two quantities of the same unit. Thus when representing a ratio, one must be mindful of the following points to be accurate:
- A ratio must not have any units.
- Ratio can also be made equivalent to fraction and vice versa, as long as the fraction is not accompanied by any units. For eg:- A/B can be written as A: B.
- The ratio is generally represented by scaling down to its prime factors.
- The scaling down is typically done only until the numbers are integral.
- The numbers, in their appropriate order, must be represented with a full colon between them i.e., ‘:’.
Now that we have covered the topic of accurately representing a ratio, let us move on to how a ratio is calculated.
How to calculate a ratio?
The ratio is simply calculated by canceling out the common factors of each term until they are scaled down to numbers that no longer have common factors. Sounds difficult? Fear not:), It is a simple division process. It is quite similar to the process of calculating rate but instead, we can avoid the hassle of units altogether.
- The two terms are considered in the required order.
- Most basic way involves taking the numbers in a fraction form, for higher understanding.
- When the ratio must be calculated between A to B, we write it as A: B= AB
.
- Once in fraction form, the numbers are canceled off and scaled-down until no more operation can be done. For eg:- 4/6= 2:3
- People with practice do not convert to fractions and directly calculate the scaled-down number.
- The final result is converted and represented in the required ratio format.
Again, we will use an example that will not only show you how ratios are calculated but also how they differ from rates. Consider the problem statement: There is a cocktail recipe for a party that demands 750ml of mango juice, 400ml of lime juice, and 1200 ml of soda. Calculate the ratio of the mango juice to the soda.
Here, the fraction form can be assumed as= quantity of mango juicequantity of soda=7501200=58=5:8
A ratio does not necessarily need to have a smaller numerator and a bigger denominator.
Calculate the ratio of the total quantity of cocktail to lime juice.
Here, the total quantity of mocktail amounts to 750+400+1200=2350
The ratio is calculated as= 2350400=478=47:8
Ratios are not calculated just for integral numbers but can also be calculated for quantities that are in decimals. We can follow the same process of division and obtain the final result accurately.
Applications of ratios in daily life:-
While there are many censuses and similar contexts that deal with ratios, finance and accounting win this round again. So let's look at some examples of ratios used in the financial field:
- Liquidity ratios such as cash ratio, quick ratio, and current ratio.
- Profitability ratios such as return on assets ratio.
- Turnover ratios
- Market value ratios
Ratios are also used in the field of chemistry, this can be both on a student level to calculate the strength of their formulas or on a much higher research level:
- Dilution ratio
- Mole ratio, etc.
A lot of aptitude problems also involve the use of ratios such as:
- Time & speed problems
- Boat and stream problems
- Weight based problems, etc.
Main Differences Between Rate and Ratio in Points
- Rate describes the frequency of occurrence of a certain event in terms of two different quantities whereas ratio describes the relationship between two quantities that possess the same units.
- Rate is calculated when the numerator varies while the denominator is fixed when taken in a fraction form. This represents the frequency of the quantity in the numerator for every one occurrence of the denominator. On the other hand, ratio represents how much of a proportion one quantity is of the other and vice versa.
- Rate is measured between quantities that do not have the same units whereas ratios are measured between two quantities that are of the same units.
- Supporting the above statement, we can infer that the rate has more than one dimension whereas the ratio is a dimensionless quantity.
- When represented in the fraction form, the rate is easier to calculate when the denominator is equal to one while the numerator can have any value. It is easier to calculate frequency this way. Ratio, once fixed, does not allow to fix any one quantity. when the denominator changes, so do the numerator, to keep the ratio constant, and vice versa.
- When the rate is calculated, it is referred to with the word 'per' and represented with the symbol '/' between the two quantities. Ratio, however, is represented with the symbol ':' between the two quantities.
- A few examples of how a rate can be represented are kilometers per hour(km/h), and bits per second(b/s). A few examples of representation of ratio are 6:5,7:12,9:2.
Conclusion
We can conclude by summarizing that rates are more about finding the frequency of either of the quantities with the other as a reference whereas ratios merely calculate the relation between the two given quantities. Hope we cleared your confusion! :)
