Ratio and proportion are most commonly used terms in mathematics. Students use these concepts to solve their mathematical problems at different level of studies while in businesses many monetary transactions are based on ratio and proportion. In our daily life, a lot of examples are available that uses the concept of ratio and proportion such as measuring time, distance, speed, weight etc. In this topic, we will briefly discuss about these two important concepts ratio & proportion and we will further elaborate the relationship between them with the help of formulas & examples.
What is Ratio
Ratio is actually the comparison of two values that have same type of nature. It indicates that how many times the quantity of one thing is bigger or lesser than the quantity of other thing. The ratio is denoted by colon “:” and written as $3:4$. It can also be written in the form of fraction such as “$3/4$” and read as ratio of $3$ to $4$ (Here $3$ & $4$ are two quantities which have same unit).
The first value $3$ is called antecedent whereas the second value $4$ is known as consequent. It is important to remember that the value of consequent must not be zero.
Example:
A classroom consists of $30$ students in which $10$ are boys and $20$ are girls. Find the ratio of boys and girls in classroom?
Solution:
The ratio between boys and girls are written as “boys: girls” or “boys/girls” and their values are $10:20$ or $10/20$.
If we further divide the ratio by $10$, the ratio will be expressed as $1:2$. It means the number of girls in a classroom is double than the number of boys.
Types of Ratios:
Ratio can be categorized in two types:
1) Part to Part Ratio
2) Part to Whole Ratio
Part to Part Ratio specifies the relationship between two different groups such as ratio of boys to girls is $5$ to $7$ and represented by $5:7$ or $5/7$.
Part to Whole Ratio specifies the relationship between same types of group such as $5/7$ of the guests in a party is women. It is also defined as the number of women in a party to the number of guests in a party.
What is proportion
Proportion is defined as an equation that presents the equality of two ratios. It means if the values or quantities of two ratios are equal to each other then the equation will be in proportion. If the values of given numbers are increasing or decreasing equally in proportion, then we can say that the ratios are directly proportional to each other.
The proportion is denoted by “: :” or “=” and can be written in the following different ways:
$10:20 : : 1:2$
$10/20 :: 1/2$
$10:20 = 1:2$
$10/20 = 1/2$
(Keep in mind that the value of consequent must not be equal to zero.)
Example:
The time required by a car to cover $120$ km per hour must be equal to the time required by a car to cover a distance of $360$ km for $3$ hours. It can be described as
$120$ km/hr = $360$ km / $3$ hrs
The proportions are of two types:
1) Direct Proportion
2) Indirect Proportion
What is the difference between two types of proportions?
If the value of one number is increasing with the increasing value of other number or value of one number is decreasing with the decreasing value of other number then it is defined as Direct Proportion. The direct proportion is denoted by $a ∝ b$.
For example, we can cover a large distance by increasing the speed of vehicle and vice versa. Here, speed and distance are directly proportional to each other and written as speed of vehicle $∝$ distance covered.
On the other hand, if the value of one number is increasing while the value of other number is decreasing and vice versa, such type of proportion is called Indirect Proportion. It is denoted by $a ∝ 1/b.$
For example, a fixed distance can be covered in less time while increasing the speed of vehicle or more time is required to cover a fixed distance with decreasing speed of vehicle. This type of proportion is called indirect proportion and written as speed of car $∝$ 1/time.
To save the time and to find out an efficient proportion solution, an online proportion calculator tool can be used by putting the known values in the input boxes.
What is the Relationship between ratio and proportion?
Sometimes, students get confused in making difference between ratio & proportion. Ratio is basically an expression which is used to compare the magnitude of two same types of quantities by following the division method while the proportion is an equation which is used to represent the relation of two ratios.
Example 1: Whether the ratio $8:12$ and $32:48$ are in proportion?
Solution: The question is whether $8:12 :: 32:48$ or not.
We can simplify the values of ratio by dividing it by $4$
$8:12 = 2:3$
And simplify the ratio $32:48$ by dividing it by $4$ for two times
$32:48 = 2:3$
It means $8:12:: 32:48$ are in proportion.
Example 2: The total number of students in a class is $42$. In which the number of students who like physics and chemistry is in the ratio of $3:4$. What are the numbers of students who like Physics and Chemistry?
Solution:
Total students = $42$
Suppose the number of students who like physics = $3x$
And
The number of students who like chemistry = $4x$
Therefore
$3x + 4x = 42$
$7x =42$
$x=42/7$
$x=6$
Put the value of $x$ in above equation to find the number of students who like physics
$3x + 4(6) = 42$
$3x = 42-24 = 18$
$3x = 18$
Put the value of $x$ in above equation to find the number of students who like physics
$3(6) + 4x = 42$
$4x=42-18$$4X= 24$
A step by step calculation is performed to solve the mathematical problems including ratio and proportion.