Ratio
Ratio, in math, is the term that is used to compare two or more numbers. It is used to indicate how big or small is one quantity when compared to another. Two quantities are being compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'. For example, in a group of 30 people, 17 of them prefer to walk in the morning and 13 of them prefer to cycle. To represent this information as a ratio, we write as 17: 13. Here, the symbol ': " is called as "is to". So, the ratio of people who prefer walking to the people who prefer cycling is read as 17 is to 13.
1.  Ratio Definition 
2.  Ratio Formula 
3.  Calculation of Ratios 
4.  Simplification of Ratios 
5.  Equivalent Ratios 
6.  Solved Examples 
7.  Practice Questions 
8.  FAQs on Ratio 
Ratio Definition
The ratio is defined as the comparison between two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The parttopart ratio denotes how two distinct entities or groups are related. For example, the ratio of boys to girls in a class is 12: 15, whereas, the parttowhole ratio denotes the relationship between a specific group to a whole lot. For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.
Ratio Formula
We use the ratio formula while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.
The fraction form that represents this ratio is a/b. To further simplify a ratio, we will follow the same procedure that we use for simplifying a fraction. a:b = a/b. Let us understand this with an example. In a class of 50 students, 23 are girls and the remaining are boys. To find the ratio of the total number of boys to the number of girls, please follow the steps shown below.
Total number of girls = 23
Total number of boys = Toal number of students  total number of girls
= 50  23
= 27
Therefore, the desired ratio is, (Number of boys: Number of girls), which is 27:23.
Ratio Scale
A ratio scale is a quantitative measurement scale that is used to classify or compare numbers. There is a special feature called zero point. A zero point in a ratio scale means that the variable or the quantity is completely absent. There are equal intervals between the points on a ratio scale. For example, to know the number of glasses of water a person drinks in a day, we can measure it by using a ratio scale, with the following options. They are 1  2, 3  4, 5  6, 7  8.
Calculation of Ratios
Please follow the steps mentioned below to calculate the ratio of two quantities.
 Find the quantities of both the objects for which we are determining the ratio.
 Write it in the form a: b.
 The sum of 'a' and 'b' would give the total quantities for both objects.
 Simplify the ratios further, if possible. The simplified ratio is the final result.
For example, if we mix one glass of chocolate syrup with 5 glasses of milk, it makes 6 glasses of chocolate milkshake. Therefore, the ratio of chocolate syrup to milk is 1:5.
Simplification of Ratios
A ratio expresses how much of one quantity is required as compared to another quantity. The two terms in the ratio can be simplified and expressed in their lowest form. Ratios when expressed in their lowest form are easy to understand. Similar to fractions, ratios can also be simplified. To simplify a ratio, please follow the steps given below.
 Write the given ratio a:b in the form of a fraction a/b.
 Find the greatest common factor of 'a' and 'b'.
 Divide the numerator and denominator of the fraction with the GCF to obtain the simplified fraction.
 Represent this fraction in the ratio form to get the result.
For example, let us simplify the ratio 18:10. On writing the ratio in the fraction form we get 18/10. The GCF of 10 and 18 is 2. By dividing the numerator and denominator by 2, we get, (18÷2)/(10÷2) = 9/5
Therefore, the simplified ratio is 9:5.
Important Notes:
 In case both the numbers 'a' and 'b' are equal in the ratio a: b, then a: b = 1.
 If a > b in the ratio a : b, then a : b > 1.
 If a < b in the ratio a : b, then a : b < 1.
 It is to be ensured that the units of the two quantities are similar before comparing them.
Equivalent Ratios
A ratio in which there is a relationship between the first and the second term, which is got either by multiplying or dividing the terms of a ratio by a number other than zero is called an equivalent ratio. For example, when the first and the second terms of the ratio 1:3 are multiplied by 3, we get, (1 × 3) : (3 × 3) or 3: 9. Here, 1:3 and 3:9 are equivalent ratios. Similarly, when both the terms of the ratio 20:10, are divided by 10, gives the ratio as 2:1. Here, 20:10 and 2:1 are equivalent ratios. An infinite number of equivalent ratios of any given ratio can be found by multiplying the antecedent and the consequent by a positive integer.
Ratio Table
A ratio table is a list containing the equivalent ratios of any given ratio in a structured manner. The following ratio table gives the relation between the ratio 1:4 and four of its equivalent ratios. The equivalent ratios are related to each other by the multiplication of a number. Equivalent ratios are obtained by multiplying or dividing the two terms of a ratio by the same number. In the example shown in the figure, let us take the ratio 1:4 and find four equivalent ratios, by multiplying both the terms of the ratio by 2, 3, 6, and 9. As a result, we get 2:8, 3:12, 6:24, and 9:36.
Topics Related to Ratio
Check out some interesting articles related to ratio.
Solved Examples on Ratio

Example 1: There are 49 boys and 28 girls in school. Express the ratio of the number of boys to that of girls.
Solution:
Given, the number of boys = 49 and the number of girls = 28. The ratio of the number of boys to that of girls = 49:28. The GCF of 49 and 28 is 7. Now, to simplify, divide the two terms by their GCF which is 7. Thus, the ratio of the number of boys to that of girls = 7:4.

Example 2: A music class has 30 students. Out of the 10 of them were adults and the rest were children. What is the ratio of the number of children to the total number of students in the music class?
Solution:
Given, the total number of students in the music class = 30 and the total number of adults = 10. Therefore, the number of children who attended the music class = 30 10, which is equal to 20. The ratio of the total number of children to the total number of students in the music class = 20: 30, which when simplified gives 2:3.

Example 3: Find the simplest form of 87:75.
Solution:
The GCF of 87 and 75 is 3. We divide each term in the ratio by 3. We get, \( \frac{87}{3}\):\( \frac{75}{3}\) = 29:25. Thus, the ratio 87:75 in the simplest form is 29:25.
FAQs on Ratio
What is Ratio?
Ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.
What are the Ways of Writing a Ratio?
A ratio can be written by separating the two quantities using a colon (:) or it can be written in the fractional form. For example, if there are 4 apples and 8 melons, then the ratio of apples to melons can be written as 4:8 or 4/8, which can be further simplified as 1:2.
How to Calculate Ratio?
Follow the steps mentioned below to calculate the ratio of two quantities:
 Find the quantities of both the objects for which we are determining the ratio.
 Write it in the form a: b.
 The sum of 'a' and 'b' would give the total quantities for both objects.
 Simplify the ratios further, if possible. The simplified ratio is the final result.
What is an Equivalent Ratio?
Two ratios are said to be equivalent if a relationship can be established either by multiplying the first ratio's two terms by a number or dividing the first ratio's two terms with a number. For example, when the ratio 1: 4 is multiplied by 2, which means multiplying both the numbers in the ratio by 2, we get, (1 × 2) : (4 × 2) or 2: 8. Here, 1:4 and 2:8 are equivalent ratios. Similarly, the ratio 30: 10, when divided by 10, gives the ratio as 3:1. Here, 30:10 and 3:1 are equivalent ratios.
What is Ratio Scale?
Sometimes there may be a need wherein we have to compare the total number of values in an ordered interval. The interval of values in a ratio scale is equally distributed. It helps us to find out the total number in each interval and find the ratio between them. The ratio scale does not support negative values. For example, to find out the total number of customers who visit a shop in a day can be found by taking a ratio scale of 510, 1015, 1520, 2025.
What is Ratio Table?
Ratio tables are a list of equivalent ratios which are obtained either by multiplying or dividing both the quantities by the same value. For example, if the ratio table starts with the ratio 1 : 3, then the successive rows will have 2:6, 4:12, 8:24, and so on, if the number that is being multiplied to both the terms are 2.