# Ratio Formula

Calculating ratios is an important part of Maths. We use the ratio formula while comparing the relationship between two numbers or quantities. Ratio is defined as the relation between the quantities of two or more objects and it indicates the amount of one object contained in the other. The general form of representing a ratio of two quantities say, a and b, is

**a : b**

where,

- a = Antecedent
- b = Consequent

Let us understand the ratio formula, and how to find the ratio between numbers, in detail in the following sections.

## What is the Ratio Formula?

The ratio is the relation between the quantities of two or more objects, indicating the amount of one object contained in the other. A ratio can be represented in the form of a fraction using the ratio formula. The ratio formula for any two quantities say, a and b, is given as,

a:b = a/b

Since a and b are individual amounts for two quantities, the total quantity combined is given as (a + b). Let us understand the ratio formula better using a few solved examples and see how to calculate ratio of 2 numbers.

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## Examples on Ratio Formula

**Example 1:** In a class of 70 students, 43 are girls and the remaining are boys. Using the ratio formula, find the ratio of the total number of boys to the number of girls.

**Solution:**

To find: Ratio of the number of boys to the number of girls

Given:

Total number of students = 70

Number of girls = 43

Number of boys = Total number of students - Number of girls

= 27

Using ratio formula,

The ratio of number of boys to the number of girls = Number of boys: Number of girls = 27:43

**Answer: Ratio of the number of boys to the number of girls = 27:43**

**Example 2:** The ratio of x and y is 6:5. If x = 78, what is the value of y?

**Solution:**&

To find: Value of x

Given: Ratio of x to y = 6:5

Using ratio formula,

x:y = 6:5

x/y = 6/5

78/y = 6/5

y = (5/6) × 78

y = 65

**Answer: Value of y = 65**

**Example 3: Find the simplest form of 80:75 using the ratio formula.**

**Solution:**

The GCF of 80 and 75 is 5.

We divide each term in the ratio by 5.

We get 80/5:75/5 = 16:15.

**Answer:** Thus, the ratio of 80:75 in the simplest form is 16:15.

## FAQs on Ratio Formula

### How to Calculate Ratio Using Ratio Formula?

Follow the steps mentioned below to calculate the ratio of two quantities using the ratio formula:

- Find the quantities of objects.
- Write it in the form p:q = p/q.
- The sum of 'p' and 'q' would give the total quantities for the two objects.
- Simplify the ratios of the objects further, if possible.
- The simplified form of the ratio is the final result.

### What are the Ways of Writing a Ratio Formula?

A ratio formula can be written by using two ways:

- By separating the two quantities using a colon (:)
- By writing it in the fractional form.

For example, if there are 2 apples and 8 melons, then the ratio of apples to melons can be written as 2:8 or 2/8, which can be further simplified as 1:4.

### What is Meant By Ratio Formula?

The ratio formula is used to establish a relationship between two or more given quantities. The general form of representing a ratio of two quantities say a and b is a : b, where, a is antecedent and b is consequent.

### How to Find the Simplest Form of Ratio Using Ratio Formula?

The simplest form of a ratio can be calculated by expressing the ratio in the form of a fraction and further simplifying the fraction. This simplified fraction can again be written as a ratio using the ratio formula.

### How to Find the Ratio of Two Numbers?

The ratio of two numbers can be calculated using the ratio formula, p:q = p/q. Let us find the ratio of 81 and 108 using the ratio formula.

- We will first write the numbers in the form of p:q = p/q. Here 81: 108 = 81/ 108.
- Now, we will simplify the fraction 81/108. We know that the GCF of 81 and 108 is 27 so we will divide both the numbers by 27 and we will get 3/4.
- This can be written as 3:4. Therefore, the ratio of 81 and 108 is 3:4

### What is the Formula for Calculating Ratios?

The formula for calculating ratios is p:q = p/q and the steps for finding the ratio of 2 numbers are given as follows.

- First, we write the given numbers in the fractional form. For example, p and q is written as p/q
- Then, we reduce it to the lowest terms.
- Then we separate the two quantities using a colon (:). This means p:q = p/q

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