# What are ratio and proportion? Explained with types, formulas, and examples . SAI India

Have you ever wondered what the difference is between ratio and proportion? If so, you’re not alone. Many people are confused about the two terms and often use them interchangeably. In this blog post, we’re going to clear up any confusion you may have about ratio and proportion.

## What Is Ratio?

Ratios are a key concept in mathematics and statistics. They play an important role in understanding how two numbers relate to each other. Ratios can be represented as fractions, decimals, or percentages.

Ratios can be represented in different ways, depending on the situation. For example, ratios can be represented using numerals (e.g. 13, 1/3), or they can be expressed as fractions (i.e. 3/5).

Ratios are important for understanding all sorts of mathematical concepts, including proportions, decimals, averages, percentages, etc. Understanding ratios is essential for doing well in math classes.

The general expression of the ratio is:

a: b

OR

a/b

## Types of Ratio

There are four types of ratios.

1. Part-to-Part Ratio
2. part to Whole Ratio
3. Whole to Whole Ratio
4. Whole-to-Part Ratio

### Part-to-part ratios

Part-to-part ratios involve dividing one number by another number that is smaller than the first number. For example, 2 parts of water divided by 3 parts of water would be a part-to-part ratio.

### Part-to-whole ratios

Part-to-whole ratios involve multiplying one number by another number that is smaller than the first number. For example, 1 part of water multiplied by 2 parts of water would be a part-to-whole ratio.

### Whole-to-whole ratios

Whole-to-whole ratios involve adding one number to another number that is smaller than the first number. For example, 1 cup of sugar added to 3 cups of sugar would be a whole-to-whole ratio.

Part-to-part ratios can be converted to whole-to-whole ratios by multiplying the part-to-part ratio by the whole number. For example, if 2 parts of water are divided by 3 parts of water, the result would be a 12 whole-to-whole ratio.

### Part-to-whole ratios

Part-to-whole ratios can also be converted to whole-to-part ratios by dividing the part-to-whole ratio by the whole number. For example, if 1 part of the water is multiplied by 2 parts of water, the result would be a 2 part-to-whole ratio.

### Whole-to-part

Whole-to-part and part-to-whole ratios can also be converted to other types of proportions using multiplication or division. For example, if 1 cup of sugar is added to 3 cups of sugar, the resulting mixture would have a 5 part-to-whole proportion.

## How to calculate the ratio?

Below is an example of calculating the ratio.

Example

In a bookstore, there are 30 products. From these 30 products, 16 are books, 8 are pencils, and 6 are notebooks. Calculate the ratios of the given products.

• Books to pencils
• Notebooks to whole products
• Notebooks to books
• Pencils to notebooks

Solution

Step 1: First of all, take the given information and write it.

Total products = 30

Books = 16

Pencils = 8

Notebooks = 6

Step 2: Now calculate the given ratios one by one.

• Books to pencils

Number of books = 16

Number of pencils = 8

Then according to ratios, it can be written as:

Books : Pencils

16 : 8

8 : 4

2 : 1

It can also be written as

2/1

• Notebooks to whole products

Number of whole products = 30

Number of notebooks = 6

The term will be referring as a part to whole ratios

Then according to ratios, it can be written as:

Notebooks : Whole products

6 : 30

2 : 10

1 : 5

It can also be written as

1/5

• Notebooks to books

Number of notebooks = 6

Number of books = 16

Then according to ratios, it can be written as:

Notebooks : Books

6 : 16

3 : 8

It can also be written as

3/ 8

• Pencils to notebooks

Number of pencils = 8

Number of notebooks = 6

Then according to ratios, it can be written as:

The ratio will be written as:

Pencils : Notebooks

8 : 6

4 : 3

It can also be written as

4/3

## What Is Proportion?

Proportion is a term that has different meanings in different branches of mathematics. In statistics, it refers to the degree to which two things share qualities or features.

For example, if you have 100 pieces of candy and 50 pieces of chocolate, then the proportion of each type of candy is 50/100 or half.

Proportions can be used to describe the relationships between numbers, percentages, and amounts. For example, if you want to know how many cups are in a container filled with 200 ounces of water, you could use a proportion (200 ounces ÷ 4 cups = 40 cups) to find the answer.

Proportions are used in many areas of daily life. For example, baking recipes often call for proportions such as 1 cup of sugar to 3 egg whites. Media presentations often include graphical representations of proportions such as bar charts and pie charts.

Construction projects also commonly use proportions such as square footage divided by a number of rooms. Knowing and using these proportions can help make tasks more efficient and accurate.

The general expression of proportion is:

p : q :: r : s

or

p : q = r : s

## Types of Proportions

There are two types of proportions.

1. Direct proportions
2. Inverse proportions

### Direct proportions

Direct proportions are the simplest type of proportion. They involve two quantities and their ratios are always 1:1. For example, if you have 3 cups of coffee and 8 teaspoons of sugar, then the direct proportion would be 3:8 and the equation for this would be 3 cups of coffee = 8 teaspoons of sugar.

It also refers to an increase in one quantity causing an increase in a second quantity or a decrease in one term causing a decrease in the second term.

### Inverse proportions

Inverse proportions are a bit more complicated than direct proportions, but still relatively easy to solve. Their equations generally involve taking one quantity and dividing it by the other, resulting in a ratio that is always negative.

An inverse proportion between two quantities A and B can be written as A:B or as -A/B. For example, let’s say you want to know how many tablespoons there are in a cup (container) filled with 800 ml water. The equation for this inverse proportion is 800 ml water = -(2 tablespoons per cup).

It also refers to an increase in one quantity causing a decrease in the second quantity or a decrease in one term causing an increase in the second term.

## How to solve proportions?

In mathematics, solving proportions is not a difficult task, you need to understand the statement of the given problem to proceed further. Follow the below example to understand how to solve proportions.

Example

30 employees are required to run 10 machines in a cloth-making factory, how many employees are required to run 15 machines?

Solution

Step 1: First of all, write the given data values of employees and machines.

employees are required to run 10 machines = 30

employees are required to run 15 machines = x

Step 2: Now take the general formula of proportion.

p : q :: r : s

Step 3: Now write the ratios of employees and machines according to the above formula.

employees : machines : : employees : machines

30 : 10 : : x : 15

Step 4: Now to calculate the value of x multiply the means and extreme values.

10 * x = 30 * 15

10 * x = 450

x = 450/10

x = 45

Hence, 45 employees are required to run 15 machines in a cloth-making factory

## Conclusion

In conclusion, ratios and proportions are mathematical concepts that play an important role in many areas of life. Whether you’re baking a cake or trying to figure out how much paint to buy for your living room, knowing how to calculate ratios and proportions can be very helpful. Use the formulas and examples in this blog post to brush up on your ratio and proportion skills, and make sure to keep a proportion calculator handy when you need it.

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