Ratio
2026-02-28 10:23 Diff
https://brightchamps.com/en-us/math/commercial-math/ratio

Ratios are classified into different types according to their function and purpose. They are used to comparing two or more values.

The main types of ratios are as follows:

Simple Ratio:
 

A simple ratio shows the comparison between two numbers. In this type of ratio, the values are expressed in their simplest form. It explains how many times one value contains another value. A simple ratio can be denoted as fractions (/) or with a colon (:)

Take a close look at this example,

Suppose, in a garden, there are 10 roses and 15 sunflowers. The ratio of roses and sunflowers are at 10:15.

To get the simplified ratio, we have to find the GCF of the given numbers.
 

For that, we need to list the factors of 10 and 15.
 

  • The factors of 10 are 1, 2, 5, and 10.
     
  • Factors of 15 are 1, 3, 5, and 15.
     

Here, 1 and 5 are the common factors of the given numbers. So, the greatest common factor of 10 and 15 is 5.
 

Next, we can divide the values by the GCF:
 

  • 10 ÷ 5 = 2
     
  • 15 ÷ 5 = 3
     

The ratio of roses and sunflowers is 2:3. It means that for every 2 roses, there are 3 sunflowers in the garden.
 

Compound Ratio:

It is a ratio formed by multiplying two or more ratios together. Here, the numerator is the product of the numerators of the original ratios and the denominator is the product of the denominators of the original ratios. For instance, a compound ratio is represented as: a:b and c:d.

When we multiply these ratios, we get a compound ratio. To get a better idea of compound ratio, look at this example:

Milan drinks 2 liters of water every 3 days and eats 4 apples every 5 months. She wants to calculate the ratio of her drinking and eating habits. How can she find the compound ratio?


To find the compound ratio, we have to multiply these two ratios.
 

  • (2 : 3) × (4 : 5)
     
  • (2 × 4) : (3 × 5) = 8 : 15
     

Hence, the compound ratio of (2 : 3) and (4 × 5) is 8:15.
 

Inverse Ratio:
 

An inverse ratio is also known as an indirect or reciprocal ratio. This ratio expresses the relationship of two quantities, in which one value increases and the other decreases equally.
 

For example:

Building a house takes 100 days, 10 days if 10 workers are employed, and 5 days if 20 workers are engaged.

Now we can measure the workers' ratio and days ratio.
 

Workers Ratio = 10:20
 

To simplify this, we have to divide the numbers by the GCF. 10 is the GCF of 10 and 20.
 

  • 10 ÷ 10 = 1
     
  • 20 ÷ 10 = 2
     

The simplified ratio is 1:2.
 

To find the day's ratio, we have to divide both numbers by their GCF.
 

10:5
 

Here, 5 is the GCF of 10 and 5.
 

  • 10 ÷ 5 = 2
     
  • 5 ÷ 5 = 1
     

The simplified ratio of days ratio is 2:1
 

Equivalent Ratio:

Equivalent ratios are two or more ratios that express the same relationship between quantities, even though the numbers may be different. They are obtained by multiplying or dividing both terms of a ratio by the same non-zero number, which keeps the comparison unchanged. Equivalent ratios, like equivalent fractions, represent a proportional relationship between two values.

Formulas:

  1. To form an equivalent ratio (multiplication):

    \(a:b=(a × n):(b × n)\)

    Where 𝑛 is any non-zero number.

  2. To form an equivalent ratio (division):

    \(a:b=(\frac{a}{n}):(\frac{b}{n}) \)

    Where 𝑛 is any common divisor of both numbers.

Examples:
 

  1. Starting ratio: 2 : 3

    Multiply both terms by 2 → 4 : 6

  2. Starting ratio: 5 : 10

    Divide both terms by 5 → 1 : 2