Ratio

Introduction

In our surroundings, many times we compare two things of the same type.

Example :

Nishika and Mihir collected some fruits from the big basket.

• From the information given in the above table, we can find how many more apples Nishika has collected than Mihir.

Method 1: can use subtraction.

22 – 11 = 11

Nishika has collected 11 apples more than Mihir.

Method 2: We can use division.

So, Nishika has collected twice as many apples as Mihir.

Here we have actually found a ratio of the apples collected by Nishika to the apples collected by Mihir.

• So,
  Number of oranges collected by Nishika / Number of oranges collected by Mihir
  =
  17 / 34
  =
  1 / 2

So, Nishika has collected half as many apples as Mihir.

What is the ratio?

• Comparing two things by division is called a Ratio.
• Ratio is a comparison of two values or quantities of the same type in the terms of ‘how many times’.
• So, to find the ratio between two objects, both the objects should have the same unit.

How to read and write the ratio?

• Ratio of the two quantities is written by using the symbol':'.
• Ratio can be read as follows:

Example :

The ratio of pens to the books is written as 7:10

It is read as: ‘7 is to 10’

The fraction can be written in the form of division as 7:10 =

Here, pens are mentioned first. So,

The ratio of books to the pens is written as 10:7

It is read as: ‘10 is to 7’

The fraction can be written in the form of division as 10:7 =

Here, pens are mentioned first. So,

‘Part to part ratio’ and ‘part to whole ratio’

Example :

Number of black and white cows = 5

Number of brown cows = 2

Total cows = 7

How to find the ratio from part to part?

The ratio of black and white cows to brown cows =

The ratio of brown cows to black and white cows =

How to find the ratio from part to whole?

The ratio of black and white cows to all cows =

The ratio of brown cows to all cows =

Note: To write the ratio keep the following points in mind.

1. Write the terms in the given manner. There should be significant order of terms.
2. Both of the objects or quantities should have the same units.
3. Write the correct numbers.

What are the equal ratios?

• Equivalent fractions of the given ratio have an equal ratio.
• When we multiply or divide the first term and second term /numerator and denominator of the ratio by the same number, we get equal ratios.
• To find an equal ratio, we can simplify the fraction of the given ratio.

Example :

• Above two ratios represent the same colour parts.
• If we multiply the numerator and denominator of the first ratio by 4, we get
  
  1 × 4 / 4 × 4
  =
  4 / 16
  → fraction of the second ratio
• If we find the simple form of the second ratio, we get the first ratio.
• So,
  1 / 4
  =
  4 / 16
• 1 : 4 = 4 : 16 → Equal ratios

Some real life examples where the concept of ratio is used.

• Cooking - To decide the quantities of the ingredients.
• Architecture – To decide the strong structure of the buildings.
• Health – To decide the quantity of the medicine according to the age of the patient.
• In Share market, Electronics and many more industries.

Did you know?