• NCERT Solutions
    • NCERT Library
  • RD Sharma
    • RD Sharma Class 12 Solutions
    • RD Sharma Class 11 Solutions Free PDF Download
    • RD Sharma Class 10 Solutions
    • RD Sharma Class 9 Solutions
    • RD Sharma Class 8 Solutions
    • RD Sharma Class 7 Solutions
    • RD Sharma Class 6 Solutions
  • Class 12
    • Class 12 Science
      • NCERT Solutions for Class 12 Maths
      • NCERT Solutions for Class 12 Physics
      • NCERT Solutions for Class 12 Chemistry
      • NCERT Solutions for Class 12 Biology
      • NCERT Solutions for Class 12 Economics
      • NCERT Solutions for Class 12 Computer Science (Python)
      • NCERT Solutions for Class 12 Computer Science (C++)
      • NCERT Solutions for Class 12 English
      • NCERT Solutions for Class 12 Hindi
    • Class 12 Commerce
      • NCERT Solutions for Class 12 Maths
      • NCERT Solutions for Class 12 Business Studies
      • NCERT Solutions for Class 12 Accountancy
      • NCERT Solutions for Class 12 Micro Economics
      • NCERT Solutions for Class 12 Macro Economics
      • NCERT Solutions for Class 12 Entrepreneurship
    • Class 12 Humanities
      • NCERT Solutions for Class 12 History
      • NCERT Solutions for Class 12 Political Science
      • NCERT Solutions for Class 12 Economics
      • NCERT Solutions for Class 12 Sociology
      • NCERT Solutions for Class 12 Psychology
  • Class 11
    • Class 11 Science
      • NCERT Solutions for Class 11 Maths
      • NCERT Solutions for Class 11 Physics
      • NCERT Solutions for Class 11 Chemistry
      • NCERT Solutions for Class 11 Biology
      • NCERT Solutions for Class 11 Economics
      • NCERT Solutions for Class 11 Computer Science (Python)
      • NCERT Solutions for Class 11 English
      • NCERT Solutions for Class 11 Hindi
    • Class 11 Commerce
      • NCERT Solutions for Class 11 Maths
      • NCERT Solutions for Class 11 Business Studies
      • NCERT Solutions for Class 11 Accountancy
      • NCERT Solutions for Class 11 Economics
      • NCERT Solutions for Class 11 Entrepreneurship
    • Class 11 Humanities
      • NCERT Solutions for Class 11 Psychology
      • NCERT Solutions for Class 11 Political Science
      • NCERT Solutions for Class 11 Economics
      • NCERT Solutions for Class 11 Indian Economic Development
  • Class 10
    • NCERT Solutions for Class 10 Maths
    • NCERT Solutions for Class 10 Science
    • NCERT Solutions for Class 10 Social Science
    • NCERT Solutions for Class 10 English
    • NCERT Solutions For Class 10 Hindi Sanchayan
    • NCERT Solutions For Class 10 Hindi Sparsh
    • NCERT Solutions For Class 10 Hindi Kshitiz
    • NCERT Solutions For Class 10 Hindi Kritika
    • NCERT Solutions for Class 10 Sanskrit
    • NCERT Solutions for Class 10 Foundation of Information Technology
  • Class 9
    • NCERT Solutions for Class 9 Maths
    • NCERT Solutions for Class 9 Science
    • NCERT Solutions for Class 9 Social Science
    • NCERT Solutions for Class 9 English
    • NCERT Solutions for Class 9 Hindi
    • NCERT Solutions for Class 9 Sanskrit
    • NCERT Solutions for Class 9 Foundation of IT
  • CBSE Sample Papers
    • Previous Year Question Papers
    • CBSE Topper Answer Sheet
    • CBSE Sample Papers for Class 12
    • CBSE Sample Papers for Class 11
    • CBSE Sample Papers for Class 10
    • Solved CBSE Sample Papers for Class 9 with Solutions 2024-2025
    • CBSE Sample Papers Class 8
    • CBSE Sample Papers Class 7
    • CBSE Sample Papers Class 6
  • Textbook Solutions
    • Lakhmir Singh
    • Lakhmir Singh Class 10 Physics
    • Lakhmir Singh Class 10 Chemistry
    • Lakhmir Singh Class 10 Biology
    • Lakhmir Singh Class 9 Physics
    • Lakhmir Singh Class 9 Chemistry
    • PS Verma and VK Agarwal Biology Class 9 Solutions
    • Lakhmir Singh Science Class 8 Solutions

Learn CBSE

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Ratio and Proportion Class 6 Notes

May 18, 2019 by Sastry CBSE

Ratio and Proportion Class 6 Notes

There are two ways of comparison:
(i) By taking difference
(ii) By division.
The (ii) way is better than (i) way.

The comparison by division is called the ratio. In this way, we see how many times one quantity is to the other quantity.
For example: If Apala got 75 marks and Meenu got 25 marks in an examination, then we can say that the marks obtained by Apala are three times the marks obtained by Meenu.

Ratio
If we compare die two quantities in terms of ‘how many times’, then this comparison is known as the ratio.
Ratio is denoted by using the symbol ‘:’

For example, Apala’s weight is 20 kg and her father’s weight is 60 kg. We say that Apala’s father’s weight and Apala’s weight are in the ratio = \(\frac { 60 }{ 20 }\) = \(\frac { 3 }{ 1 }\) = 3 : 1.

For comparison by ratio, the two quantities must be in the same units. If they are not, they must be expressed in the same units before the ratio is taken.

The same ratio may occur in different situations.
For example,
(i) Length of a room is 15 cm and breadth is 10 m. So, the ratio of length of the room to the breadth of the room = \(\frac { 15 }{ 10 }\) = \(\frac { 3 }{ 2 }\) = 3 : 2

(ii) There are 30 girls and 20 boys in a class. Then, ratio of the number of girls to the number of boys = \(\frac { 30 }{ 20 }\) = \(\frac { 3 }{ 2 }\) = 3 : 2.

A ratio may be treated as a fraction. Thus, the ratio 2 : 3 may be treated as \(\frac { 2 }{ 3 }\).

A ratio equivalent to a given ratio can be obtained by multiplying or dividing the numerator and denominator by the same number. Thus, few ratios equivalent to 2 : 3 are 4 : 6, 6 : 9, 8 : 12, etc.

Similarly, few ratios equivalent to 64 : 32 are 32 : 16, 16 : 8, 8 : 4, 4 : 2, 2 : 1, etc. If the fractions corresponding to equivalent ratios are equivalent, then the two ratios are equivalent.

The orders in which the quantities are taken to express their ratio is important. Note that the ratio 2 : 3 is different from 3 : 2.

A ratio can be expressed in its lowest form. For example, ratio 60 : 24 is \(\frac { 60 }{ 24 }\) in the form of a fraction. In its lowest form \(\frac { 60 }{ 24 }\) = \(\frac { 5 }{ 2 }\) = 5 : 2. thus, in its lowest form ratio 60 : 24 is treated as 5 : 2.

Proportion
If two ratios are equal we say that they are in proportion and use the symbol to equate the two ratios.
For example, 2 : 4 = 60 : 120
we write 2 : 4 :: 60 : 120
and say that 2, 4, 60 and 120 are in proportion.
Again,
2 : 5 ≠ 60 : 15
We say that 2, 5, 60 and 15 are not in proportion.
So, if two ratios are not equal, then we say that they are not in proportion.

Four quantities are said to be in proportion if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities. Thus, four quantities 3, 10, 15, 50 are in proportion, since \(\frac { 3 }{ 10 }\) = \(\frac { 15 }{ 30 }\) .
We write 3 : 10 :: 15 : 50 and read as 3 is to 10 as 15 is to 50.
Here, the first and the fourth terms, i.e., 3 and 50 are called the extreme terms while the second and the third terms, i.e., 10 and 15 are called the middle terms.

The order of terms in a proportion is important, 3, 10, 15, 50 are in proportion but 3, 10, 50, 15 are not, since \(\frac { 3 }{ 10 }\) ≠ \(\frac { 50 }{ 15 }\).

Unitary Method
The method in which, first we find the value of one unit and then the value of the required number of units is called the Unitary Method.

For example, if the mice of 6 toys is ₹ 90 and we are to find out the price of 4 toys, then first we find the price of 1 toy as ₹ \(\frac { 90 }{ 6 }\) or ₹ 15. From this, we find the price of 4 toys as ₹ 15 × 4 or ₹ 60.

Class 6 Maths Notes

Filed Under: Class 6

LearnCBSE.in Student Education Loan
  • Student Nutrition - How Does This Effect Studies
  • Words by Length
  • NEET MCQ
  • Factoring Calculator
  • Rational Numbers
  • CGPA Calculator
  • TOP Universities in India
  • TOP Engineering Colleges in India
  • TOP Pharmacy Colleges in India
  • Coding for Kids
  • Math Riddles for Kids with Answers
  • General Knowledge for Kids
  • General Knowledge
  • Scholarships for Students
  • NSP - National Scholarip Portal
  • Class 12 Maths NCERT Solutions
  • Class 11 Maths NCERT Solutions
  • NCERT Solutions for Class 10 Maths
  • NCERT Solutions for Class 9 Maths
  • NCERT Solutions for Class 8 Maths
  • NCERT Solutions for Class 7 Maths
  • NCERT Solutions for Class 6 Maths
  • NCERT Solutions for Class 6 Science
  • NCERT Solutions for Class 7 Science
  • NCERT Solutions for Class 8 Science
  • NCERT Solutions for Class 9 Science
  • NCERT Solutions for Class 10 Science
  • NCERT Solutions for Class 11 Physics
  • NCERT Solutions for Class 11 Chemistry
  • NCERT Solutions for Class 12 Physics
  • NCERT Solutions for Class 12 Chemistry
  • NCERT Solutions for Class 10 Science Chapter 1
  • NCERT Solutions for Class 10 Science Chapter 2
  • Metals and Nonmetals Class 10
  • carbon and its compounds class 10
  • Periodic Classification of Elements Class 10
  • Life Process Class 10
  • NCERT Solutions for Class 10 Science Chapter 7
  • NCERT Solutions for Class 10 Science Chapter 8
  • NCERT Solutions for Class 10 Science Chapter 9
  • NCERT Solutions for Class 10 Science Chapter 10
  • NCERT Solutions for Class 10 Science Chapter 11
  • NCERT Solutions for Class 10 Science Chapter 12
  • NCERT Solutions for Class 10 Science Chapter 13
  • NCERT Solutions for Class 10 Science Chapter 14
  • NCERT Solutions for Class 10 Science Chapter 15
  • NCERT Solutions for Class 10 Science Chapter 16

Free Resources

RD Sharma Class 12 Solutions RD Sharma Class 11
RD Sharma Class 10 RD Sharma Class 9
RD Sharma Class 8 RD Sharma Class 7
CBSE Previous Year Question Papers Class 12 CBSE Previous Year Question Papers Class 10
NCERT Books Maths Formulas
CBSE Sample Papers Vedic Maths
NCERT Library

NCERT Solutions

NCERT Solutions for Class 10
NCERT Solutions for Class 9
NCERT Solutions for Class 8
NCERT Solutions for Class 7
NCERT Solutions for Class 6
NCERT Solutions for Class 5
NCERT Solutions for Class 4
NCERT Solutions for Class 3
NCERT Solutions for Class 2
NCERT Solutions for Class 1

Quick Resources

English Grammar Hindi Grammar
Textbook Solutions Maths NCERT Solutions
Science NCERT Solutions Social Science NCERT Solutions
English Solutions Hindi NCERT Solutions
NCERT Exemplar Problems Engineering Entrance Exams
Like us on Facebook Follow us on Twitter
Watch Youtube Videos NCERT Solutions App