Summary of Basics of Maths | Complete Ratio & Proportion | Viral Maths by Navneet Sir

Summary of "Basics of Maths | Complete Ratio & Proportion | Viral Maths by Navneet Sir"

This extensive video tutorial by Navneet Sir covers the fundamental concepts of Ratio and Proportion in a detailed and student-friendly manner. The session is designed to build a strong foundation for learners preparing for competitive exams like SSC, Bank, Railway, and others. The instructor emphasizes clarity, practical examples, and multiple solving techniques to ensure comprehensive understanding.

Main Ideas, Concepts, and Lessons Conveyed

1. Introduction to Ratio

Definition: Ratio is a comparison between two or more quantities.
Purpose: Helps in comparing quantities without revealing exact values.
Representation: Ratios can be written as fractions (e.g., 1/2) or with a colon (e.g., 1:2).
Simplification: Ratios should be simplified by dividing both terms by their greatest common divisor.
Relation to Fractions: Ratio and fraction are essentially the same; both express parts of a whole or comparison.

2. Basics of Proportion

Definition: Proportion is an equality between two ratios.
Example: 2:3 = 4:6 means both ratios are proportional.
Verification: Simplify ratios and check if they are equal.
Applications: Used to solve problems involving comparison of multiple quantities.

3. Simplification and Operations on Ratios

Simplifying Ratios: Divide both terms by the highest common factor.
Adding/Subtracting Ratios: Possible only if the internal difference (gap between terms) in both ratios is the same.
Multiplying Ratios: Multiplying both terms by the same number scales the ratio but keeps the proportion intact.

4. Unique Number (Variable x) in Ratios

When actual quantities are unknown but the ratio is given, use a variable (e.g., 4x and 5x) to represent real values.
Helps in solving algebraic problems involving ratios.

5. Approaches to Solve Complex Ratio Problems

Impostor Approach: When a term appears in two ratios with different values, adjust the ratios so that the common term matches.
Hide and Seek Approach: To find values of variables in equations like 2a=3b=4c, hide the variable and multiply the other terms to find the ratio.
Pendant Approach: Using LCM of coefficients to simplify ratios in equations.
Sandwich Approach: Visualizing ratio multiplication vertically and horizontally to solve multi-term ratios.
Mahabharata Approach: Multiplying terms diagonally and canceling common terms to find the ratio of variables.
Panda Approach: Used in income-expenditure-savings problems to find unknowns by cross multiplication.

6. Ratio in Practical Problems

Distribution Problems: Dividing amounts based on given ratios.
Age Problems: Using ratios to find present ages and differences.
Income and Expenditure: Calculating savings and differences using Ratio and Proportion.
Coin Problems: Understanding fraction values of coins and solving problems involving total values and number of coins.
Increment/Decrease in Ratios: Adjusting ratios when quantities increase or decrease by a certain percentage or amount.

7. Important Rules and Tips

Units must be the same when comparing quantities.
Always simplify ratios before solving.
When subtracting ratios, internal gaps must be equal.
Use variables to represent unknown quantities in ratios.
Practice multiple approaches to find the most efficient method.
Understand the concept of fraction value in coin-related problems.
Convert fractional ratios to whole numbers using LCM.

Detailed Methodologies / Instructions

How to Simplify Ratios:
- Find the greatest common divisor (GCD).
- Divide both terms by the GCD.
Checking Proportion:
- Simplify both ratios.
- If equal, they are in proportion.
Subtracting Ratios:
- Check if the difference between terms in both ratios is equal.
- If yes, subtract corresponding terms.
Using Variable x in Ratios:
- If ratio is a:b and actual values unknown, represent as ax and bx.
- Solve for x using given conditions.
Impostor Approach:
- Identify the common term (impostor) appearing in two ratios.
- Adjust ratios by multiplying so the impostor's values match.
- Then combine or compare ratios.
Hide and Seek Approach:
- For equations like 2a=3b=4c, hide the variable you want to find.
- Multiply the other terms.
- Simplify to get the ratio.
Sandwich Approach:
- Multiply vertically (bread) and horizontally (potato filling).
- Add and compare results to solve for variables.