Types of Ratios with Examples

Duration: 15 min

This video lesson is available to enrolled students.

Enroll to watch — TCS SuperSet Course

AI Summary

An AI-generated summary of this video lecture.

This educational video offers a comprehensive lecture on the mathematical concepts of Ratio and Proportion, presented by instructor Yash Jain. The session begins with a foundational definition of a ratio as a comparison of two quantities, supported by visual aids such as a 3D pie chart and a diagram illustrating part-to-whole relationships. The instructor emphasizes that ratios can be expressed in three distinct formats: colon, word, or fraction. The core of the lecture is dedicated to exploring five specific types of ratios: Duplicate, Sub-Duplicate, Triplicate, Sub-Triplicate, and Inverse ratios. Using the consistent example of the ratio 8:1, the instructor systematically demonstrates the mathematical derivation for each type. A significant portion of the video is devoted to clarifying the concept of Inverse Ratios, particularly addressing the common misconception regarding the inversion of three-term ratios. The lesson culminates in an explanation of Compound Ratios, defining the method of multiplying antecedents and consequents term-wise, and concludes with a practical calculation involving fractions.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide reading 'RATIO & PROPORTION' next to a colorful 3D pie chart. The instructor introduces the topic, defining a ratio as a comparison of two quantities. He displays a diagram showing 'part' and 'whole' relationships to visualize the concept. He notes that ratios can be written in three forms: colon, word, or fraction. The instructor then introduces 'Duplicate Ratio,' writing the formula a:b => a^2:b^2. He applies this to the example 8:1, calculating the duplicate ratio as 8^2:1^2, which equals 64:1. The slide features the 'Knowledge Gate Eduventures' logo at the bottom.

  2. 2:00 – 5:00 02:00-05:00

    The lecture continues with 'Sub-Duplicate Ratio,' defined as sqrt(a):sqrt(b). Applying this to 8:1, the result is sqrt(8):sqrt(1), simplified to 2sqrt(2):1. Next, 'Triplicate Ratio' is introduced with the formula a^3:b^3. For the example 8:1, this becomes 8^3:1^3, resulting in 512:1. The instructor then explains 'Sub-Triplicate Ratio' as cbrt(a):cbrt(b). Using the same example, cbrt(8):cbrt(1) simplifies to 2:1. Throughout this section, the instructor uses handwritten notes on a digital whiteboard to show the step-by-step derivation for each ratio type, with the background featuring a pink pattern with stars and hearts.

  3. 5:00 – 10:00 05:00-10:00

    The focus shifts to 'Inverse Ratio.' The instructor defines it as 1/a : 1/b, which simplifies to b:a. He emphasizes that for a two-term ratio, this is simply reversing the terms. However, for a three-term ratio like a:b:c, he explicitly states that reversing to c:b:a is incorrect. He derives the correct inverse ratio as 1/a : 1/b : 1/c. To simplify this, he suggests finding the LCM of the denominators. He provides a concrete example: finding the inverse ratio of 3:4:6. He calculates the LCM of 3, 4, and 6 as 12, then multiplies the inverse fractions (1/3, 1/4, 1/6) by 12 to get the final integer ratio 4:3:2. The instructor uses red ink to highlight the correct and incorrect methods.

  4. 10:00 – 14:55 10:00-14:55

    The final topic is 'Compound Ratio.' The instructor defines it as the ratio formed by taking the product of antecedents and the product of consequents of two or more ratios. The formula for two ratios m:n and p:q is given as mp:nq. He extends this to three ratios, showing that a:b:c and d:e:f result in ace:bdf. To conclude, he solves a problem: finding the compound ratio of 2/3, 7/9, and 12/35. He multiplies the numerators (2 x 7 x 12) and denominators (3 x 9 x 35) and simplifies the resulting fraction. The video ends with a 'Thanks for watching' slide. The background changes to a yellow pattern with stars and triangles for this final example.

The video systematically builds knowledge from basic ratio definitions to complex variations. It effectively uses a single example (8:1) to maintain continuity while teaching different ratio types. The distinction made for inverse ratios of three terms is a key learning point. The progression from simple definitions to compound calculations provides a complete overview of ratio manipulation techniques. The visual aids and step-by-step derivations ensure clarity for students preparing for exams.