Demo: What is Ratio & Proportion, Definition & Examples

Duration: 12 min

This video lesson is available to enrolled students.

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  1. About Course: About the Course
  2. Programming, Data Structures, OOP & Java: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
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  8. Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  9. Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep, Computer Fundamentals, Cyber Safety and Security, Computer Software, Operating System, Word Processing (MS Word), Computer Networks, Presentation Software (MS PowerPoint)
  10. Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
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  13. Mathematics - I, II, III, IV / गणित - I, II, III, IV: Permutation and Combination / क्रमचय और संचय, Logarithm / लघुगणक, Linear Algebra / रैखिक बीजगणित, Algebra / बीजगणित, Calculus / कलन, Trigonometry / त्रिकोणमिति, Vectors / सदिश, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps / शोध प्रक्रिया के चरण, Graph Theory, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Euclidean Geometry and Mensuration / यूक्लिडीय ज्यामिति और क्षेत्रमिति, Statistics and Probability / सांख्यिकी और प्रायिकता, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ, Plane Mensuration / समतल क्षेत्रमिति, Sampling / प्रतिचयन, Percentage / प्रतिशत, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Ratio and Proportion / अनुपात और समानुपात
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  21. MIS / DSS / Expert Systems: Information Systems
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a foundational introduction to the mathematical concepts of ratio and proportion. The lesson begins by defining a ratio as a comparison of two or more quantities in terms of 'how many times' one quantity equals another. The instructor emphasizes that ratios must compare quantities of the same kind and unit, such as comparing apples to apples or kilograms to kilograms. The video demonstrates three distinct notations for ratios: the colon form (a:b), the word form ('a to b'), and the fractional form (a/b). Key terminology is introduced, identifying the first term as the antecedent and the second term as the consequent. The lesson then transitions to proportion, defined as an equation stating that two ratios are equivalent. Using visual examples like cookie packages and cost comparisons, the instructor illustrates how to identify proportions using the double colon symbol (::) and explains the roles of extreme and mean terms within a proportion.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for "RATIO & PROPORTION" featuring an inset whiteboard explaining that a ratio is "a comparison of 2 quantities." The graphic uses colored dots to demonstrate parts and wholes, noting that ratios "Can be written 3 ways: colon, word, or fraction form." The presenter gestures towards the screen while breaking down specific counts like "1:2" and "3 to 11." The scene then transitions to a new slide titled "DEFINITION OF RATIO" against a pink background with space doodles. The instructor defines a ratio as the comparison of two or more numbers in terms of 'how many times' and emphasizes that ratios compare quantities of the same kind using division. The instructor annotates the slide to highlight 'two or more numbers' and adds a handwritten note specifying 'min 2 term'. He also writes examples showing the relationship between fractions and ratios, such as a/b = 1/2 or a:b = 1:2.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues defining the concept of a ratio as a comparison of two or more numbers in terms of 'how many times' one quantity is equal to another. The lesson emphasizes that ratios compare quantities of the same kind using division and requires the numbers to have the same unit. The instructor uses handwritten examples like 'a:b = 1:2' and 'a:b:c = 1:2:3' to illustrate the notation and relationships between terms. He writes 'b=2a' to demonstrate a specific ratio relationship. The instructor defines a ratio as the comparison of two or more numbers in terms of 'how many times' one quantity is equal to another. He emphasizes that quantities must be of the same kind and have the same unit for comparison, using handwritten examples like distance (d) and time (t). The lesson progresses to show valid ratios with matching units versus invalid ones, such as comparing speed (s) directly to distance (d). Finally, the mathematical representation of a ratio is introduced as a fraction (a:b = 1/2).

  3. 5:00 – 10:00 05:00-10:00

    The lesson defines a ratio as the comparison of two or more numbers in terms of 'how many times' one quantity is equal to another. It explains that ratios can be written as fractions (e.g., 2/5), using the word 'to' (e.g., 2 to 5), or with a colon (e.g., 2:5). The instructor highlights that the first term is called the antecedent and the second term is the consequent, emphasizing that comparisons must be made between items of the same kind. The video transitions from a specific word problem comparing the cost of apples and lemons to defining the mathematical concept of proportion. The instructor explains that a proportion is an equation stating two ratios are equivalent, using the example of cookie mix packages to illustrate this relationship. Visual aids include handwritten notes showing how ratios like 20/1 and 40/2 are equivalent, denoted by the double colon symbol (::).

  4. 10:00 – 11:45 10:00-11:45

    The video segment defines a proportion as an equation stating that two ratios are equivalent, using the example of cookie mix packages. It introduces the notation for proportions (x:y :: z:w) and explains how to read them as 'x is to y as z is to w'. The lesson further breaks down the components of a proportion, identifying x and w as extreme proportions and y and z as mean proportions. The instructor underlines key terms like 'two ratios are equivalent' and circles variables in the fraction form x/y = z/w. The text on screen clarifies that 'x is first proportion, y is second proportion, z is third proportion, w is fourth proportion.' The segment concludes by reinforcing the structure of a proportion equation where y and w are non-zero.

The lecture systematically builds the concept of ratio from basic definition to notation, then extends it into proportion. The core pedagogical strategy involves contrasting valid and invalid comparisons to enforce the rule of 'same kind' units. The instructor uses consistent visual cues, such as checkmarks for valid ratios and crosses for invalid ones, to reinforce this constraint. The transition from ratio to proportion is marked by the introduction of equivalence and the double colon symbol. Key formulas like a/b = z/w are presented alongside verbal translations to aid comprehension.

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