Addendo Property & Equivalent Ratio Property

Duration: 16 min

This video lesson is available to enrolled students.

Return to /learn/RSSB-BASIC-COMPUTER-INSTRUCTOR/paper-1-basic-numeracy/ratio-and-proportion-ratios/basic-concepts-properties-of-proportion/asset-addendo-property-equivalent-ratio-property after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, Logarithm, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, प्रतिशत / Percentage, औसत / Average, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, Statistics, Probability, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समय और कार्य / Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Paper-1 & 2 | Data Interpretation: आँकड़ा निर्वचन / Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Data Arrangement, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making
  7. Paper-1 | General Science: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, समसामयिकी / Current Affairs
  9. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits
  10. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Calculus, Relational Algebra, SQL, NoSQL
  11. Paper-2 | Data Structures & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Algorithm Analysis, Sorting Algorithms, Intro to Compilers, Hashing
  12. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, Data Link Layer - Ethernet, DLL: Error Control, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Application Layer, Hardware basics, Network Security, Ethical Hacking
  13. Paper-2 | Operating Systems: Introduction to OS, Process Management, Memory Management, File Management, Deadlock
  14. Paper-2 | Computer Organization and Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer, Number System, Number Representation
  15. Paper 2 | System Analysis and Design: Fundamentals of Systems and Information Systems, Fundamentals of Software Engineering, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance, Software Testing
  16. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Paper 2 | OOPS , C++ , JAVA: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  18. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  19. Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection
  20. Paper-2 | Data Processing (Ms-Office): MS Office Applications, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  21. Paper-2 | Internet and Web Technologies: HTML Basics, CSS, XML, JavaScript-Basics, Internet Fundamentals, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, Terms & Abbreviations, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर नेटवर्क / Computer Networks
  22. Paper 2 | Pedagogy: वृद्धि और विकास / Growth and Development, विकास के सिद्धांत / Theories of Development, Concept of Pedagogy, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, आकलन और मूल्यांकन / Assessment and Evaluation, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  23. Live Classes: RSSB Live Sessions
  24. Paper 1 - Full Mock Tests:
  25. Paper 2 - Full Mock Tests:
  26. BCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lesson on Ratio and Proportion, presented by Yash Jain, focuses on two key algebraic properties: the Addendo Property and the Equivalent Ratio Property. The video begins by defining a ratio as a comparison of two quantities before introducing the Addendo Property, which states that if multiple ratios are equal (a/b = c/d = e/f), their common value is preserved when the sums of their antecedents and consequents are taken. This is demonstrated numerically using 2/3 = 6/9 = 8/12, where (2+6+8)/(3+9+12) simplifies to 16/24, which reduces back to 2/3. The instructor then provides a formal algebraic proof by setting the equal ratios to a constant k, expressing numerators as multiples of denominators (a=bk, c=dk), and showing that the combined fraction simplifies to k. A generalized version using variables p, q, r, s, t, u is also presented to show that multiplying terms by constants maintains equivalence. The lesson applies the Addendo Property to solve a problem where p:q = r:s = t:u = 2:3, finding (p+r+t)/(q+s+u) to be 2/3. The second half introduces the Equivalent Ratio Property, which states that if a:b :: c:d, then (a±c):(b±d) :: a:b. This is proven by setting a/b = c/d = k and showing that (a+c)/(b+d) simplifies to k. The property is extended to forms like (pa+qc)/(pb+qd). A final problem asks for the value of (ab+cd)/(b²+d²) given a:b = c:d = 2:3, which is solved by recognizing the expression as an application of the Equivalent Ratio Property with p=b and q=d, yielding 2/3. The lesson concludes with a thank-you slide.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lesson opens with a title slide for Ratio and Proportion, defining ratio as the comparison of two quantities. The instructor introduces the Addendo Property with the rule: if a:b = c:d = e:f, then each ratio equals (a+c+e):(b+d+f). A numerical example using 2/3 = 6/9 = 8/12 is shown, where (2+6+8)/(3+9+12) = 16/24 simplifies to 2/3. Red annotations highlight corresponding terms and circle the final combined fraction, reinforcing the visual connection between individual ratios and their sum.

  2. 2:00 – 5:00 02:00-05:00

    The instructor transitions from the numerical example to a formal algebraic proof of the Addendo Property. By setting a/b = c/d = e/f = k, the numerators are expressed as multiples of denominators: a=bk, c=dk, e=fk. Substituting these into (a+c+e)/(b+d+f) yields (bk+dk+fk)/(b+d+f), which factors to k(b+d+f)/(b+d+f) and cancels to k. This proves that the combined fraction equals the original ratio, establishing the extended proportion a/b = c/d = e/f = (a+c+e)/(b+d+f).

  3. 5:00 – 10:00 05:00-10:00

    The proof is generalized using new variables p, q, r, s, t, u to represent terms in equivalent fractions ma/mb, nc/nd, oe/of. The combined fraction (p+r+t)/(q+s+u) is shown to equal (ma+nc+oe)/(mb+nd+of), confirming that multiplying terms by constants preserves the ratio. The Addendo Property is then applied to a problem: if p:q = r:s = t:u = 2:3, then (p+r+t)/(q+s+u) = 2/3. The lesson transitions to the Equivalent Ratio Property, stating that if a:b :: c:d, then (a±c):(b±d) :: a:b.

  4. 10:00 – 15:00 10:00-15:00

    The Equivalent Ratio Property is proven by setting a/b = c/d = k (k ≠ 0) and showing that (a+c)/(b+d) simplifies to k(b+d)/(b+d) = k. The property is extended algebraically to forms like (pa+qc)/(pb+qd). A problem on an orange slide asks: if a:b = c:d = 2:3, what is (ab+cd)/(b²+d²)? The instructor re-expresses the target fraction as (ba+dc)/(bb+dd), identifying it with p=b and q=d, so the value is 2/3 by the Equivalent Ratio Property.

  5. 15:00 – 15:45 15:00-15:45

    The lesson concludes with a white slide headed 'Equivalent Ratio Property' that recaps two examples, boxing (ab+cd)/(b²+d²) and ending with a generalized form (4a-3c+9e)/(4b-3d+9f). A final 'THANKS FOR WATCHING' slide closes the video, signaling the end of the instructional content on ratio properties.

The lesson systematically builds from concrete examples to abstract proofs, a pedagogical approach that helps students internalize ratio properties. The Addendo Property is first demonstrated numerically, then proven algebraically using a constant k, and finally generalized with additional variables. This three-step progression (example → proof → generalization) is a key teaching pattern worth noting for exam preparation. The Equivalent Ratio Property follows a similar structure, with the proof emphasizing that (a±c)/(b±d) preserves the common ratio k. The final problem on (ab+cd)/(b²+d²) is particularly instructive because it requires recognizing that the expression fits the (pa+qc)/(pb+qd) form with p=b and q=d, a non-obvious substitution that tests conceptual understanding rather than rote application. Students should focus on identifying when a given fraction can be rewritten to match the property's standard form, as this is the core skill being assessed.

Loading lesson…