Addendo Property & Equivalent Ratio Property

Duration: 16 min

This video lesson is available to enrolled students.

Return to /learn/NTA-UGC-NET-PAPER---1/paper-1-unit-5-mathematical-reasoning-and-aptitude/mixture-and-alligation/proportion-and-variation/asset-addendo-property-equivalent-ratio-property after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Paper - 1 | Unit - 1 | Teaching Aptitude: शिक्षण की अवधारणा एवं उद्देश्य / Concept and Objectives of Teaching, शिक्षण के स्तर / Levels of Teaching, शिक्षार्थी की विशेषताएँ / Learner's Characteristics, अधिगम: प्रकृति एवं सिद्धांत / Learning: Nature and Theories, संज्ञान, स्मृति एवं अधिसंज्ञान / Cognition, Memory and Metacognition, शिक्षण को प्रभावित करने वाले कारक / Factors Affecting Teaching, प्रभावी शिक्षण एवं शिक्षक / Effective Teaching and the Teacher, अनुदेशनात्मक उद्देश्य एवं पाठ नियोजन / Instructional Objectives and Lesson Planning, शिक्षण विधियाँ / Methods of Teaching, ऑफ़लाइन एवं ऑनलाइन शिक्षण विधियाँ / Offline and Online Teaching Methods, शिक्षण सहायक प्रणाली / Teaching Support System, मूल्यांकन प्रणाली / Evaluation Systems, Sāṃkhya, व्यक्तिगत व्यवहार / Individual Behaviour, मानव संसाधन प्रबंधन / Human Resource Management, बाल्यावस्था में विकास के क्षेत्र / Domains of Child Development, संवेग का जैविक आधार / Biological Basis of Emotion, उपनिषद और भगवद्गीता / Upanishads and Bhagavad Gita, केन्द्रीय और परिधीय तंत्रिका तंत्र / Central and Peripheral Nervous Systems
  2. Paper - 1 | Unit - 2 | Research Aptitude: अनुसंधान: अर्थ, लक्षण व वैज्ञानिक विधि / Research: Meaning, Features and Scientific Method, अनुसंधान के प्रतिमान एवं उपागम / Research Paradigms and Approaches, अनुसंधान के प्रकार / Types of Research, चर एवं मापन / Variables and Measurement, अनुसंधान की विधियाँ / Methods of Research, अनुसंधान के चरण / Steps of Research, प्रतिचयन / Sampling, आँकड़ा संग्रह के उपकरण एवं विधियाँ / Tools and Methods of Data Collection, आँकड़ा विश्लेषण एवं शोध सांख्यिकी / Data Analysis and Statistics in Research, शोध-प्रबंध एवं लेख लेखन / Thesis and Article Writing, अनुसंधान में ICT का अनुप्रयोग / Application of ICT in Research, शोध नैतिकता / Research Ethics
  3. Paper - 1 | Unit - 3 | Comprehension: प्रत्यक्ष बोध / Literal Comprehension, गद्यांश में शब्दावली और भाषा / Vocabulary and Language in Context, निष्कर्षात्मक बोध / Inferential Comprehension, आलोचनात्मक बोध / Critical Comprehension, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Restoration and Eighteenth-Century Drama, Modern British Fiction, William Shakespeare, Mid-Twentieth-Century and Contemporary British Fiction, American Drama
  4. Paper - 1 | Unit - 4 | Communication: संचार: अर्थ, प्रकृति एवं प्रक्रिया / Communication: Meaning, Nature and Process, संचार के प्रकार एवं स्तर / Types and Levels of Communication, मौखिक एवं अमौखिक संचार / Verbal and Non-verbal Communication, संकेत विज्ञान एवं अर्थ / Semiotics and Meaning, संचार के मॉडल एवं सिद्धांत / Models and Theories of Communication, प्रभावी संचार / Effective Communication, संचार की बाधाएँ / Barriers to Communication, कक्षा संचार / Classroom Communication, जनसंचार माध्यम: प्रकार एवं विकास / Mass Media: Types and Evolution, जनसंचार एवं समाज / Mass Media and Society, डिजिटल एवं नव माध्यम / Digital and New Media, Static General Knowledge, Morphology and Syntax, जन स्वास्थ्य पोषण / Public Health Nutrition, Newtonian Motion and Stability, GK- Current Affairs, Indian Economy, Art and Architecture, India after Independence
  5. Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: संख्या पद्धति एवं सरलीकरण / Number System and Simplification, बीजगणित एवं आयु / Algebra and Ages, प्रतिशतता / Percentage, अनुपात, समानुपात, साझेदारी एवं मिश्रण / Ratio, Proportion, Partnership and Mixtures, औसत / Averages, लाभ, हानि एवं बट्टा / Profit, Loss and Discount, साधारण एवं चक्रवृद्धि ब्याज / Simple and Compound Interest, समय एवं कार्य / Time and Work, चाल, समय एवं दूरी / Speed, Time and Distance, क्षेत्रमिति एवं ज्यामिति / Mensuration and Geometry, क्रमचय, संचय एवं प्रायिकता / Permutation, Combination and Probability, श्रेणी / Series, कूटलेखन-कूटवाचन / Coding-Decoding, संबंध, दिशा एवं क्रम / Relationships, Directions and Ranking, व्यवस्था, पहेलियाँ, घड़ी एवं कैलेंडर / Arrangements, Puzzles, Clock and Calendar, Mathematical Foundations, Polity, जीवनी, Deconstruction, Gender and Queer Theory, Modern British and Irish Poetry, Central Force and Scattering, Chemical thermodynamics, Microscopic techniques, संविधान का दर्शन / Philosophy of the Constitution, Waves, Optics and Charged-Particle Motion, Membrane structure and function, Analysis, Markov Chains, Univariate and Joint Distributions
  6. Paper - 1 | Unit - 6 | Logical Reasoning: युक्ति की संरचना / Structure of Arguments, पद, परिभाषा एवं भाषा के उपयोग / Terms, Definitions and Uses of Language, निरुपाधिक प्रतिज्ञप्तियाँ / Categorical Propositions, निरुपाधिक न्यायवाक्य / Categorical Syllogism, वेन आरेख / Venn Diagrams, निगमन, आगमन एवं सादृश्यता / Deduction, Induction and Analogy, तर्कदोष / Fallacies, भारतीय तर्कशास्त्र: प्रमाण / Indian Logic: Pramanas, अनुमान एवं व्याप्ति / Anumana and Vyapti, हेत्वाभास / Hetvabhasa, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Aristotle, पाश्चात्य दर्शन की विचारधाराएँ / Western Schools of Philosophy, Kant, Sadhana Paada, Vaiśeṣika
  7. Paper - 1 | Unit - 7 | Data Interpretation: आँकड़े एवं आलेखीय निरूपण / Data and Graphical Representation, आँकड़ा निर्वचन: तालिका / Data Interpretation: Tables
  8. Paper - 1 | Unit - 8 | Information and Communication Technology: कंप्यूटर की मूल बातें और हार्डवेयर / Computer Fundamentals and Hardware, मेमोरी, भंडारण और डेटा निरूपण / Memory, Storage and Data Representation, कंप्यूटर सॉफ्टवेयर / Computer Software, ऑफिस अनुप्रयोग / Office Applications, मल्टीमीडिया और फ़ाइल प्रारूप / Multimedia and File Formats, कंप्यूटर नेटवर्क / Computer Networks, इंटरनेट और वर्ल्ड वाइड वेब / Internet and World Wide Web, ई-मेल और ऑनलाइन संचार / Email and Online Communication, साइबर सुरक्षा / Cyber Security, डिजिटल नैतिकता, बौद्धिक संपदा और समाज / Digital Ethics, IPR and Society, क्लाउड और वितरित कंप्यूटिंग / Cloud and Distributed Computing, उभरती प्रौद्योगिकियाँ / Emerging Technologies, शिक्षा और शासन में ICT / ICT in Education and Governance, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Electronic Data Interchange and E-Commerce, Internet Fundamentals, Web Design & Development, Web Publishing & Hosting, Emerging Technologies, Terms & Abbreviations, Basics of COA, Introduction to OS, Introduction to CN, Data Communication, Net Layer: IP Addressing, Network Security, Number System, Number Representation, Society, Law & Ethics, Keyboard Shortcuts, Website, Browser & Services, भौगोलिक संकेतों का संरक्षण / Protection of Geographical Indications
  9. Paper - 1 | Unit - 9 | People Development and Environment: पारितंत्र और जैव विविधता / Ecosystems and Biodiversity, मानव और पर्यावरण की अंतःक्रिया / Human and Environment Interaction, विकास और पर्यावरण / Development and Environment, प्राकृतिक संसाधन: वन, जल और मृदा / Natural Resources – Forests, Water and Soil, ऊर्जा संसाधन / Energy Resources, वायु प्रदूषण / Air Pollution, जल प्रदूषण और उपचार / Water Pollution and Treatment, ध्वनि प्रदूषण / Noise Pollution, अपशिष्ट प्रबंधन / Waste Management, पर्यावरणीय स्वास्थ्य और विषविज्ञान / Environmental Health and Toxicology, जलवायु परिवर्तन और वैश्विक पर्यावरणीय समस्याएँ / Climate Change and Global Environmental Issues, प्राकृतिक प्रकोप और आपदा प्रबंधन / Natural Hazards and Disaster Management, भारतीय पर्यावरण कानून और नीतियाँ / Indian Environmental Laws and Policies, अंतर्राष्ट्रीय पर्यावरण समझौते / International Environmental Agreements, Environment, Geography, कारखाना और उद्योग व्यवस्थाएँ / Factory and Industry Systems, Earth Materials, Surface Features and Processes, संक्रामक रोग और प्रतिरक्षण / Communicable Diseases and Immunization
  10. Paper - 1 | Unit - 10 | Higher Education System: प्राचीन भारत में शिक्षा / Education in Ancient India, प्राचीन भारत के उच्च शिक्षा केंद्र / Ancient Centres of Higher Learning, औपनिवेशिक काल की शिक्षा नीतियाँ और आयोग / Colonial Education Policies and Commissions, औपनिवेशिक कॉलेज, विश्वविद्यालय व सुधारक / Colonial Colleges, Universities and Reformers, स्वतंत्र भारत में शिक्षा आयोग और नीतियाँ / Education Commissions and Policies after Independence, राष्ट्रीय शिक्षा नीति 2020 / National Education Policy 2020, उच्च शिक्षा संस्थानों के प्रकार / Types of Higher Education Institutions, अधिगम कार्यक्रम और अकादमिक क्रेडिट / Learning Programmes and Academic Credits, व्यावसायिक, तकनीकी और कौशल आधारित शिक्षा / Professional, Technical and Skill-Based Education, मूल्य शिक्षा और पर्यावरण शिक्षा / Value Education and Environmental Education, शासन, प्रशासन और वित्तपोषण / Governance, Administration and Financing, उच्च शिक्षा का नियमन, प्रत्यायन और रैंकिंग / Regulation, Accreditation and Ranking
  11. Live Classes: NTA UGC NET 2025 Live Class
  12. Full Mock Tests:
  13. 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…