Short Trick to bring given set of numbers in proportion

Duration: 14 min

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Module outline

  1. Child Development and Pedagogy / बाल विकास एवं शिक्षाशास्त्र: Concept of Development / विकास की अवधारणा, Psychological Theories of Development / विकास के मनोवैज्ञानिक सिद्धांत, Individual Differences, Personality and Gender / व्यक्तिगत भिन्नताएँ, व्यक्तित्व एवं जेंडर, Intelligence and Creativity / बुद्धि एवं सृजनात्मकता, Learning and Its Theories / अधिगम एवं इसके सिद्धांत, How Children Think and Learn / बालक कैसे सोचते एवं सीखते हैं, Emotion, Motivation, Mental Health and Guidance / संवेग, अभिप्रेरणा, मानसिक स्वास्थ्य एवं निर्देशन, Inclusive Education / समावेशी शिक्षा, Teaching-Learning Process / शिक्षण-अधिगम प्रक्रिया, Teaching Methods and Strategies / शिक्षण विधियाँ एवं रणनीतियाँ, Assessment and Evaluation / आकलन एवं मूल्यांकन, Lesson Planning and Teaching Skills / पाठ योजना और शिक्षण कौशल, Teaching Resources and Educational Technology / शिक्षण संसाधन और शैक्षिक प्रौद्योगिकी, Classroom Management and Communication / कक्षा प्रबंधन और सम्प्रेषण, Teacher Identity and Professional Development / शिक्षक पहचान और व्यावसायिक विकास, Educational Thinkers, Aims and National Policies / शैक्षिक विचारक, उद्देश्य एवं राष्ट्रीय नीतियाँ, Life Skills, Values, Peace and Environmental Education / जीवन कौशल, मूल्य, शांति एवं पर्यावरण शिक्षा, Social Science Pedagogy / सामाजिक विज्ञान शिक्षणशास्त्र, Social and Political Life / सामाजिक एवं राजनीतिक जीवन, Science Pedagogy / विज्ञान शिक्षण शास्त्र
  2. Language I — हिंदी / Hindi: भाषा, लिपि और वर्ण-विचार, संधि, शब्द-स्रोत और शब्द-रचना, समास, शब्द-भेद: विकारी और अविकारी, लिंग, वचन, कारक, काल और वाच्य, वाक्य-विचार और शुद्ध लेखन, शब्द-भंडार, रस, छंद, अलंकार और शब्द-शक्ति, हिंदी साहित्य, अपठित बोध, हिंदी शिक्षणशास्त्र, ICT in Education / शिक्षा में ICT
  3. Language II — English: Sounds, Spelling and Word Formation, Parts of Speech, Nouns and Pronouns, Articles, Determiners and Adjectives, Verbs and Modals, Tenses and Subject–Verb Agreement, Adverbs, Prepositions and Conjunctions, Sentence Structure, Voice and Narration, Vocabulary, Sentence Correction and Writing Skills, Poetry and English Literature, Reading Comprehension, Pedagogy of English Language
  4. Language II — اردو / Urdu: رسم الخط، املا اور تلفظ, ذخیرۂ الفاظ, قواعد, محاورے اور ضرب الامثال, شعر و سخن, اردو ادب کی تاریخ, تفہیمِ عبارت, اردو کی تدریس
  5. Language II — संस्कृत / Sanskrit: वर्णविचारः एवं संज्ञाप्रकरणम्, सन्धिप्रकरणम्, शब्दरूपाणि, धातुरूपाणि, कारकाणि एवं विभक्तयः, उपसर्गाः एवं अव्ययानि, प्रत्ययप्रकरणम्, समासप्रकरणम्, वाच्यप्रकरणम्, संख्याज्ञानम्, शब्दज्ञानम् एवं अनुवादः, अपठितावबोधनम्, संस्कृतसाहित्यम् एवं काव्यशास्त्रम्, संस्कृतशिक्षणशास्त्रम्
  6. Mathematics / गणित: Number System & Place Value / संख्या पद्धति एवं स्थानीय मान, Basic Operations, Simplification & Patterns / मूलभूत संक्रियाएँ, सरलीकरण एवं पैटर्न, Factors, Divisibility, HCF & LCM / गुणनखंड, विभाज्यता, म.स.प. एवं ल.स.प., Fractions & Decimals / भिन्न एवं दशमलव, Squares, Cubes, Exponents & Surds / वर्ग, घन, घातांक एवं करणी, Measurement: Length, Mass, Capacity, Time & Money / मापन: लंबाई, भार, धारिता, समय एवं मुद्रा, Algebra / बीजगणित, Ratio, Proportion, Average & Ages / अनुपात, समानुपात, औसत एवं आयु, Percentage, Profit–Loss & Interest / प्रतिशत, लाभ-हानि एवं ब्याज, Time & Work and Speed–Distance / समय-कार्य एवं चाल-दूरी, Lines, Angles, Shapes & Coordinates / रेखाएँ, कोण, आकृतियाँ एवं निर्देशांक, Triangles, Quadrilaterals, Circles & Trigonometry / त्रिभुज, चतुर्भुज, वृत्त एवं त्रिकोणमिति, Mensuration: Perimeter, Area & Volume / क्षेत्रमिति: परिमाप, क्षेत्रफल एवं आयतन, Data Handling, Statistics & Probability / आँकड़ा प्रबंधन, सांख्यिकी एवं प्रायिकता, Mathematics Pedagogy / गणित शिक्षणशास्त्र, Mathematical Operations & Arithmetical Reasoning / गणितीय संक्रियाएँ एवं अंकगणितीय तर्क
  7. Environmental Studies / पर्यावरण अध्ययन: Family, Friends and Community / परिवार, मित्र और समुदाय, Plants / पौधे, Animals / जंतु, Farming and Animal Husbandry / खेती और पशुपालन, Food and Nutrition / भोजन और पोषण, Body and Health / शरीर और स्वास्थ्य, Water / जल, Shelter / आवास, Travel, Transport and Communication / यात्रा, परिवहन और संचार, Maps, Directions and India / मानचित्र, दिशाएँ और भारत, Things We Make and Do / हम क्या बनाते और करते हैं, Earth, Sky and Disasters / पृथ्वी, आकाश और आपदाएँ, Environment, Ecology and Wildlife / पर्यावरण, पारिस्थितिकी और वन्यजीव, Natural Resources, Pollution and Climate Change / प्राकृतिक संसाधन, प्रदूषण और जलवायु परिवर्तन, Pedagogy of Environmental Studies / पर्यावरण अध्ययन का शिक्षणशास्त्र, Ancient Indian History / प्राचीन भारत का इतिहास, Earth, Globe and Maps / पृथ्वी, ग्लोब एवं मानचित्र, Physical Geography / भौतिक भूगोल, Natural Vegetation, Wildlife and World Regions / प्राकृतिक वनस्पति, वन्य जीवन एवं विश्व के प्रदेश, Geography of India / भारत का भूगोल, Resources and Development / संसाधन एवं विकास, Indian Constitution / भारतीय संविधान, Government: Union, State and Local / सरकार: केंद्र, राज्य एवं स्थानीय, Force, Pressure, Work and Energy / बल, दाब, कार्य एवं ऊर्जा, Heat and Sound / ऊष्मा एवं ध्वनि, Light / प्रकाश, Universe and Natural Phenomena / ब्रह्मांड एवं प्राकृतिक परिघटनाएँ, Matter and Its Structure / पदार्थ एवं उसकी संरचना, Metals, Non-metals and Materials of Daily Use / धातु, अधातु एवं दैनिक उपयोग की सामग्री, Living World: Classification, Cell and Tissues / सजीव जगत: वर्गीकरण, कोशिका एवं ऊतक, Human Body and Organ Systems / मानव शरीर एवं अंग तंत्र, Food, Nutrition and Health / भोजन, पोषण एवं स्वास्थ्य, Environment and Ecology / पर्यावरण एवं पारिस्थितिकी, Uttar Pradesh GK / उत्तर प्रदेश सामान्य ज्ञान, Plants: Nutrition, Transport and Reproduction / पादपों में पोषण, परिवहन एवं जनन, Sports / खेल जगत, International Relations & Organisations / अंतरराष्ट्रीय संबंध एवं संगठन, Key Appointments & Office Holders / प्रमुख नियुक्तियाँ एवं पदधारक
  8. Extra Practice (beyond syllabus) / अतिरिक्त अभ्यास (पाठ्यक्रम से बाहर): Indian Economy: Data & Current Affairs / भारतीय अर्थव्यवस्था: आँकड़े एवं समसामयिकी, Indian Art & Culture / भारतीय कला एवं संस्कृति, Science & Technology / विज्ञान एवं प्रौद्योगिकी, Environment & Climate Affairs / पर्यावरण एवं जलवायु समसामयिकी, Defence & Security / रक्षा एवं सुरक्षा, Static General Knowledge / स्थिर सामान्य ज्ञान, Government Schemes, Governance & Infrastructure / सरकारी योजनाएँ, शासन एवं आधारभूत संरचना, Ranking, Seating Arrangement & Puzzles / क्रम, बैठक व्यवस्था एवं पहेली, Calendar & Clock / कैलेंडर एवं घड़ी, Dice & Cubes / पासा एवं घन, Medieval Indian History / मध्यकालीन भारत का इतिहास, Colonial India and Social Reform / औपनिवेशिक भारत एवं समाज सुधार, Indian National Movement and Independent India / भारतीय राष्ट्रीय आंदोलन एवं स्वतंत्र भारत, Technology, Measurement and Motion / प्रौद्योगिकी, मापन एवं गति, Chemical Reactions, Acids, Bases and Salts / रासायनिक अभिक्रियाएँ, अम्ल, क्षार एवं लवण, Economics and Indian Economy / अर्थशास्त्र एवं भारतीय अर्थव्यवस्था, Electricity and Magnetism / विद्युत एवं चुंबकत्व, Bihar GK / बिहार सामान्य ज्ञान, Rajasthan GK / राजस्थान सामान्य ज्ञान, Curriculum and School Activities / पाठ्यचर्या और विद्यालयी गतिविधियाँ, Computer Hardware and Peripherals / कंप्यूटर हार्डवेयर एवं परिधीय उपकरण
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture by Yash Jain introduces ratio and proportion, focusing on a shortcut for finding the number to add or subtract from four given numbers (a, b, c, d) so that they become proportional. The instructor first defines a ratio as a comparison of two quantities and presents the general problem: what should be added or subtracted to a, b, c, d so that they are in proportion? A concrete example asks what should be added to each of 5, 9, 11, and 18. The standard algebraic method is demonstrated: introduce a variable y, write the terms as 5+y, 9+y, 11+y, and 18+y, set up the proportion (5+y)/(9+y) = (11+y)/(18+y), cross-multiply to get (5+y)(18+y) = (11+y)(9+y), expand both sides, and simplify to 90 + 23y = 99 + 20y, yielding y = 3. The instructor then introduces a shortcut formula involving |ad - bc| / (a + d) or related expressions, illustrated by subtracting the fractions 5/9 and 11/18 to obtain a difference of 3. A second example with numbers 19, 37, 47, and 86 is worked using cross-multiplication: 19 x 86 = 1634 and 37 x 47 = 1739, with the difference 105 highlighted. The lecture then shifts to the subtraction variant: what should be subtracted from each of 5, 9, 11, and 18? The terms are written as 5-y, 9-y, 11-y, and 18-y, the proportion (5-y)/(9-y) = (11-y)/(18-y) is set up, cross-multiplied and simplified to give y = -3 (or equivalently +3 in the final boxed answer). The video concludes with a thank-you slide.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an introduction slide titled 'RATIO & PROPORTION - BY YASH JAIN', defining a ratio as 'a comparison of 2 quantities'. The instructor presents the general problem: 'What should be added/subtracted to a, b, c, d so that they are in proportion?' and then displays the specific example: 'Que: What should be added to each of 5, 9, 11, 18 to make them in proportion?' with 'each' underlined. The instructor begins writing the terms on the board, introducing a variable x (later y) to represent the unknown number being added, progressively writing 5+x, 9+x, 11+x, and 18+x to set up the proportion.

  2. 2:00 – 5:00 02:00-05:00

    The instructor writes the proportion setup '5+y : 9+y :: 11+y : 18+y' and the fraction form (5+y)/(9+y) = (11+y)/(18+y). Cross-multiplication is shown as '(5+y)(18+y) = (11+y)(9+y)', with the left side expanding to '90 + 18y' and then fully as '90 + 18y + 5y + y² = 99 + 99y + 11y + y²'. The equation simplifies to '90 + 23y = 99 + 20y', and the final value y=3 is calculated and boxed. A new problem with numbers 19, 37, 47, and 86 is briefly introduced before returning to the previous solution.

  3. 5:00 – 10:00 05:00-10:00

    The instructor demonstrates a shortcut trick using the numbers 5, 9, 11, and 18. The fractions 5/9 and 11/18 are set up for subtraction, with calculations '99 - 90 = 9' and '23 - 20 = 3' shown to find the difference. The result is used to form the proportion '9/3 = 3', marked with a checkmark. A general formula involving 'a, b, c, d' and the expression '|ad - bc| / (a + d)' is written down. A second worked example in red shows the question 'Que: What should be added to each of 19, 37, 47, 86 to make them in proportion?' with cross-multiplication '19 x 86 = 1634' and '37 x 47 = 1739', difference '1739 - 1634 = 105' underlined. The final frame switches to a new question: 'Que: What should be subtracted from each of a, b, c, d to make them in proportion?' with terms 'a-y, b-y, c-y, d-y' written.

  4. 10:00 – 13:47 10:00-13:47

    The video demonstrates the subtraction variant: 'What should be subtracted from each of 5, 9, 11, 18 to make them in proportion?' The instructor writes the expressions (5-y), (9-y), (11-y), and (18-y) and sets up the proportion equation '(5-y)/(9-y) = (11-y)/(18-y)'. Cross-multiplication gives '(18-y)(5-y) = (11-y)(9-y)', which is expanded and simplified to '-3y = 9', leading to the final answer y = -3. The instructor highlights the result and shows a verification step using ratios 2/6 and 8/15. The final slide displays the ratio equation in a red box with X marks, and a separate red circle contains the value '+3', followed by a 'THANKS FOR WATCHING' message.

The lecture teaches two methods for solving proportion problems of the form 'what number should be added or subtracted from four given numbers to make them proportional.' The first method is standard algebra: introduce a variable, set up the proportion by equating the ratio of the first two terms to the ratio of the last two, cross-multiply, expand, and solve for the variable. The second method is a shortcut formula involving |ad - bc| / (a + d) or related expressions, which allows faster computation. The instructor demonstrates both methods with the numbers 5, 9, 11, and 18 (yielding y = 3 for addition) and provides a second example with 19, 37, 47, and 86. The subtraction variant is also covered, showing that the same algebraic setup applies with (a-y) terms instead of (a+y) terms, yielding y = -3 (equivalently +3 in the final boxed answer). The key takeaway is that adding or subtracting the same number to all four terms preserves the structure of the proportion, and cross-multiplication is the primary tool for solving such equations.

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