Demo: Basics of Percentages, Percentage - Fraction Conversions

Duration: 13 min

This video lesson is available to enrolled students.

Return to /learn/CTET-PAPER-1/mathematics/commercial-arithmetic-6iw4eh/percentage-basics-conversion-ls799b/asset-demo-basics-of-percentages-percentage-fraction-conversions after enrolling

Inside: a video lesson and guided study material.

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, Curriculum and School Activities / पाठ्यचर्या और विद्यालयी गतिविधियाँ, Lesson Planning and Teaching Skills / पाठ योजना और शिक्षण कौशल, Teaching Resources and Educational Technology / शिक्षण संसाधन और शैक्षिक प्रौद्योगिकी, Educational Thinkers, Aims and National Policies / शैक्षिक विचारक, उद्देश्य एवं राष्ट्रीय नीतियाँ, Classroom Management and Communication / कक्षा प्रबंधन और सम्प्रेषण, Teacher Identity and Professional Development / शिक्षक पहचान और व्यावसायिक विकास, Social Science Pedagogy / सामाजिक विज्ञान शिक्षणशास्त्र, Social and Political Life / सामाजिक एवं राजनीतिक जीवन, Science Pedagogy / विज्ञान शिक्षण शास्त्र, Life Skills, Values, Peace and Environmental Education / जीवन कौशल, मूल्य, शांति एवं पर्यावरण शिक्षा, Constitution, Commissions, Acts and Schemes in Education / संविधान, आयोग, अधिनियम एवं योजनाएँ
  2. 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, Alphabet & Number Test / वर्णमाला एवं संख्या परीक्षण, Non-Verbal Reasoning / अशाब्दिक तर्क, Dice & Cubes / पासा एवं घन, Mathematical Operations & Arithmetical Reasoning / गणितीय संक्रियाएँ एवं अंकगणितीय तर्क, Ranking, Seating Arrangement & Puzzles / क्रम, बैठक व्यवस्था एवं पहेली, Calendar & Clock / कैलेंडर एवं घड़ी, Venn Diagrams & Logical Deduction / वेन आरेख एवं तार्किक निगमन
  3. 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, Physical Geography / भौतिक भूगोल, Resources and Development / संसाधन एवं विकास, Force, Pressure, Work and Energy / बल, दाब, कार्य एवं ऊर्जा, Environment and Ecology / पर्यावरण एवं पारिस्थितिकी, Science & Technology / विज्ञान एवं प्रौद्योगिकी, Heat and Sound / ऊष्मा एवं ध्वनि, Light / प्रकाश, Universe and Natural Phenomena / ब्रह्मांड एवं प्राकृतिक परिघटनाएँ, Chemical Reactions, Acids, Bases and Salts / रासायनिक अभिक्रियाएँ, अम्ल, क्षार एवं लवण, Natural Vegetation, Wildlife and World Regions / प्राकृतिक वनस्पति, वन्य जीवन एवं विश्व के प्रदेश, Environment & Climate Affairs / पर्यावरण एवं जलवायु समसामयिकी
  4. Language I/II — 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
  5. Language I/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
  6. Language I/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
  7. Language I/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
  8. Language I/II — বাংলা / Bengali: ভাষা, ধ্বনি ও বর্ণ, সন্ধি ও বানান, শব্দের উৎস ও গঠন, সমাস, পদ পরিচয়, কারক ও বিভক্তি, ক্রিয়া ও কাল, বাক্যতত্ত্ব, শব্দার্থ ও বাগর্থ, পাঠ অনুধাবন ও সাহিত্য, নির্মিতি ও পত্রলিখন, বাংলা শিক্ষণবিদ্যা
  9. Extra Practice (beyond syllabus) / अतिरिक्त अभ्यास (पाठ्यक्रम से बाहर): Computer Hardware and Peripherals / कंप्यूटर हार्डवेयर एवं परिधीय उपकरण, International Relations & Organisations / अंतरराष्ट्रीय संबंध एवं संगठन, Indian Economy: Data & Current Affairs / भारतीय अर्थव्यवस्था: आँकड़े एवं समसामयिकी
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video lecture, presented by Yash Jain, provides a comprehensive introduction to the fundamentals of percentages and their conversion into fractions. The lesson begins by establishing the core conceptual understanding of a percentage as a value per hundred, using practical examples like discounts to illustrate how 25% represents Rs. 25 off every Rs. 100 of price. The instructor systematically scales this logic to higher values such as Rs. 200 and Rs. 300, demonstrating proportional calculations for various items including T-shirts and pants. The curriculum then transitions to real-world applications, covering shopping mall discounts, academic marks, population changes, and company performance metrics. A significant portion of the lecture is dedicated to mathematical conversions, specifically teaching how to convert percentages into fractions by dividing by 100 and simplifying the result. This includes handling complex cases involving mixed fractions like 16 + (2/3)% and 83 + (1/3)%. The final segment introduces an important property of percentages, deriving the formula for calculating P% of X as (P/100) * X. The instructor demonstrates this property through step-by-step calculations, such as finding 20% of 800 and comparing A% of B with B% of A, effectively bridging the gap between conceptual understanding and computational application.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture opens with a title slide introducing the topic of Percentages by Yash Jain, setting the stage for the lesson. The instructor immediately moves to basic concepts, posing a critical question: 'What does a discount of 25% mean?' The core definition is established on-screen stating that for every Rs. 100 price, a customer receives a discount of Rs. 25. This foundational concept is reinforced by calculating the net price for a reference value of Rs. 100, showing the subtraction '100 - 25'. The instructor then scales this logic to demonstrate proportional discounts for higher price points, specifically calculating the discount for Rs. 200 as Rs. 50 and for Rs. 300 as Rs. 75, visually displaying the arithmetic '200 - 50' and '300 - 75' to solidify the understanding of percentage as a rate per hundred.

  2. 2:00 – 5:00 02:00-05:00

    Building on the base reference of Rs. 100, the instructor applies the discount concept to a handwritten table listing specific items with varying prices. The visible text shows calculations for a T-shirt priced at 300 (discount 75), Pants at 400 (discount 100), Lower at 200 (discount 50), and Hand gloves at 100 (discount 25). This practical application transitions into a broader discussion on the applications of percentages, with text on screen listing 'Shopping Mall Discounts', 'Marks' (80%, 70%, 60%), and 'Increase or decrease in performance or population'. The instructor demonstrates calculating specific percentage values, such as 30% of 200 resulting in 60 and 30% of 100 resulting in 30. The segment concludes by introducing the rules for converting percentages into fractions, explicitly writing 'Percentage to Fraction (Divide by 100)' and 'Fraction to Percentage (Multiply by 100)' on the board.

  3. 5:00 – 10:00 05:00-10:00

    This segment focuses on the mechanical process of converting percentages to fractions using specific examples. The instructor solves 25% by writing '25/100' and simplifying it to '1/4'. Similarly, 60% is converted to '60/100', simplified to '3/5', and expressed as a ratio '3:5'. The lesson advances to handling mixed fraction percentages, starting with 16 + (2/3)%. The instructor converts the mixed number to an improper fraction '50/3', divides by 100, and simplifies the result to '1/6'. A new example is introduced at the end of this window involving 83 + (1/3)%, where the mixed number is converted to '250/3' before division by 100. The visual evidence shows the step-by-step reduction of these complex fractions, emphasizing the rule to convert mixed numbers to improper fractions first before applying the division by 100 rule.

  4. 10:00 – 12:43 10:00-12:43

    The final section introduces 'An Important Property of Percentages', deriving the general formula for calculating P% of X as (P/100) * X, which simplifies to PX/100. The instructor demonstrates this with a specific calculation of '20% of 800', showing the conversion to '20/100 * 800' and arriving at the result '160'. The lesson concludes by presenting a comparative property on screen: 'A% of B' versus 'B% of A', using the example '75% of 32' and '32% of 75'. The video ends with a closing slide displaying the text 'THANKYOU FOR WATCHING', marking the conclusion of the instructional content on percentage and fraction conversions.

The lecture effectively progresses from conceptual definitions to computational fluency. The teaching strategy relies heavily on the 'per hundred' baseline, using Rs. 100 as a constant reference to explain discounts before scaling to arbitrary numbers like 200 or 300. This scaffolding allows students to grasp the proportional nature of percentages before tackling abstract calculations. The transition from practical applications like shopping discounts and marks to formal mathematical conversions (percent to fraction) is logical, ensuring students understand the utility of percentages in real life before mastering the arithmetic. The handling of mixed fractions like 16 + (2/3)% is a critical technical skill emphasized, requiring the conversion to improper fractions before division. The final property of percentages (A% of B = B% of A) serves as a powerful shortcut for mental math, rounding out the lesson with both fundamental rules and advanced properties. The consistent use of on-screen text to display formulas like 'P/100 * X' and specific calculations ensures that the visual evidence supports the verbal instruction, making it suitable for revision notes.

Loading lesson…