Short Trick to convert given ratio into required ratio

Duration: 8 min

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  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
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  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
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  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 lecture by Yash Jain teaches a shortcut for ratio and proportion problems asking what number must be added to or subtracted from each term of a given ratio a:b so that it becomes c:d. The lesson begins by defining a ratio as a comparison of two quantities and posing the general question: what should be added or subtracted to each term of a:b to convert it into c:d? The instructor first demonstrates the standard algebraic method using two examples. For subtraction, he solves what should be subtracted from each term of 15:19 to make it 3:4 by setting up (15-y)/(19-y) = 3/4, cross-multiplying to get 4(15-y) = 3(19-y), expanding to 60 - 4y = 57 - 3y, and solving for y. For addition, he solves what should be added to each term of 9:16 to make it 2:3 by setting up (9+y)/(16+y) = 2/3, cross-multiplying to get 3(9+y) = 2(16+y), expanding to 27 + 3y = 32 + 2y, and solving to find y = 5. The core of the lesson is then a direct shortcut formula that avoids solving equations entirely. The instructor introduces the general formula |ad - bc| / |(a+c) - (b+d)|, then simplifies the denominator to |a-c| (or equivalently the difference of the target ratio terms). The method is: cross-multiply the original and target ratios, subtract the two products to get a numerator difference, then divide by the absolute difference of the target ratio terms. Applying this to 9:16 becoming 2:3, he calculates 9*3 = 27 and 16*2 = 32, subtracts to get 5, divides by 3-2 = 1, yielding the answer 5. He notes this saves time compared to algebra, referencing a timer showing 40 seconds crossed out and replaced with 60 seconds. The lesson concludes with two practice examples: adding to 11:21 to get 3:5 (calculating 11*5 = 55, 21*3 = 63, difference 8, divided by 5-3 = 2 to get answer 4), and subtracting from 23:38 to get 4:7 (calculating 23*7 = 161, 38*4 = 152, difference 9, divided by 7-4 = 3 to get answer 3). The consistent rule is: cross-multiply, subtract products, divide by the difference of target ratio terms.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The opening slide displays the heading 'RATIO & PROPORTION - BY YASH JAIN' with a whiteboard panel reading 'Ratio a comparison of 2 quantities' illustrated with colored dots labeled part, whole and total. A pink slide poses the general question 'What should be added/subtracted to each term of a:b to convert them to c:d?' At 35s an orange slide introduces the first specific example: 'Que: What should be added to each term of 9 : 16 so that new ratio becomes 2 : 3?' The instructor writes the fraction 9/16 with an arrow pointing to 2/3, then sets up (9+y)/(16+y) = 2/3 and cross-multiplies to '3(9+y) = 2(16+y)', expanding to '27+3y = 32+2y' and solving to get y = 5.

  2. 2:00 – 5:00 02:00-05:00

    The instructor first solves a subtraction problem for the ratio 15:19 to become 3:4 by setting up (15-y)/(19-y) = 3/4 and cross-multiplying to get 4(15-y) = 3(19-y), expanding to 60 - 4y = 57 - 3y. He then transitions back to the addition problem for 9:16 becoming 2:3 and introduces a general shortcut formula using absolute values of cross-products: |ad-bc| / |(a+c)-(b+d)|. He simplifies the denominator to |a-c|, highlighting it with a red circle. Applying the shortcut, he calculates 9*3 = 27 and 16*2 = 32, subtracts to get 5, and divides by the difference of target ratio terms (3-2 = 1), writing the final answer 5/1 on the board. A timer drawn on the board shows '40 sec' crossed out and replaced with '60 sec', indicating a time-saving goal.

  3. 5:00 – 7:54 05:00-07:54

    The instructor applies the shortcut to two additional practice problems. For 'What should be added to each term of 11 : 21 so that new ratio becomes 3 : 5?', he calculates 11*5 = 55 and 21*3 = 63, finds the difference 63-55 = 8, and divides by 5-3 = 2 to get the answer 4. For 'What should be subtracted from each term of 23 : 38 so that new ratio becomes 4 : 7?', he calculates 23*7 = 161 and 38*4 = 152, finds the difference 161-152 = 9, and divides by 7-4 = 3 to get the answer 3. The consistent method is cross-multiplying original and target ratio terms, subtracting the products, and dividing by the difference of the new ratio terms.

The central teaching point is a direct shortcut formula for converting one ratio to another by adding or subtracting the same number from each term. The standard algebraic approach sets up (a±y)/(b±y) = c/d and solves for y through cross-multiplication. The shortcut bypasses this by computing |ad - bc| divided by the absolute difference of the target ratio terms. The numerator comes from cross-multiplying the original ratio's first term with the target's second term and vice versa, then subtracting. The denominator is simply the difference between the two terms of the target ratio. This works for both addition and subtraction problems, as demonstrated with 9:16 to 2:3 (answer 5), 15:19 to 3:4, 11:21 to 3:5 (answer 4), and 23:38 to 4:7 (answer 3). The instructor emphasizes time efficiency, noting the shortcut saves significant calculation steps compared to full algebraic solving.

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