What is Ratio & Proportion, Definition & Examples
Duration: 12 min
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The video is an educational lecture on Ratio and Proportion by Yash Jain from Knowledge Gate Eduventures. It begins by defining ratio as a comparison of quantities, illustrating it with visual aids like colored dots. The instructor explains the mathematical definition, notation (colon, fraction, "to"), and the requirement for quantities to be of the same kind. He provides a real-world example involving the cost of fruits. The second half defines proportion as the equivalence of two ratios, explaining terms like antecedent, consequent, extreme, and mean proportion, concluding with standard notation. The lecture is structured to build from basic definitions to practical applications and then to the concept of proportion.
Chapters
0:00 – 2:00 00:00-02:00
The video opens with a title card displaying "RATIO & PROPORTION" in bold text alongside a colorful 3D pie chart graphic. The instructor introduces the topic, transitioning to a slide titled "Ratio a comparison of 2 quantities". This slide features a visual representation using colored dots (pink, blue, green, yellow) to illustrate parts of a whole. The text on the slide explicitly states "Ratio a comparison of 2 quantities" and shows examples like "1:2" for pink to blue and "3 to 11" for green to total. The instructor begins explaining that a ratio is a way to compare quantities, setting the stage for the formal definition. He mentions that ratios can be written in three ways: colon, word, or fraction form.
2:00 – 5:00 02:00-05:00
The lecture moves to a formal slide titled "Definition of Ratio". The text defines ratio as "the comparison of two or more numbers in terms of 'how many times'". The instructor writes on the screen, deriving relationships like `b = 2a` and `a:b = 1:2`. He explains that ratios can be written in three ways: colon, word, or fraction form. He writes `a:b:c = 1:2:3` to show ratios involving three terms. The slide emphasizes that the comparison is efficient when quantities are of the same kind. The instructor underlines key phrases like "two or more numbers" and "how many times" to highlight the core definition. He also notes that the sign used to denote a ratio is ':'.
5:00 – 10:00 05:00-10:00
The instructor elaborates on the terminology, defining 'a' as the antecedent (first term) and 'b' as the consequent (second term). A crucial point is made about units: "Comparison of same item must be done in ratio. A Kilogram can't be compared with a gram." He provides a detailed example involving a character named Popatlal who purchased a dozen lemons for Rs 20 and a dozen apples for Rs 100. The slide shows the calculation: "Cost of Apples/ Cost of Lemons = 100/20 = 5". The instructor concludes that apples are 5 times more expensive than lemons, reinforcing the concept of ratio as a multiplier. He also notes that ratios can be simplified forms of quantities.
10:00 – 11:45 10:00-11:45
The final section introduces "What is Proportion?". The slide defines it as "an equation that says that two ratios are equivalent". An example is given: "one package of cookie mix results in 20 cookies... two packages will result in 40 cookies," leading to the equation `20/1 = 40/2`. The notation `x:y :: z:w` is introduced. The instructor explains that `x` and `w` are extreme proportions, while `y` and `z` are mean proportions. The video concludes with a "THANKS FOR WATCHING" slide, wrapping up the lesson on these fundamental mathematical relationships.
The video provides a clear, step-by-step progression from the basic definition of ratio to the more complex concept of proportion. It effectively uses visual aids and real-world examples to clarify abstract mathematical terms. The distinction between antecedent and consequent, and extreme and mean proportion, is clearly defined. The emphasis on unit consistency is a key takeaway for students. The lecture serves as a solid foundation for understanding these mathematical relationships.