Addendo Property & Equivalent Ratio Property
Duration: 16 min
This video lesson is available to enrolled students.
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This educational video provides a comprehensive lecture on the properties of Ratio and Proportion, specifically focusing on the Addendo Property and the Equivalent Ratio Property. The instructor, Yash Jain, begins by defining these properties and providing algebraic proofs to establish their validity. He demonstrates how to apply these rules to simplify complex ratio expressions, showing that the sum of numerators divided by the sum of denominators equals the original ratio value. The lecture progresses to more advanced applications, including ratios with coefficients and mixed algebraic terms, culminating in a solved example problem that utilizes these properties to find a specific value without knowing individual variable magnitudes.
Chapters
0:00 – 2:00 00:00-02:00
The video opens with a title slide displaying 'RATIO & PROPORTION' alongside a colorful 3D pie chart graphic. The instructor introduces the topic, stating that the session will cover the 'Properties of Proportion'. The visual context is set with a clean, educational slide design featuring the instructor's name, Yash Jain, and the branding 'Knowledge Gate Educator'. This introductory segment establishes the learning objective for the lesson.
2:00 – 5:00 02:00-05:00
The instructor introduces the 'Addendo Property' with a slide stating: 'If a : b = c : d = e : f, value of each ratio is (a + c + e) : (b + d + f)'. He writes the general form on the board: a/b = c/d = e/f = (a+c+e+...)/(b+d+f+...). To prove this, he sets each ratio equal to a constant k, so a=bk, c=dk, and e=fk. He substitutes these into the sum of numerators and denominators, showing that (bk+dk+fk)/(b+d+f) simplifies back to k, proving the property holds true. He illustrates this with the numerical example 2/3 = 6/9 = 8/12, where (2+6+8)/(3+9+12) equals 16/24, which simplifies to 2/3.
5:00 – 10:00 05:00-10:00
The lecture extends the Addendo Property to include coefficients, showing that if a/b = c/d = e/f, then (am+cn+ep)/(bm+dn+fp) also equals the original ratio. The instructor then transitions to the 'Equivalent Ratio Property', defined on the slide as: 'If a : b :: c : d then (a ± c) : (b ± d) :: a : b'. He provides an algebraic proof for this as well, starting with a/b = c/d = k, which implies a=bk and c=dk. Substituting these into (a+c)/(b+d) yields (bk+dk)/(b+d), which factors to k(b+d)/(b+d), simplifying to k. This confirms that the ratio of the sum or difference of antecedents to the sum or difference of consequents remains constant.
10:00 – 15:00 10:00-15:00
The instructor demonstrates complex applications of the Equivalent Ratio Property. He shows examples like (2a+3c)/(2b+3d) and (ab+cd)/(b^2+d^2), explaining how to manipulate the ratios to fit the property's form. A specific problem is presented: 'If a:b = c:d = 2:3 then what is the value of (ab+cd)/(b^2+d^2)?'. He solves this by recognizing that the expression can be broken down or manipulated using the property. He writes out the steps, showing how to substitute variables or use the ratio value directly to find the final answer, emphasizing that individual values of a, b, c, and d are not needed if the ratio is known.
15:00 – 15:45 15:00-15:45
The video concludes with a black screen displaying the text 'THANKS FOR WATCHING' in bold white and orange letters. The instructor wraps up the session, having covered the theoretical definitions, algebraic proofs, and practical examples of the Addendo and Equivalent Ratio properties. The final visual serves as a clear end marker for the educational content.
The video systematically builds understanding of Ratio and Proportion properties, starting with the fundamental Addendo Property and moving to the more versatile Equivalent Ratio Property. By providing algebraic proofs and numerical examples, the instructor ensures students understand not just the 'how' but the 'why' behind these mathematical rules. The progression from simple sums to complex algebraic expressions prepares learners for advanced problem-solving in competitive exams.