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RATIO AND PROPORTION

The video provides a comprehensive explanation of Ratio and Proportion. The instructor begins by defining Ratio (4:21) as a measure of the quantity of one thing with respect to another, often expressed as a fraction (e.24-6:54). Next, the concept of Proportion is introduced (7:11-8:48), which is used to equalize two ratios. The video then delves into types of proportion (8:53), including: Third Proportion (9:02-10:00) Fourth Proportion (9:58-10:38) Mean Proportion (10:38-13:20), which is calculated as the square root of the product of the given numbers. The instructor also covers Ratio to Fraction conversion (13:29-14:02) and Equivalent Ratios (14:03-15:27). Compound Ratio is explained (15:40-17:16) as the multiple of one antecedent with another when two or more ratios are provided. Several rules for solving ratio questions are discussed: Componendo Rule (17:30-18:22) Dividendo Rule (18:24-19:00) Componendo and Dividendo Rule (19:16-20:32) Invertendo Rule (20:53-21:17) Alternendo Rule (21:38-22:04) The video concludes with various problem-solving examples, including: Finding `a:b:c` given `a:b` and `b:c` (23:31-25:58). Calculating compound ratios (26:34-31:11). Determining mean ratios (31:16-32:40). Solving for unknown variables in proportional equations (33:15-37:09). Dividing an amount into shares based on given ratios (38:01-48:19). Coin-based ratio questions (48:42-54:16). Dividing a sum among individuals in a given fractional ratio (54:31-57:04). Finding numbers when their ratio and difference are known (58:11-1:01:21). A word problem involving property division among three sons based on proportional shares (1:02:58-1:09:14). Calculating rotation in degrees based on time (1:10:04-1:11:18). A problem involving blending two varieties of tea in the ratio of their costs (1:11:58-1:17:07).