Summary
Highlights
The video introduces the concepts of percentage, rate, and base using an example of a bag costing 500 pesos with a 50% discount. It defines rate as the percent with the percent sign, base as the original amount (often after 'of'), and percentage as the part or portion of the base (often beside 'is').
The video presents the formulas: Percentage (P) = Rate (R) * Base (B), Rate (R) = Percentage (P) / Base (B), and Base (B) = Percentage (P) / Rate (R). A triangle diagram is introduced as a mnemonic device to easily remember these formulas.
The first example demonstrates how to find the percentage: 'What is 20% of 300?'. The steps involve identifying the rate (20%) and base (300), converting the rate to a decimal (0.20), and then multiplying the decimal rate by the base. The answer is 60.
A second example for finding percentage is provided: 'If the original price is 150 pesos and the rate of discount is 25%, what is the amount of reduction?'. The original price is the base, the discount rate is the rate, and the amount of reduction is the percentage. The calculation shows 25% of 150 is 37.50 pesos.
This section explains how to find the rate: 'What percent of 24 is 12?'. Here, 24 is the base and 12 is the percentage. The formula R = P/B is used, dividing 12 by 24 to get 0.5. This decimal is then converted to a percentage by moving the decimal point two places to the right and adding the percent sign, resulting in 50%.
Another problem for finding the rate: 'Ali had 450 ml of alcohol... after a week he consumed 45 ml. What percent of the alcohol was consumed?'. 450 ml is the base, and 45 ml is the percentage. Dividing 45 by 450 yields 0.1, which converts to 10%.
The video moves on to finding the base: '15 is 20% of what number?'. 15 is the percentage, and 20% is the rate. The formula B = P/R is applied. The rate 20% is converted to 0.20, and 15 is divided by 0.20. The division of a whole number by a decimal is explained, resulting in an answer of 75.
The final example for finding the base: 'Marco has a daily allowance of 10 pesos a day, which is 40% of his classmate's daily allowance. How much is his classmate's daily allowance?'. 10 pesos is the percentage, and 40% is the rate. The rate (40%) is converted to 0.40, and 10 is divided by 0.40, revealing the classmate's allowance is 25 pesos.