- Use the formula \(\text{Percentage} = \frac{a}{b} \times 100\%\) to find the percent of \(a\) in \(b\).
- Ensure units are consistent by converting different units (e.g., hours to minutes, rupees to paisa, meters to cm) before dividing.
- The results are as follows:
- 1(a) \(\boxed{50\%}\)
- 1(b) \(\boxed{40\%}\)
- 1(c) \(\boxed{33.33\%}\)
- 1(d) \(\boxed{25\%}\)
- 1(e) \(\boxed{4\%}\)
- 1(f) \(\boxed{15\%}\)
- 2(a) \(\boxed{80\%}\)
Explanation
- Analyzing the Percentage Formula
To determine what percent a value \(a\) is of another value \(b\), we use the fundamental formula for calculating percentages:
\[ \text{Percentage} = \left( \frac{a}{b} \right) \times 100\% \]
This formula calculates the ratio of the part to the total and scales it by 100 to express it as a percentage. In each case, it is essential to ensure that both values, \(a\) and \(b\), are expressed in the same units before performing the division.
- Solving Percentage Questions from Part 1
For the questions in part 1:
AFor 10 out of 20, the calculation is \(\left( \frac{10}{20} \right) \times 100\% = 0.5 \times 100\% = 50\%\).
BFor 240 out of 600, the calculation is \(\left( \frac{240}{600} \right) \times 100\% = 0.4 \times 100\% = 40\%\).
CFor 1 out of 3, the calculation is \(\left( \frac{1}{3} \right) \times 100\% \approx 33.33\%\).
D15 minutes as a percent of 1 hour requires consistent units. Since 1 hour = 60 minutes, the calculation is \(\left( \frac{15}{60} \right) \times 100\% = 0.25 \times 100\% = 25\%\).
E20 paisa as a percent of Rs 5 requires converting rupees to paisa. Since Rs 1 = 100 paisa, Rs 5 = 500 paisa. The calculation is \(\left( \frac{20}{500} \right) \times 100\% = 0.04 \times 100\% = 4\%\).
(f) 30 cm as a percent of 2 meters requires consistent units. Since 1 meter = 100 cm, 2 meters = 200 cm. The calculation is \(\left( \frac{30}{200} \right) \times 100\% = 0.15 \times 100\% = 15\%\).
- Solving the Class Attendance Question
For the question in part 2, which involves students in a class:
AThere are 16 present students out of 20 total students. The calculation is \(\left( \frac{16}{20} \right) \times 100\% = 0.8 \times 100\% = 80\%\).
This shows that 80% of the students were present in class.
Examples
Understanding percentages is highly practical in everyday life. For instance, when you are shopping and see a 20% discount on an item originally priced at \(\$50\), you can quickly calculate the savings as \(\$50 \times 0.20 = \$10\), meaning you pay \(\$40\). Similarly, when tracking academic performance, if you score 45 out of 50 on a test, you can calculate your grade as \(\left( \frac{45}{50} \right) \times 100\% = 90\%\), helping you monitor your progress effectively. Mastery of these simple conversions is essential for managing personal finances, grades, and resource allocation.