Explanation: To understand the conversion of a fraction to a percentage, it is essential to know the relationship between fractions, decimals, and percentages. A percentage is a way of expressing a number as a fraction of 100. Therefore, to convert a fraction to a percentage, you multiply the fraction by 100.
Let's take the fraction 3/5 as an example. The fraction 3/5 means 3 parts out of 5. To convert this to a percentage, we need to express it as a fraction of 100. This can be done by multiplying the fraction by 100.
The formula to convert a fraction to a percentage is:
\[ \text{Percentage} = \left( \frac{\text{Numerator}}{\text{Denominator}} \right) \times 100 \]
For the fraction 3/5:
\[ \text{Percentage} = \left( \frac{3}{5} \right) \times 100 \]
First, we perform the division:
\[ \frac{3}{5} = 0.6 \]
Next, we multiply by 100 to convert the decimal to a percentage:
\[ 0.6 \times 100 = 60 \]
Therefore, the fraction 3/5 is equivalent to 60%.
This method can be applied to any fraction to convert it to a percentage. It is a fundamental skill in basic arithmetic and is often tested in various competitive examinations in India, such as UPSC, SSC, Bank PO, CLAT, and MAT. Understanding this conversion is crucial for solving problems related to percentages, fractions, and decimals in these exams.
The common mistakes students make include forgetting to multiply by 100, misunderstanding the relationship between fractions and percentages, and incorrectly simplifying the fraction before converting. To avoid these mistakes, it is important to follow the formula and understand the underlying concept of converting a fraction to a percentage.