When comparing fractions, a straightforward method is to convert each fraction into a decimal by dividing the numerator (the top number) by the denominator (the bottom number). This approach simplifies the comparison, as it is often easier to evaluate decimal values than to compare fractions directly.
For example, to compare the fractions \( \frac{3}{4} \) and \( \frac{4}{5} \), you would perform the following calculations:
1. \( \frac{3}{4} = 3 \div 4 = 0.75 \)
2. \( \frac{4}{5} = 4 \div 5 = 0.80 \)
Since \( 0.80 \) is greater than \( 0.75 \), it follows that \( \frac{4}{5} \) is the larger fraction.
Continuing with another example, consider \( \frac{46}{15} \) and \( \frac{13}{4} \):
1. \( \frac{46}{15} = 46 \div 15 \approx 3.07 \)
2. \( \frac{13}{4} = 13 \div 4 = 3.25 \)
Here, \( 3.25 \) is greater than \( 3.07 \), indicating that \( \frac{13}{4} \) is the larger fraction.
For the fractions \( \frac{2}{17} \) and \( \frac{3}{29} \):
1. \( \frac{2}{17} = 2 \div 17 \approx 0.118 \)
2. \( \frac{3}{29} = 3 \div 29 \approx 0.103 \)
In this case, \( 0.118 \) is greater than \( 0.103 \), so \( \frac{2}{17} \) is the larger fraction.
Lastly, when comparing \( \frac{25}{40} \) and \( \frac{60}{96} \):
1. \( \frac{25}{40} = 25 \div 40 = 0.625 \)
2. \( \frac{60}{96} = 60 \div 96 = 0.625 \)
Both fractions yield the same decimal value, indicating that they are equal.
This method of converting fractions to decimals is a reliable technique for determining which fraction is larger or if they are equal, enhancing your ability to compare fractions effectively.