To compare the fractions \( \frac{2}{5} \) and \( \frac{1}{2} \), it's helpful to find a common denominator or convert them to decimal form.
- Common Denominator Method:
- The common denominator for 5 and 2 is 10.
- Convert \( \frac{2}{5} \) to a fraction with a denominator of 10: \[ \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \]
- Convert \( \frac{1}{2} \): \[ \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \]
Now we can compare \( \frac{4}{10} \) and \( \frac{5}{10} \):
- \( \frac{4}{10} < \frac{5}{10} \)
- Decimal Method:
- Convert \( \frac{2}{5} \) to decimal: \[ \frac{2}{5} = 0.4 \]
- Convert \( \frac{1}{2} \) to decimal: \[ \frac{1}{2} = 0.5 \]
Now we can compare \( 0.4 \) and \( 0.5 \):
- \( 0.4 < 0.5 \)
In both methods, we find that \( \frac{2}{5} \) is less than \( \frac{1}{2} \): \[ \frac{2}{5} < \frac{1}{2} \]