To compare the fractions \(\frac{3}{8}\) and \(\frac{1}{5}\), we need to find a common denominator.
The denominators are 8 and 5. The least common multiple (LCM) of 8 and 5 can be found as follows:
- The multiples of 8 are: 8, 16, 24, 32, 40, ...
- The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, ...
The smallest common multiple is 40.
Now, we will convert each fraction to have a denominator of 40.
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For \(\frac{3}{8}\): \[ \frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \]
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For \(\frac{1}{5}\): \[ \frac{1}{5} = \frac{1 \times 8}{5 \times 8} = \frac{8}{40} \]
Now we compare \(\frac{15}{40}\) and \(\frac{8}{40}\).
Since \(15 > 8\), we see that:
\[ \frac{3}{8} > \frac{1}{5} \]
Thus, \(\frac{3}{8}\) is the larger fraction.
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