To find a common denominator for the fractions \(\frac{2}{7}\) and \(\frac{3}{8}\), you need to find the least common multiple (LCM) of the denominators, which are 7 and 8.
The multiples of 7 are: 7, 14, 21, 28, 35, ...
The multiples of 8 are: 8, 16, 24, 32, 40, ...
The smallest common multiple in both lists is 56.
Now, we'll convert each fraction to have this common denominator:
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For \(\frac{2}{7}\): \[ \frac{2}{7} \times \frac{8}{8} = \frac{16}{56} \]
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For \(\frac{3}{8}\): \[ \frac{3}{8} \times \frac{7}{7} = \frac{21}{56} \]
So, the fractions \(\frac{2}{7}\) and \(\frac{3}{8}\) converted to have a common denominator of 56 are:
\[ \frac{16}{56} \text{ and } \frac{21}{56} \]