To add the fractions \( \frac{3}{5} + \frac{7}{8} + \frac{3}{10} \), we first need to find a common denominator.
The denominators are 5, 8, and 10. The least common multiple (LCM) of these numbers is 40.
Next, we convert each fraction to have a denominator of 40:
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For \( \frac{3}{5} \): \[ \frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40} \]
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For \( \frac{7}{8} \): \[ \frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40} \]
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For \( \frac{3}{10} \): \[ \frac{3}{10} = \frac{3 \times 4}{10 \times 4} = \frac{12}{40} \]
Now, we can add the fractions: \[ \frac{24}{40} + \frac{35}{40} + \frac{12}{40} = \frac{24 + 35 + 12}{40} = \frac{71}{40} \]
To convert \( \frac{71}{40} \) to a mixed number, we divide 71 by 40:
- 71 divided by 40 is 1 with a remainder of 31.
Thus, we can express \( \frac{71}{40} \) as: \[ 1 \frac{31}{40} \]
Now, the fraction \( \frac{31}{40} \) is already in simplest form since 31 is a prime number and does not have common factors with 40.
Therefore, the final answer in mixed number form is: \[ 1 \frac{31}{40} \]