To add the mixed numbers \(2 \frac{3}{5}\) and \(4 \frac{1}{10}\), we can follow these steps:
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Convert mixed numbers to improper fractions.
For \(2 \frac{3}{5}\): \[ 2 \frac{3}{5} = 2 \times 5 + 3 = 10 + 3 = 13 \quad \Rightarrow \quad \frac{13}{5} \]
For \(4 \frac{1}{10}\): \[ 4 \frac{1}{10} = 4 \times 10 + 1 = 40 + 1 = 41 \quad \Rightarrow \quad \frac{41}{10} \]
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Find a common denominator.
The denominators are 5 and 10. The least common denominator (LCD) is 10.
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Convert \(\frac{13}{5}\) to have a denominator of 10.
\[ \frac{13}{5} = \frac{13 \times 2}{5 \times 2} = \frac{26}{10} \]
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Now add the two fractions.
\[ \frac{26}{10} + \frac{41}{10} = \frac{26 + 41}{10} = \frac{67}{10} \]
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Convert the improper fraction back to a mixed number.
\(\frac{67}{10}\) can be converted as follows:
- 67 divided by 10 is 6 with a remainder of 7.
- So, \(\frac{67}{10} = 6 \frac{7}{10}\).
Thus, the sum \(2 \frac{3}{5} + 4 \frac{1}{10} = 6 \frac{7}{10}\).