To add the mixed numbers \(1 \frac{2}{3}\) and \(2 \frac{5}{8}\), follow these steps:
-
Convert the mixed numbers to improper fractions.
- For \(1 \frac{2}{3}\): \[ 1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3} \]
- For \(2 \frac{5}{8}\): \[ 2 \frac{5}{8} = \frac{8 \times 2 + 5}{8} = \frac{21}{8} \]
-
Find a common denominator to add the fractions. The least common denominator of 3 and 8 is 24.
- Convert \(\frac{5}{3}\) to a fraction with a denominator of 24: \[ \frac{5}{3} = \frac{5 \times 8}{3 \times 8} = \frac{40}{24} \]
- Convert \(\frac{21}{8}\) to a fraction with a denominator of 24: \[ \frac{21}{8} = \frac{21 \times 3}{8 \times 3} = \frac{63}{24} \]
-
Now add the two fractions: \[ \frac{40}{24} + \frac{63}{24} = \frac{40 + 63}{24} = \frac{103}{24} \]
-
Convert \(\frac{103}{24}\) back to a mixed number:
- Divide \(103\) by \(24\):
\[
103 \div 24 = 4 \quad \text{(whole number part)}
\]
- The remainder is \(103 - (24 \times 4) = 103 - 96 = 7\).
- So, we can express it as a mixed number: \[ 4 \frac{7}{24} \]
- Divide \(103\) by \(24\):
\[
103 \div 24 = 4 \quad \text{(whole number part)}
\]
Thus, the answer is \(4 \frac{7}{24}\).
In the requested format: \[ 4 , [7]/[24] \]