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Answer:
1. Convert each mixed number to an improper fraction.
2. Find a common denominator.
3. Add the fractions.
4. Convert the result back to a mixed number if necessary.
[tex] - \(7 \frac{1}{8}\):[/tex]
[tex]7 \frac{1}{8} = \frac{7 \times 8 + 1}{8} = \frac{56 + 1}{8} = \frac{57}{8}[/tex]
[tex]- \(6 \frac{3}{4}\):[/tex]
[tex]6 \frac{3}{4} = \frac{6 \times 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4}[/tex]
- The denominators are 8 and 4. The least common multiple of 8 and 4 is 8.
- Convert \frac{27}{4}) to a fraction with a denominator of 8:
[tex]\frac{27}{4} = \frac{27 \times 2}{4 \times 2} = \frac{54}{8}[/tex]
[tex] \frac{57}{8} + \frac{54}{8} = \frac{57 + 54}{8} = \frac{111}{8}[/tex]
[tex]{\frac{111}{8} = 13 \frac{7}{8} \quad \text{(since 111 divided by 8 is 13 with a remainder of 7)}}[/tex]
[tex] 7 \frac{1}{8} = \frac{57}{8}[/tex]
[tex]6 \frac{3}{4} = \frac{27}{4} = \frac{54}{8}[/tex]
[tex]\frac{57}{8} + \frac{54}{8} = \frac{111}{8} = 13 \frac{7}{8}[/tex]