1. **Problem:** Add the mixed numbers and fractions as given. 2. **Formula:** To add or subtract mixed numbers, convert them to improper fractions or add whole numbers and fractions separately. 3. **Step-by-step solutions:** **1) 12 3/4 + 0** - Adding zero does not change the number. - Answer: $12 \frac{3}{4}$ **2) 8 1/2 + 3/4** - Convert to improper fractions: $8 \frac{1}{2} = \frac{17}{2}$ - $\frac{17}{2} + \frac{3}{4} = \frac{34}{4} + \frac{3}{4} = \frac{37}{4}$ - Convert back: $9 \frac{1}{4}$ **3) 7 1/10 + 2 4/5** - Convert to improper fractions: $7 \frac{1}{10} = \frac{71}{10}$, $2 \frac{4}{5} = \frac{14}{5} = \frac{28}{10}$ - Add: $\frac{71}{10} + \frac{28}{10} = \frac{99}{10} = 9 \frac{9}{10}$ **4) 3 1/4 + 2 5/6** - Convert to improper fractions: $3 \frac{1}{4} = \frac{13}{4}$, $2 \frac{5}{6} = \frac{17}{6}$ - Find common denominator 12: $\frac{13}{4} = \frac{39}{12}$, $\frac{17}{6} = \frac{34}{12}$ - Add: $\frac{39}{12} + \frac{34}{12} = \frac{73}{12} = 6 \frac{1}{12}$ **5) 14 1/5 + 12 1/10 + 1 14/15** - Convert to improper fractions: - $14 \frac{1}{5} = \frac{71}{5}$ - $12 \frac{1}{10} = \frac{121}{10}$ - $1 \frac{14}{15} = \frac{29}{15}$ - Find common denominator 30: - $\frac{71}{5} = \frac{426}{30}$ - $\frac{121}{10} = \frac{363}{30}$ - $\frac{29}{15} = \frac{58}{30}$ - Add: $\frac{426}{30} + \frac{363}{30} + \frac{58}{30} = \frac{847}{30} = 28 \frac{7}{30}$ **6) 1 - 2/17** - Convert 1 to fraction: $\frac{17}{17}$ - Subtract: $\frac{17}{17} - \frac{2}{17} = \frac{15}{17}$ **7) 5 3/4 - 2 1/4** - Convert to improper fractions: $5 \frac{3}{4} = \frac{23}{4}$, $2 \frac{1}{4} = \frac{9}{4}$ - Subtract: $\frac{23}{4} - \frac{9}{4} = \frac{14}{4} = 3 \frac{1}{2}$ **8) 12 2/3 - 15 1/7** - Convert to improper fractions: $12 \frac{2}{3} = \frac{38}{3}$, $15 \frac{1}{7} = \frac{106}{7}$ - Find common denominator 21: - $\frac{38}{3} = \frac{266}{21}$ - $\frac{106}{7} = \frac{318}{21}$ - Subtract: $\frac{266}{21} - \frac{318}{21} = -\frac{52}{21} = -2 \frac{10}{21}$ **9) 18 1/4 - 11 2/3** - Convert to improper fractions: $18 \frac{1}{4} = \frac{73}{4}$, $11 \frac{2}{3} = \frac{35}{3}$ - Find common denominator 12: - $\frac{73}{4} = \frac{219}{12}$ - $\frac{35}{3} = \frac{140}{12}$ - Subtract: $\frac{219}{12} - \frac{140}{12} = \frac{79}{12} = 6 \frac{7}{12}$ **10) 22 1/2 - 20 2/3 - 6 1/4** - Convert to improper fractions: - $22 \frac{1}{2} = \frac{45}{2}$ - $20 \frac{2}{3} = \frac{62}{3}$ - $6 \frac{1}{4} = \frac{25}{4}$ - Find common denominator 12: - $\frac{45}{2} = \frac{270}{12}$ - $\frac{62}{3} = \frac{248}{12}$ - $\frac{25}{4} = \frac{75}{12}$ - Subtract stepwise: - $\frac{270}{12} - \frac{248}{12} = \frac{22}{12}$ - $\frac{22}{12} - \frac{75}{12} = -\frac{53}{12} = -4 \frac{5}{12}$ 4. **Final answers:** 1) $12 \frac{3}{4}$ 2) $9 \frac{1}{4}$ 3) $9 \frac{9}{10}$ 4) $6 \frac{1}{12}$ 5) $28 \frac{7}{30}$ 6) $\frac{15}{17}$ 7) $3 \frac{1}{2}$ 8) $-2 \frac{10}{21}$ 9) $6 \frac{7}{12}$ 10) $-4 \frac{5}{12}$