1. **State the problems:** We need to subtract the mixed fractions: - $5 \frac{1}{8} - 3 \frac{7}{16}$ - $16 \frac{3}{8} - 8 \frac{7}{9}$ - $15 - 3 \frac{4}{11}$ 2. **Formula and rules:** To subtract mixed fractions, convert them to improper fractions or convert to a common denominator, then subtract the numerators. 3. **Problem 6:** $5 \frac{1}{8} - 3 \frac{7}{16}$ - Convert to improper fractions: $5 \frac{1}{8} = \frac{5 \times 8 + 1}{8} = \frac{41}{8}$ $3 \frac{7}{16} = \frac{3 \times 16 + 7}{16} = \frac{55}{16}$ - Find common denominator: $16$ - Convert $\frac{41}{8}$ to sixteenths: $\frac{41 \times 2}{16} = \frac{82}{16}$ - Subtract: $\frac{82}{16} - \frac{55}{16} = \frac{27}{16}$ - Convert back to mixed number: $1 \frac{11}{16}$ 4. **Problem 7:** $16 \frac{3}{8} - 8 \frac{7}{9}$ - Convert to improper fractions: $16 \frac{3}{8} = \frac{16 \times 8 + 3}{8} = \frac{131}{8}$ $8 \frac{7}{9} = \frac{8 \times 9 + 7}{9} = \frac{79}{9}$ - Find common denominator: $72$ (LCM of 8 and 9) - Convert fractions: $\frac{131}{8} = \frac{131 \times 9}{72} = \frac{1179}{72}$ $\frac{79}{9} = \frac{79 \times 8}{72} = \frac{632}{72}$ - Subtract: $\frac{1179}{72} - \frac{632}{72} = \frac{547}{72}$ - Convert back to mixed number: $\frac{547}{72} = 7 \frac{43}{72}$ 5. **Problem 8:** $15 - 3 \frac{4}{11}$ - Convert $3 \frac{4}{11}$ to improper fraction: $\frac{3 \times 11 + 4}{11} = \frac{37}{11}$ - Convert 15 to fraction with denominator 11: $15 = \frac{15 \times 11}{11} = \frac{165}{11}$ - Subtract: $\frac{165}{11} - \frac{37}{11} = \frac{128}{11}$ - Convert back to mixed number: $\frac{128}{11} = 11 \frac{7}{11}$ **Final answers:** - $5 \frac{1}{8} - 3 \frac{7}{16} = 1 \frac{11}{16}$ - $16 \frac{3}{8} - 8 \frac{7}{9} = 7 \frac{43}{72}$ - $15 - 3 \frac{4}{11} = 11 \frac{7}{11}$