Subtracting Fractions
1. The problem is to subtract fractions from whole numbers and express the answer as mixed numbers if possible.
2. The formula for subtracting a fraction from a whole number $a - \frac{b}{c}$ is to rewrite $a$ as $\frac{ac}{c}$ and then subtract: $$a - \frac{b}{c} = \frac{ac}{c} - \frac{b}{c} = \frac{ac - b}{c}.$$ If the numerator is larger than the denominator, convert to a mixed number.
3. Let's solve each step by step:
1) $5 - \frac{8}{12} = \frac{5 \times 12}{12} - \frac{8}{12} = \frac{60 - 8}{12} = \frac{52}{12} = 4 \frac{4}{12} = 4 \frac{1}{3}$
2) $3 - \frac{11}{15} = \frac{3 \times 15}{15} - \frac{11}{15} = \frac{45 - 11}{15} = \frac{34}{15} = 2 \frac{4}{15}$
3) $2 - \frac{10}{16} = \frac{2 \times 16}{16} - \frac{10}{16} = \frac{32 - 10}{16} = \frac{22}{16} = 1 \frac{6}{16} = 1 \frac{3}{8}$
4) $7 - \frac{4}{9} = \frac{7 \times 9}{9} - \frac{4}{9} = \frac{63 - 4}{9} = \frac{59}{9} = 6 \frac{5}{9}$
5) $8 - \frac{3}{7} = \frac{8 \times 7}{7} - \frac{3}{7} = \frac{56 - 3}{7} = \frac{53}{7} = 7 \frac{4}{7}$
6) $4 - \frac{2}{5} = \frac{4 \times 5}{5} - \frac{2}{5} = \frac{20 - 2}{5} = \frac{18}{5} = 3 \frac{3}{5}$
7) $7 - \frac{1}{3} = \frac{7 \times 3}{3} - \frac{1}{3} = \frac{21 - 1}{3} = \frac{20}{3} = 6 \frac{2}{3}$
8) $9 - \frac{6}{7} = \frac{9 \times 7}{7} - \frac{6}{7} = \frac{63 - 6}{7} = \frac{57}{7} = 8 \frac{1}{7}$
9) $3 - \frac{9}{14} = \frac{3 \times 14}{14} - \frac{9}{14} = \frac{42 - 9}{14} = \frac{33}{14} = 2 \frac{5}{14}$
10) $5 - \frac{17}{20} = \frac{5 \times 20}{20} - \frac{17}{20} = \frac{100 - 17}{20} = \frac{83}{20} = 4 \frac{3}{20}$
11) $9 - \frac{4}{6} = \frac{9 \times 6}{6} - \frac{4}{6} = \frac{54 - 4}{6} = \frac{50}{6} = 8 \frac{2}{6} = 8 \frac{1}{3}$
12) $2 - \frac{8}{13} = \frac{2 \times 13}{13} - \frac{8}{13} = \frac{26 - 8}{13} = \frac{18}{13} = 1 \frac{5}{13}$
13) $4 - \frac{7}{11} = \frac{4 \times 11}{11} - \frac{7}{11} = \frac{44 - 7}{11} = \frac{37}{11} = 3 \frac{4}{11}$
14) $6 - \frac{1}{2} = \frac{6 \times 2}{2} - \frac{1}{2} = \frac{12 - 1}{2} = \frac{11}{2} = 5 \frac{1}{2}$
4. Each answer is simplified and converted to a mixed number where possible.
5. This method helps understand subtraction of fractions from whole numbers by converting the whole number to an equivalent fraction and then subtracting.
Final answers as mixed numbers:
1) $4 \frac{1}{3}$
2) $2 \frac{4}{15}$
3) $1 \frac{3}{8}$
4) $6 \frac{5}{9}$
5) $7 \frac{4}{7}$
6) $3 \frac{3}{5}$
7) $6 \frac{2}{3}$
8) $8 \frac{1}{7}$
9) $2 \frac{5}{14}$
10) $4 \frac{3}{20}$
11) $8 \frac{1}{3}$
12) $1 \frac{5}{13}$
13) $3 \frac{4}{11}$
14) $5 \frac{1}{2}$