1. The problem is to subtract fractions with unlike denominators and simplify the result. 2. The formula for subtracting fractions with unlike denominators is: $$\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$$ where $a$, $b$, $c$, and $d$ are integers and $b \neq 0$, $d \neq 0$. 3. After subtracting, simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD). 4. Now, solve each problem step-by-step: **(a)** $\frac{1}{2} - \frac{1}{4}$ $$= \frac{1 \times 4 - 1 \times 2}{2 \times 4} = \frac{4 - 2}{8} = \frac{2}{8} = \frac{1}{4}$$ **(b)** $\frac{1}{3} - \frac{1}{6}$ $$= \frac{1 \times 6 - 1 \times 3}{3 \times 6} = \frac{6 - 3}{18} = \frac{3}{18} = \frac{1}{6}$$ **(c)** $\frac{3}{8} - \frac{1}{4}$ $$= \frac{3 \times 4 - 1 \times 8}{8 \times 4} = \frac{12 - 8}{32} = \frac{4}{32} = \frac{1}{8}$$ **(d)** $\frac{2}{5} - \frac{3}{10}$ $$= \frac{2 \times 10 - 3 \times 5}{5 \times 10} = \frac{20 - 15}{50} = \frac{5}{50} = \frac{1}{10}$$ **(e)** $\frac{5}{8} - \frac{1}{2}$ $$= \frac{5 \times 2 - 1 \times 8}{8 \times 2} = \frac{10 - 8}{16} = \frac{2}{16} = \frac{1}{8}$$ **(f)** $\frac{2}{3} - \frac{2}{9}$ $$= \frac{2 \times 9 - 2 \times 3}{3 \times 9} = \frac{18 - 6}{27} = \frac{12}{27} = \frac{4}{9}$$ **(g)** $\frac{1}{2} - \frac{1}{6}$ $$= \frac{1 \times 6 - 1 \times 2}{2 \times 6} = \frac{6 - 2}{12} = \frac{4}{12} = \frac{1}{3}$$ **(h)** $\frac{4}{5} - \frac{8}{15}$ $$= \frac{4 \times 15 - 8 \times 5}{5 \times 15} = \frac{60 - 40}{75} = \frac{20}{75} = \frac{4}{15}$$ **(i)** $\frac{2}{3} - \frac{1}{4}$ $$= \frac{2 \times 4 - 1 \times 3}{3 \times 4} = \frac{8 - 3}{12} = \frac{5}{12}$$ **(j)** $\frac{6}{7} - \frac{1}{3}$ $$= \frac{6 \times 3 - 1 \times 7}{7 \times 3} = \frac{18 - 7}{21} = \frac{11}{21}$$ **(k)** $\frac{5}{6} - \frac{3}{4}$ $$= \frac{5 \times 4 - 3 \times 6}{6 \times 4} = \frac{20 - 18}{24} = \frac{2}{24} = \frac{1}{12}$$ **(l)** $\frac{7}{8} - \frac{3}{4}$ $$= \frac{7 \times 4 - 3 \times 8}{8 \times 4} = \frac{28 - 24}{32} = \frac{4}{32} = \frac{1}{8}$$ **(m)** $\frac{11}{12} - \frac{3}{8}$ $$= \frac{11 \times 8 - 3 \times 12}{12 \times 8} = \frac{88 - 36}{96} = \frac{52}{96} = \frac{13}{24}$$ **(n)** $\frac{9}{10} - \frac{3}{4}$ $$= \frac{9 \times 4 - 3 \times 10}{10 \times 4} = \frac{36 - 30}{40} = \frac{6}{40} = \frac{3}{20}$$ **(o)** $\frac{5}{16} - \frac{1}{4}$ $$= \frac{5 \times 4 - 1 \times 16}{16 \times 4} = \frac{20 - 16}{64} = \frac{4}{64} = \frac{1}{16}$$ **(p)** $\frac{3}{5} - \frac{1}{6}$ $$= \frac{3 \times 6 - 1 \times 5}{5 \times 6} = \frac{18 - 5}{30} = \frac{13}{30}$$ **(q)** $\frac{5}{6} - \frac{3}{4}$ (repeat from k) $$= \frac{1}{12}$$ **(r)** $\frac{2}{3} - \frac{3}{5}$ $$= \frac{2 \times 5 - 3 \times 3}{3 \times 5} = \frac{10 - 9}{15} = \frac{1}{15}$$ **(s)** $\frac{1}{6} - \frac{1}{18}$ $$= \frac{1 \times 18 - 1 \times 6}{6 \times 18} = \frac{18 - 6}{108} = \frac{12}{108} = \frac{1}{9}$$ **(t)** $\frac{11}{14} - \frac{2}{7}$ $$= \frac{11 \times 7 - 2 \times 14}{14 \times 7} = \frac{77 - 28}{98} = \frac{49}{98} = \frac{1}{2}$$ **(u)** $\frac{1}{2} - \frac{4}{9}$ $$= \frac{1 \times 9 - 4 \times 2}{2 \times 9} = \frac{9 - 8}{18} = \frac{1}{18}$$ **(v)** $\frac{4}{9} - \frac{1}{4}$ $$= \frac{4 \times 4 - 1 \times 9}{9 \times 4} = \frac{16 - 9}{36} = \frac{7}{36}$$ **(w)** $\frac{11}{15} - \frac{3}{10}$ $$= \frac{11 \times 10 - 3 \times 15}{15 \times 10} = \frac{110 - 45}{150} = \frac{65}{150} = \frac{13}{30}$$ **(x)** $\frac{3}{4} - \frac{1}{6}$ $$= \frac{3 \times 6 - 1 \times 4}{4 \times 6} = \frac{18 - 4}{24} = \frac{14}{24} = \frac{7}{12}$$ Final answers rewritten: 1) $\frac{1}{4}$ 2) $\frac{1}{6}$ 3) $\frac{1}{8}$ 4) $\frac{1}{10}$ 5) $\frac{1}{8}$ 6) $\frac{4}{9}$ 7) $\frac{1}{3}$ 8) $\frac{4}{15}$ 9) $\frac{5}{12}$ 10) $\frac{11}{21}$ 11) $\frac{1}{12}$ 12) $\frac{1}{8}$ 13) $\frac{13}{24}$ 14) $\frac{3}{20}$ 15) $\frac{1}{16}$ 16) $\frac{13}{30}$ 17) $\frac{1}{12}$ 18) $\frac{1}{15}$ 19) $\frac{1}{9}$ 20) $\frac{1}{2}$ 21) $\frac{1}{18}$ 22) $\frac{7}{36}$ 23) $\frac{13}{30}$ 24) $\frac{7}{12}$ Each subtraction is done by finding a common denominator, subtracting numerators, and simplifying the fraction to lowest terms.