1. We are asked to add pairs of fractions. The general formula for adding fractions is: $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ are integers and $b,d \neq 0$. 2. Important rule: To add fractions, find a common denominator (usually the product of the denominators), convert each fraction to an equivalent fraction with this common denominator, then add the numerators. 3. Let's solve each addition step-by-step: **(a) $\frac{3}{5} + \frac{1}{4}$** - Common denominator: $5 \times 4 = 20$ - Convert: $\frac{3}{5} = \frac{3 \times 4}{20} = \frac{12}{20}$, $\frac{1}{4} = \frac{1 \times 5}{20} = \frac{5}{20}$ - Add numerators: $12 + 5 = 17$ - Result: $\frac{17}{20}$ **(b) $\frac{2}{3} + \frac{1}{10}$** - Common denominator: $3 \times 10 = 30$ - Convert: $\frac{2}{3} = \frac{20}{30}$, $\frac{1}{10} = \frac{3}{30}$ - Add: $20 + 3 = 23$ - Result: $\frac{23}{30}$ **(c) $\frac{1}{6} + \frac{4}{11}$** - Common denominator: $6 \times 11 = 66$ - Convert: $\frac{1}{6} = \frac{11}{66}$, $\frac{4}{11} = \frac{24}{66}$ - Add: $11 + 24 = 35$ - Result: $\frac{35}{66}$ **(d) $\frac{1}{9} + \frac{3}{8}$** - Common denominator: $9 \times 8 = 72$ - Convert: $\frac{1}{9} = \frac{8}{72}$, $\frac{3}{8} = \frac{27}{72}$ - Add: $8 + 27 = 35$ - Result: $\frac{35}{72}$ **(e) $\frac{1}{3} + \frac{5}{15}$** - Note: $\frac{5}{15} = \frac{1}{3}$ (simplify by dividing numerator and denominator by 5) - Add: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ **(f) $\frac{2}{8} + \frac{4}{11}$** - Simplify $\frac{2}{8} = \frac{1}{4}$ - Common denominator: $4 \times 11 = 44$ - Convert: $\frac{1}{4} = \frac{11}{44}$, $\frac{4}{11} = \frac{16}{44}$ - Add: $11 + 16 = 27$ - Result: $\frac{27}{44}$ **(g) $\frac{5}{10} + \frac{8}{9}$** - Simplify $\frac{5}{10} = \frac{1}{2}$ - Common denominator: $2 \times 9 = 18$ - Convert: $\frac{1}{2} = \frac{9}{18}$, $\frac{8}{9} = \frac{16}{18}$ - Add: $9 + 16 = 25$ - Result: $\frac{25}{18} = 1 \frac{7}{18}$ (improper fraction to mixed number) **(h) $\frac{3}{5} + \frac{6}{20}$** - Simplify $\frac{6}{20} = \frac{3}{10}$ - Common denominator: $5 \times 10 = 50$ - Convert: $\frac{3}{5} = \frac{30}{50}$, $\frac{3}{10} = \frac{15}{50}$ - Add: $30 + 15 = 45$ - Result: $\frac{45}{50} = \frac{9}{10}$ **(i) $\frac{4}{10} + \frac{7}{12}$** - Simplify $\frac{4}{10} = \frac{2}{5}$ - Common denominator: $5 \times 12 = 60$ - Convert: $\frac{2}{5} = \frac{24}{60}$, $\frac{7}{12} = \frac{35}{60}$ - Add: $24 + 35 = 59$ - Result: $\frac{59}{60}$ **(j) $\frac{9}{12} + \frac{5}{24}$** - Simplify $\frac{9}{12} = \frac{3}{4}$ - Common denominator: $4 \times 24 = 24$ (since 24 is multiple of 4) - Convert: $\frac{3}{4} = \frac{18}{24}$, $\frac{5}{24} = \frac{5}{24}$ - Add: $18 + 5 = 23$ - Result: $\frac{23}{24}$ Final answers: (a) $\frac{17}{20}$ (b) $\frac{23}{30}$ (c) $\frac{35}{66}$ (d) $\frac{35}{72}$ (e) $\frac{2}{3}$ (f) $\frac{27}{44}$ (g) $\frac{25}{18} = 1 \frac{7}{18}$ (h) $\frac{9}{10}$ (i) $\frac{59}{60}$ (j) $\frac{23}{24}$