1 3/4 + 2 4/5

To add the mixed numbers \(1 \frac{3}{4}\) and \(2 \frac{4}{5}\), follow these steps: 1. **Convert the mixed numbers to improper fractions:** - For \(1 \frac{3}{4}\): \[ 1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \] - For \(2 \frac{4}{5}\): \[ 2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} \] 2. **Find a common denominator:** The denominators are 4 and 5. The least common multiple of 4 and 5 is 20. 3. **Convert the fractions to have the same denominator:** - For \(\frac{7}{4}\): \[ \frac{7}{4} = \frac{7 \times 5}{4 \times 5} = \frac{35}{20} \] - For \(\frac{14}{5}\): \[ \frac{14}{5} = \frac{14 \times 4}{5 \times 4} = \frac{56}{20} \] 4. **Add the two fractions:** \[ \frac{35}{20} + \frac{56}{20} = \frac{35 + 56}{20} = \frac{91}{20} \] 5. **Convert the improper fraction back to a mixed number:** \(\frac{91}{20}\) can be converted to a mixed number by dividing 91 by 20. - \(91 \div 20 = 4\) (whole number) - Remainder: \(91 - 80 = 11\) Thus, \(\frac{91}{20} = 4 \frac{11}{20}\). So, the final result is: \[ 1 \frac{3}{4} + 2 \frac{4}{5} = 4 \frac{11}{20} \]