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: \[ 1 \frac{3}{4} + 2 \frac{4}{5} = 4 \frac{11}{20} \]