7 7/20-4,75+3 4/5

To solve the expression \( 7 \frac{7}{20} - 4.75 + 3 \frac{4}{5} \), let's convert all the mixed numbers and decimals into improper fractions or decimals for easier calculation.

1. Convert \( 7 \frac{7}{20} \) into an improper fraction: \[ 7 \frac{7}{20} = \frac{7 \times 20 + 7}{20} = \frac{140 + 7}{20} = \frac{147}{20} \]

2. Convert \( 4.75 \) to a fraction: \[ 4.75 = \frac{475}{100} = \frac{19}{4} \]

3. Convert \( 3 \frac{4}{5} \) into an improper fraction: \[ 3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} \]

Now substitute these conversions back into the original expression: \[ \frac{147}{20} - \frac{19}{4} + \frac{19}{5} \]

Next, we need a common denominator to combine these fractions. The least common multiple of 20, 4, and 5 is 20.

Now we will convert each fraction to have a denominator of 20:

• The first fraction is already \( \frac{147}{20} \).
• For \( \frac{19}{4} \): \[ \frac{19}{4} = \frac{19 \times 5}{4 \times 5} = \frac{95}{20} \]
• For \( \frac{19}{5} \): \[ \frac{19}{5} = \frac{19 \times 4}{5 \times 4} = \frac{76}{20} \]

Now substitute back into the expression: \[ \frac{147}{20} - \frac{95}{20} + \frac{76}{20} \]

Combine the fractions: \[ \frac{147 - 95 + 76}{20} = \frac{147 - 95 + 76}{20} = \frac{128}{20} \]

Now simplify \( \frac{128}{20} \): \[ \frac{128 \div 4}{20 \div 4} = \frac{32}{5} \]

Thus, the final answer is:

\[ \frac{32}{5} \text{ or } 6 \frac{2}{5} \]

So, the result of \( 7 \frac{7}{20} - 4.75 + 3 \frac{4}{5} \) is \( \frac{32}{5} \) or \( 6 \frac{2}{5} \).