To subtract the mixed numbers \( 4 \frac{1}{5} \) and \( 2 \frac{4}{5} \), we can follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
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For \( 4 \frac{1}{5} \): \[ 4 \frac{1}{5} = \frac{(4 \times 5) + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5} \]
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For \( 2 \frac{4}{5} \): \[ 2 \frac{4}{5} = \frac{(2 \times 5) + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} \]
Step 2: Subtract the improper fractions.
Now we can perform the subtraction: \[ \frac{21}{5} - \frac{14}{5} \]
Since both fractions have the same denominator, we can simply subtract the numerators: \[ \frac{21 - 14}{5} = \frac{7}{5} \]
Step 3: Convert the result back to a mixed number.
Now, convert \( \frac{7}{5} \) back to a mixed number:
- Divide the numerator by the denominator:
- \( 7 \div 5 = 1 \) with a remainder of \( 2 \).
- So, \( \frac{7}{5} \) can be expressed as: \[ 1 \frac{2}{5} \]
Final Answer
Thus, the result of \( 4 \frac{1}{5} - 2 \frac{4}{5} \) is: \[ \boxed{1 \frac{2}{5}} \]
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