Question

[1 4/5+(1/4+1/5)]-2 2/5

Answer 1

To solve the expression \([1 \frac{4}{5} + ( \frac{1}{4} + \frac{1}{5}) ] - 2 \frac{2}{5}\), we will follow these steps:

1. Convert mixed numbers to improper fractions.
2. Simplify the expression inside the brackets.
3. Subtract the final term.

### Step 1: Convert mixed numbers to improper fractions

Convert \(1 \frac{4}{5}\) and \(2 \frac{2}{5}\):

\[
1 \frac{4}{5} = \frac{5 \cdot 1 + 4}{5} = \frac{9}{5}
\]
\[
2 \frac{2}{5} = \frac{5 \cdot 2 + 2}{5} = \frac{12}{5}
\]

### Step 2: Simplify the expression inside the brackets

Calculate \(\frac{1}{4} + \frac{1}{5}\):

To add \(\frac{1}{4}\) and \(\frac{1}{5}\), we need a common denominator, which is 20.

\[
\frac{1}{4} = \frac{5}{20}
\]
\[
\frac{1}{5} = \frac{4}{20}
\]
\[
\frac{1}{4} + \frac{1}{5} = \frac{5}{20} + \frac{4}{20} = \frac{9}{20}
\]

Now plug this back into the expression:

\[
1 \frac{4}{5} + \left( \frac{1}{4} + \frac{1}{5} \right) = \frac{9}{5} + \frac{9}{20}
\]

To add \(\frac{9}{5}\) and \(\frac{9}{20}\), we again need a common denominator. The least common denominator of 5 and 20 is 20.

Convert \(\frac{9}{5}\) to a denominator of 20:

\[
\frac{9}{5} = \frac{36}{20}
\]

Now add:

\[
\frac{36}{20} + \frac{9}{20} = \frac{45}{20}
\]

### Step 3: Subtract \(2 \frac{2}{5}\)

Now substitute back into the expression:

\[
[1 \frac{4}{5} + ( \frac{1}{4} + \frac{1}{5}) ] - 2 \frac{2}{5}
= \frac{45}{20} - \frac{12}{5}
\]

Convert \(\frac{12}{5}\) to a denominator of 20:

\[
\frac{12}{5} = \frac{48}{20}
\]

Now subtract:

\[
\frac{45}{20} - \frac{48}{20} = \frac{-3}{20}
\]

### Final Result

The final result of the expression \([1 \frac{4}{5} + ( \frac{1}{4} + \frac{1}{5}) ] - 2 \frac{2}{5}\) is:

\[
\boxed{-\frac{3}{20}}
\]