Simplify the following :
`1""3/25+7/20-2/5`

Answer

To simplify the expression \(1 \frac{3}{25} + \frac{7}{20} - \frac{2}{5}\), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \(1 \frac{3}{25}\) can be converted to an improper fraction.

\[ 1 \frac{3}{25} = \frac{1 \times 25 + 3}{25} = \frac{25 + 3}{25} = \frac{28}{25} \]

### Step 2: Rewrite the expression
Now we can rewrite the expression using the improper fraction:

\[ \frac{28}{25} + \frac{7}{20} - \frac{2}{5} \]

### Step 3: Find the Least Common Multiple (LCM)
Next, we need to find the LCM of the denominators \(25\), \(20\), and \(5\).

- The prime factorization of \(25\) is \(5^2\).
- The prime factorization of \(20\) is \(2^2 \times 5\).
- The prime factorization of \(5\) is \(5\).

The LCM will take the highest power of each prime:

\[ \text{LCM} = 2^2 \times 5^2 = 4 \times 25 = 100 \]

### Step 4: Convert each fraction to have the same denominator
Now we convert each fraction to have a denominator of \(100\):

1. For \(\frac{28}{25}\):
\[ \frac{28}{25} = \frac{28 \times 4}{25 \times 4} = \frac{112}{100} \]

2. For \(\frac{7}{20}\):
\[ \frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100} \]

3. For \(\frac{2}{5}\):
\[ \frac{2}{5} = \frac{2 \times 20}{5 \times 20} = \frac{40}{100} \]

### Step 5: Combine the fractions
Now we can combine the fractions:

\[ \frac{112}{100} + \frac{35}{100} - \frac{40}{100} = \frac{112 + 35 - 40}{100} = \frac{107}{100} \]

### Step 6: Convert to a mixed number
Finally, we convert \(\frac{107}{100}\) to a mixed number:

\[ 107 \div 100 = 1 \quad \text{(with a remainder of 7)} \]

So,

\[ \frac{107}{100} = 1 \frac{7}{100} \]

### Final Answer
The simplified expression is:

\[ 1 \frac{7}{100} \]