Simpilfy:
`3 + 1 (1)/(5)+(2)/(3)-(7)/(15)`

Answer

To simplify the expression \( 3 + 1 \frac{1}{5} + \frac{2}{3} - \frac{7}{15} \), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 1 \frac{1}{5} \) can be converted to an improper fraction.
- Multiply the whole number (1) by the denominator (5) and add the numerator (1):
\[ 1 \times 5 + 1 = 5 + 1 = 6 \]
- Therefore, \( 1 \frac{1}{5} = \frac{6}{5} \).

So, the expression now becomes:
\[ 3 + \frac{6}{5} + \frac{2}{3} - \frac{7}{15} \]

### Step 2: Convert the whole number to a fraction
Next, convert the whole number \( 3 \) to a fraction with a common denominator. We can express \( 3 \) as:
\[ 3 = \frac{3 \times 15}{15} = \frac{45}{15} \]

Now the expression is:
\[ \frac{45}{15} + \frac{6}{5} + \frac{2}{3} - \frac{7}{15} \]

### Step 3: Find a common denominator
The denominators we have are \( 15, 5, \) and \( 3 \). The least common multiple (LCM) of these numbers is \( 15 \).

### Step 4: Convert all fractions to have the common denominator
- The fraction \( \frac{6}{5} \) needs to be converted:
\[ \frac{6}{5} = \frac{6 \times 3}{5 \times 3} = \frac{18}{15} \]
- The fraction \( \frac{2}{3} \) needs to be converted:
\[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \]

Now the expression is:
\[ \frac{45}{15} + \frac{18}{15} + \frac{10}{15} - \frac{7}{15} \]

### Step 5: Combine the fractions
Now that all fractions have the same denominator, we can combine them:
\[ \frac{45 + 18 + 10 - 7}{15} = \frac{66}{15} \]

### Step 6: Simplify the fraction
Now we need to simplify \( \frac{66}{15} \). The greatest common divisor (GCD) of \( 66 \) and \( 15 \) is \( 3 \).
- Divide both the numerator and the denominator by \( 3 \):
\[ \frac{66 \div 3}{15 \div 3} = \frac{22}{5} \]

### Final Answer
The simplified expression is:
\[ \frac{22}{5} \]

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