Simplify the following expressions :
`6/15 + 3/2`

Answer

To simplify the expression \( \frac{6}{15} + \frac{3}{2} \), we can follow these steps:

### Step 1: Find a common denominator
The denominators of the fractions are 15 and 2. The least common multiple (LCM) of 15 and 2 is 30.

### Step 2: Convert each fraction to have the common denominator
- For \( \frac{6}{15} \):
\[ \frac{6}{15} = \frac{6 \times 2}{15 \times 2} = \frac{12}{30} \]

- For \( \frac{3}{2} \):
\[ \frac{3}{2} = \frac{3 \times 15}{2 \times 15} = \frac{45}{30} \]

### Step 3: Add the fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{12}{30} + \frac{45}{30} = \frac{12 + 45}{30} = \frac{57}{30} \]

### Step 4: Simplify the resulting fraction
To simplify \( \frac{57}{30} \), we can find the greatest common divisor (GCD) of 57 and 30. The GCD is 3.
- Divide both the numerator and the denominator by 3:
\[ \frac{57 \div 3}{30 \div 3} = \frac{19}{10} \]

### Step 5: Convert to a mixed number (if necessary)
The fraction \( \frac{19}{10} \) can be expressed as a mixed number:
\[ 19 \div 10 = 1 \quad \text{(whole number)} \]
The remainder is 9, so we can write:
\[ \frac{19}{10} = 1 \frac{9}{10} \]

Thus, the simplified form of the expression \( \frac{6}{15} + \frac{3}{2} \) is:
\[ 1 \frac{9}{10} \]