Solve the following expression :
`16/5 - 3/8 + 11/10`

Answer

To solve the expression \( \frac{16}{5} - \frac{3}{8} + \frac{11}{10} \), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the denominators
The denominators are 5, 8, and 10.

- The prime factorization of 5 is \( 5^1 \).
- The prime factorization of 8 is \( 2^3 \).
- The prime factorization of 10 is \( 2^1 \times 5^1 \).

To find the LCM, we take the highest power of each prime:
- For 2, the highest power is \( 2^3 \) (from 8).
- For 5, the highest power is \( 5^1 \) (from both 5 and 10).

Thus, the LCM is:
\[ LCM = 2^3 \times 5^1 = 8 \times 5 = 40 \]

### Step 2: Convert each fraction to have the common denominator of 40
Now we convert each fraction:

1. For \( \frac{16}{5} \):
\[ \frac{16}{5} = \frac{16 \times 8}{5 \times 8} = \frac{128}{40} \]

2. For \( \frac{3}{8} \):
\[ \frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \]

3. For \( \frac{11}{10} \):
\[ \frac{11}{10} = \frac{11 \times 4}{10 \times 4} = \frac{44}{40} \]

### Step 3: Combine the fractions
Now we can combine the fractions:
\[ \frac{128}{40} - \frac{15}{40} + \frac{44}{40} = \frac{128 - 15 + 44}{40} \]

### Step 4: Perform the arithmetic in the numerator
Calculating the numerator:
\[ 128 - 15 = 113 \]
\[ 113 + 44 = 157 \]

So we have:
\[ \frac{157}{40} \]

### Step 5: Convert to mixed number (if needed)
To convert \( \frac{157}{40} \) to a mixed number:
- Divide 157 by 40, which gives 3 with a remainder of 37.
Thus,
\[ \frac{157}{40} = 3 \frac{37}{40} \]

### Final Answer
The final answer is:
\[ 3 \frac{37}{40} \]

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