`6(3)/(8)-3(1)/(16)+5(1)/(8)=?`

Options

A. `6(5)/(16)`
B. `4(5)/(16)`
C. `9(3)/(16)`
D. `8(7)/(16)`

Explanation

To solve the expression \( 6 \frac{3}{8} - 3 \frac{1}{16} + 5 \frac{1}{8} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers into improper fractions.

1. For \( 6 \frac{3}{8} \):
\[ 6 \frac{3}{8} = \frac{6 \times 8 + 3}{8} = \frac{48 + 3}{8} = \frac{51}{8} \]

2. For \( 3 \frac{1}{16} \):
\[ 3 \frac{1}{16} = \frac{3 \times 16 + 1}{16} = \frac{48 + 1}{16} = \frac{49}{16} \]

3. For \( 5 \frac{1}{8} \):
\[ 5 \frac{1}{8} = \frac{5 \times 8 + 1}{8} = \frac{40 + 1}{8} = \frac{41}{8} \]

Now we can rewrite the expression:
\[ \frac{51}{8} - \frac{49}{16} + \frac{41}{8} \]

### Step 2: Find a Common Denominator
The denominators are 8 and 16. The least common multiple (LCM) of 8 and 16 is 16. We will convert all fractions to have a denominator of 16.

1. Convert \( \frac{51}{8} \) to a denominator of 16:
\[ \frac{51}{8} = \frac{51 \times 2}{8 \times 2} = \frac{102}{16} \]

2. The fraction \( \frac{49}{16} \) remains the same.

3. Convert \( \frac{41}{8} \) to a denominator of 16:
\[ \frac{41}{8} = \frac{41 \times 2}{8 \times 2} = \frac{82}{16} \]

Now the expression is:
\[ \frac{102}{16} - \frac{49}{16} + \frac{82}{16} \]

### Step 3: Combine the Fractions
Now that all fractions have the same denominator, we can combine them:
\[ \frac{102 - 49 + 82}{16} \]

Calculating the numerator:
\[ 102 - 49 = 53 \]
\[ 53 + 82 = 135 \]

So we have:
\[ \frac{135}{16} \]

### Step 4: Convert to Decimal (if needed)
To convert \( \frac{135}{16} \) to a decimal:
\[ 135 \div 16 = 8.4375 \]

### Final Answer
Thus, the final answer is:
\[ \frac{135}{16} \text{ or } 8.4375 \]

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