`(7)5/32+(23)1/3-(12)1/8=?`

Options

A. (18)35/69
B. (17)35/96
C. (18)35/96
D. (5)7/48

Answer

To solve the expression \( (7) \frac{5}{32} + (23) \frac{1}{3} - (12) \frac{1}{8} \), we will follow these steps:

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

1. For \( 7 \frac{5}{32} \):
\[ 7 \frac{5}{32} = \frac{7 \times 32 + 5}{32} = \frac{224 + 5}{32} = \frac{229}{32} \]

2. For \( 23 \frac{1}{3} \):
\[ 23 \frac{1}{3} = \frac{23 \times 3 + 1}{3} = \frac{69 + 1}{3} = \frac{70}{3} \]

3. For \( 12 \frac{1}{8} \):
\[ 12 \frac{1}{8} = \frac{12 \times 8 + 1}{8} = \frac{96 + 1}{8} = \frac{97}{8} \]

### Step 2: Rewrite the Expression
Now we can rewrite the expression using the improper fractions:
\[ \frac{229}{32} + \frac{70}{3} - \frac{97}{8} \]

### Step 3: Find the Least Common Multiple (LCM)
Next, we need to find the LCM of the denominators \( 32, 3, \) and \( 8 \). The LCM is \( 96 \).

### Step 4: Convert Each Fraction to the Common Denominator
Now we convert each fraction to have a denominator of \( 96 \).

1. For \( \frac{229}{32} \):
\[ \frac{229}{32} = \frac{229 \times 3}{32 \times 3} = \frac{687}{96} \]

2. For \( \frac{70}{3} \):
\[ \frac{70}{3} = \frac{70 \times 32}{3 \times 32} = \frac{2240}{96} \]

3. For \( \frac{97}{8} \):
\[ \frac{97}{8} = \frac{97 \times 12}{8 \times 12} = \frac{1164}{96} \]

### Step 5: Combine the Fractions
Now we can combine the fractions:
\[ \frac{687}{96} + \frac{2240}{96} - \frac{1164}{96} = \frac{687 + 2240 - 1164}{96} \]

### Step 6: Perform the Addition and Subtraction
Calculating the numerator:
\[ 687 + 2240 - 1164 = 1763 \]
Thus, we have:
\[ \frac{1763}{96} \]

### Step 7: Convert to Mixed Number
Now we convert \( \frac{1763}{96} \) to a mixed number:
1. Divide \( 1763 \) by \( 96 \):
\[ 1763 \div 96 = 18 \quad \text{(whole number)} \]
Remainder:
\[ 1763 - (18 \times 96) = 1763 - 1728 = 35 \]
So, we can express it as:
\[ 18 \frac{35}{96} \]

### Final Answer
Thus, the final answer is:
\[ (7) \frac{5}{32} + (23) \frac{1}{3} - (12) \frac{1}{8} = 18 \frac{35}{96} \]