`1(1)/(8)+1(6)/(7)+3(3)/(5)=?`

Options

A. `8(121)/(140)`
B. `6(163)/(280)`
C. `9(197)/(280)`
D. `7(117)/(140)`

Explanation

To solve the expression \(1 \frac{1}{8} + 1 \frac{6}{7} + 3 \frac{3}{5}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \(1 \frac{1}{8}\) to an improper fraction:
\[ 1 \frac{1}{8} = \frac{1 \times 8 + 1}{8} = \frac{9}{8} \]

2. Convert \(1 \frac{6}{7}\) to an improper fraction:
\[ 1 \frac{6}{7} = \frac{1 \times 7 + 6}{7} = \frac{13}{7} \]

3. Convert \(3 \frac{3}{5}\) to an improper fraction:
\[ 3 \frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{18}{5} \]

### Step 2: Find the Least Common Multiple (LCM)
Next, we need to find the LCM of the denominators \(8\), \(7\), and \(5\):
- The LCM of \(8\), \(7\), and \(5\) is calculated as:
\[ LCM(8, 7, 5) = 8 \times 7 \times 5 = 280 \]

### Step 3: Rewrite Each Fraction with the LCM as the Denominator
Now, we will rewrite each fraction with \(280\) as the denominator:

1. For \(\frac{9}{8}\):
\[ \frac{9}{8} = \frac{9 \times 35}{8 \times 35} = \frac{315}{280} \]

2. For \(\frac{13}{7}\):
\[ \frac{13}{7} = \frac{13 \times 40}{7 \times 40} = \frac{520}{280} \]

3. For \(\frac{18}{5}\):
\[ \frac{18}{5} = \frac{18 \times 56}{5 \times 56} = \frac{1008}{280} \]

### Step 4: Add the Fractions
Now, we can add the fractions:
\[ \frac{315}{280} + \frac{520}{280} + \frac{1008}{280} = \frac{315 + 520 + 1008}{280} = \frac{1843}{280} \]

### Step 5: Convert the Improper Fraction to a Mixed Number
To convert \(\frac{1843}{280}\) to a mixed number, we divide \(1843\) by \(280\):
- \(1843 \div 280 = 6\) (whole number part)
- Remainder: \(1843 - (6 \times 280) = 1843 - 1680 = 163\)

Thus, we can express it as:
\[ 6 \frac{163}{280} \]

### Final Answer
The final answer is:
\[ \boxed{6 \frac{163}{280}} \]