What should come in place of question mark (?) in the following questions ?
`1""3/7-1""1/5=?-4""1/8+1""1/8`

Options

A. `3""7/(72)`
B. `3""4/(72)`
C. `3""8/(35)`
D. `3""(12)/(35)`

Answer

To solve the equation \( 1 \frac{3}{7} - 1 \frac{1}{5} = ? - 4 \frac{1}{8} + 1 \frac{1}{8} \), we will follow these steps:

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

1. \( 1 \frac{3}{7} = \frac{7 \times 1 + 3}{7} = \frac{10}{7} \)
2. \( 1 \frac{1}{5} = \frac{5 \times 1 + 1}{5} = \frac{6}{5} \)
3. \( 4 \frac{1}{8} = \frac{8 \times 4 + 1}{8} = \frac{33}{8} \)
4. \( 1 \frac{1}{8} = \frac{8 \times 1 + 1}{8} = \frac{9}{8} \)

### Step 2: Rewrite the Equation
Now, we can rewrite the equation using these improper fractions:
\[ \frac{10}{7} - \frac{6}{5} = ? - \frac{33}{8} + \frac{9}{8} \]

### Step 3: Simplify the Right Side
Combine the fractions on the right side:
\[ ? - \frac{33}{8} + \frac{9}{8} = ? - \frac{24}{8} = ? - 3 \]

### Step 4: Solve the Left Side
Now, we need to solve the left side:
\[ \frac{10}{7} - \frac{6}{5} \]
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 7 and 5 is 35.

Convert each fraction:
1. \( \frac{10}{7} = \frac{10 \times 5}{7 \times 5} = \frac{50}{35} \)
2. \( \frac{6}{5} = \frac{6 \times 7}{5 \times 7} = \frac{42}{35} \)

Now we can subtract:
\[ \frac{50}{35} - \frac{42}{35} = \frac{8}{35} \]

### Step 5: Set Up the Equation
Now we have:
\[ \frac{8}{35} = ? - 3 \]

### Step 6: Solve for ?
To find \( ? \), we can rearrange the equation:
\[ ? = \frac{8}{35} + 3 \]

Convert 3 to a fraction with a denominator of 35:
\[ 3 = \frac{3 \times 35}{1 \times 35} = \frac{105}{35} \]

Now add the fractions:
\[ ? = \frac{8}{35} + \frac{105}{35} = \frac{113}{35} \]

### Step 7: Convert Back to Mixed Number
Convert \( \frac{113}{35} \) back to a mixed number:
1. Divide 113 by 35, which gives 3 with a remainder of 8.
2. Thus, \( \frac{113}{35} = 3 \frac{8}{35} \).

### Final Answer
The value that should come in place of the question mark is:
\[ ? = 3 \frac{8}{35} \]