What approximate value will come in place of question mark (?) in the following questions. (You are not expected to calculate the exact value)
`(125.98)/(154.03) xx (198.02)/(17.99) - (156.05)/(101.98) xx (51.03)/(78.03) = ?`

Options

A. 8
B. 25
C. 35
D. 50

Answer

To find the approximate value of the expression

\[ \frac{125.98}{154.03} \times \frac{198.02}{17.99} - \frac{156.05}{101.98} \times \frac{51.03}{78.03} = ? \]

we will simplify each term by rounding the numbers to their nearest whole numbers.

### Step 1: Approximate the values
- For \(125.98\), we can approximate it to \(126\).
- For \(154.03\), we can approximate it to \(154\).
- For \(198.02\), we can approximate it to \(198\).
- For \(17.99\), we can approximate it to \(18\).
- For \(156.05\), we can approximate it to \(156\).
- For \(101.98\), we can approximate it to \(102\).
- For \(51.03\), we can approximate it to \(51\).
- For \(78.03\), we can approximate it to \(78\).

Now, substituting these approximations into the expression gives us:

\[ \frac{126}{154} \times \frac{198}{18} - \frac{156}{102} \times \frac{51}{78} \]

### Step 2: Simplify each fraction
1. **First term**:
\[ \frac{126}{154} \approx \frac{126}{154} \text{ (we can simplify this later)} \]
\[ \frac{198}{18} = 11 \]

2. **Second term**:
\[ \frac{156}{102} \approx \frac{156}{102} \text{ (we can simplify this later)} \]
\[ \frac{51}{78} = \frac{51}{78} = \frac{51 \div 51}{78 \div 51} = \frac{1}{\frac{78}{51}} \approx \frac{1}{1.53} \approx 0.65 \]

### Step 3: Simplifying the first term
Now, let's simplify the first term:

\[ \frac{126}{154} = \frac{63}{77} \approx \frac{9}{11} \approx 0.818 \]

Now, we can multiply this with \(11\):

\[ 0.818 \times 11 \approx 9 \]

### Step 4: Simplifying the second term
Now, simplifying the second term:

\[ \frac{156}{102} \approx \frac{78}{51} \approx 1.53 \text{ (approximately)} \]

Now we can multiply this with \(0.65\):

\[ 1.53 \times 0.65 \approx 1 \]

### Step 5: Final calculation
Now, we can substitute these values back into our expression:

\[ 9 - 1 = 8 \]

Thus, the approximate value that comes in place of the question mark (?) is:

\[ \boxed{8} \]