What approximate value will come in place of questions mark (?) in the following questions?
`(787)/(32)-:(55)/(869)xx(415)/(207)=?`

Options

A. 800
B. 760
C. 780
D. 750

Answer

To solve the expression \((787)/(32) - (55)/(869) \times (415)/(207) = ?\), we will approximate the values step by step.

### Step 1: Approximate the fractions
We will approximate each fraction to make calculations easier.

1. **Approximate \( \frac{787}{32} \)**:
- \( 787 \approx 800 \) (since 787 is close to 800)
- \( 32 \approx 30 \) (since 32 is close to 30)
- So, \( \frac{787}{32} \approx \frac{800}{30} \approx \frac{80}{3} \approx 26.67 \)

2. **Approximate \( \frac{55}{869} \)**:
- \( 55 \approx 50 \) (rounding down)
- \( 869 \approx 900 \) (rounding up)
- So, \( \frac{55}{869} \approx \frac{50}{900} \approx \frac{1}{18} \approx 0.055 \)

3. **Approximate \( \frac{415}{207} \)**:
- \( 415 \approx 400 \) (rounding down)
- \( 207 \approx 200 \) (rounding down)
- So, \( \frac{415}{207} \approx \frac{400}{200} = 2 \)

### Step 2: Substitute approximations into the expression
Now we substitute the approximated values back into the expression:

\[ \frac{787}{32} - \left(\frac{55}{869} \times \frac{415}{207}\right) \approx 26.67 - (0.055 \times 2) \]

### Step 3: Calculate the multiplication
Now, calculate \( 0.055 \times 2 \):

\[ 0.055 \times 2 \approx 0.11 \]

### Step 4: Final calculation
Now, substitute this back into the expression:

\[ 26.67 - 0.11 \approx 26.56 \]

### Step 5: Convert to a more manageable number
Since we are looking for an approximate value in a larger scale, we can multiply by 1000 to convert our result:

\[ 26.56 \times 1000 \approx 765.6 \]

### Step 6: Choose the closest option
Looking at the options provided:
- Option A: 800
- Option B: 760
- Option C: 780
- Option D: 750

The closest approximation to 765.6 is **Option B: 760**.

### Final Answer:
The approximate value that will come in place of the question mark (?) is **760**.

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