`(1)/(7)+(999(692)/(693))xx99` is equal to

Options

A. 1
B. 99000
C. 99800
D. 99900

Answer

To solve the expression \(\frac{1}{7} + 999 \left(\frac{692}{693}\right) \times 99\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the original expression:
\[ \frac{1}{7} + 999 \left(\frac{692}{693}\right) \times 99 \]

### Step 2: Simplify \(999 \left(\frac{692}{693}\right) \times 99\)
We can rewrite \(999\) as \(1000 - 1\):
\[ 999 \left(\frac{692}{693}\right) \times 99 = (1000 - 1) \left(\frac{692}{693}\right) \times 99 \]

### Step 3: Distribute \(99\)
Now, we can distribute \(99\) inside the parentheses:
\[ = 1000 \left(\frac{692}{693}\right) \times 99 - 1 \left(\frac{692}{693}\right) \times 99 \]
This simplifies to:
\[ = \frac{1000 \times 692 \times 99}{693} - \frac{692 \times 99}{693} \]

### Step 4: Combine the terms
Now we can combine the two fractions:
\[ = \frac{(1000 \times 692 \times 99 - 692 \times 99)}{693} \]
Factoring out \(692 \times 99\):
\[ = \frac{692 \times 99 (1000 - 1)}{693} = \frac{692 \times 99 \times 999}{693} \]

### Step 5: Simplify the fraction
Since \(99\) is equal to \(\frac{693}{7}\), we can substitute:
\[ = \frac{692 \times 99}{693} + \frac{1}{7} \]

### Step 6: Combine the fractions
Now we can add \(\frac{1}{7}\) to the simplified term:
\[ = \frac{1 + 692}{7} = \frac{693}{7} \]

### Step 7: Final calculation
Finally, we simplify \(\frac{693}{7}\):
\[ = 99 \]

Thus, the final answer is:
\[ \boxed{99000} \]