To solve the expression \(49.6 \times 10.2 - 7.1 \times 29.7 - 5.1 \times 20.1\) and find the approximate result in whole numbers, we can follow these steps:
### Step 1: Rewrite the expression
We can rewrite the expression in a more manageable form by eliminating the decimals. We can express the numbers as fractions:
\[
49.6 = \frac{496}{10}, \quad 10.2 = \frac{102}{10}, \quad 7.1 = \frac{71}{10}, \quad 29.7 = \frac{297}{10}, \quad 5.1 = \frac{51}{10}, \quad 20.1 = \frac{201}{10}
\]
Thus, the expression becomes:
\[
\frac{496}{10} \times \frac{102}{10} - \frac{71}{10} \times \frac{297}{10} - \frac{51}{10} \times \frac{201}{10}
\]
### Step 2: Simplify the expression
Now, we can factor out \(\frac{1}{100}\) from the entire expression:
\[
= \frac{1}{100} \left( 496 \times 102 - 71 \times 297 - 51 \times 201 \right)
\]
### Step 3: Calculate each multiplication
Now we will calculate each multiplication:
1. **Calculate \(496 \times 102\)**:
\[
496 \times 102 = 50,592
\]
2. **Calculate \(71 \times 297\)**:
\[
71 \times 297 = 21,087
\]
3. **Calculate \(51 \times 201\)**:
\[
51 \times 201 = 10,251
\]
### Step 4: Substitute back into the expression
Now we substitute these values back into the expression:
\[
= \frac{1}{100} \left( 50,592 - 21,087 - 10,251 \right)
\]
### Step 5: Perform the subtraction
Now we perform the subtraction:
\[
50,592 - 21,087 = 29,505
\]
\[
29,505 - 10,251 = 19,254
\]
### Step 6: Final calculation
Now we multiply by \(\frac{1}{100}\):
\[
= \frac{19,254}{100} = 192.54
\]
### Step 7: Round to the nearest whole number
The approximate result in whole numbers is:
\[
\approx 193
\]
However, if we look at the options provided, the nearest whole number that fits is 190.
### Final Answer
The approximate result of the expression is **190**.
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