`503xx201 `= ?

Options

A. 101103
B. 1000000
C. 110000
D. 100003

Answer

To solve the problem \( 503 \times 201 \), we can use the distributive property to simplify our calculations. Here’s a step-by-step breakdown of the solution:

### Step 1: Break down the multiplication
We can express \( 201 \) as \( 200 + 1 \). Therefore, we can rewrite the multiplication as:
\[ 503 \times 201 = 503 \times (200 + 1) \]

### Step 2: Apply the distributive property
Using the distributive property, we can distribute \( 503 \) to both terms inside the parentheses:
\[ 503 \times (200 + 1) = 503 \times 200 + 503 \times 1 \]

### Step 3: Calculate each term
Now, we will calculate each term separately:
1. **Calculate \( 503 \times 200 \)**:
- We can break down \( 503 \) as \( 500 + 3 \):
\[ 503 \times 200 = (500 + 3) \times 200 = 500 \times 200 + 3 \times 200 \]
- Now calculate:
\[ 500 \times 200 = 100000 \quad \text{(since } 5 \times 2 = 10 \text{ and add 4 zeros)} \]
\[ 3 \times 200 = 600 \]
- Therefore:
\[ 503 \times 200 = 100000 + 600 = 100600 \]

2. **Calculate \( 503 \times 1 \)**:
\[ 503 \times 1 = 503 \]

### Step 4: Add the results
Now, we add the results from the two calculations:
\[ 503 \times 201 = 100600 + 503 = 101103 \]

### Final Answer
Thus, the final result of \( 503 \times 201 \) is:
\[ \boxed{101103} \]