Question

Simplify: 976548 X 9999

• A. 9764503452
• B. 9764513452
• C. 9764523452
• D. 9764533452

Hint:

This trick is very useful. To multiply any number N by a number consisting of 'k' nines, calculate \( N \times (10^k - 1) \). This is simply N followed by 'k' zeros, from which you subtract N. For example, \( 123 \times 99 = 12300 - 123 = 12177 \).

Answer 1

The Correct Option is A

Step 1: Understanding the Problem
We need to calculate the product of 976548 and 9999. Direct multiplication would be time-consuming. We should use a shortcut.

Step 2: Key Formula or Approach
The trick for multiplying by a number consisting of all 9s is to use the distributive property of multiplication. We can write 9999 as \( (10000 - 1) \). So, the problem becomes: \[ 976548 \times (10000 - 1) \] Using the distributive property \( a \times (b - c) = (a \times b) - (a \times c) \), we get: \[ (976548 \times 10000) - (976548 \times 1) \]
Step 3: Detailed Explanation
1. Multiply by 10000:
Multiplying a number by 10000 is the same as adding four zeros to the end of it. \[ 976548 \times 10000 = 9765480000 \] 2. Subtract the original number:
Now, we subtract 976548 from this result. \[ \begin{array}{@{}c@{\,}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c} & 9 & 7 & 6 & 5 & 4 & 8 & 0 & 0 & 0 & 0
- & & & & & 9 & 7 & 6 & 5 & 4 & 8
\hline & 9 & 7 & 6 & 4 & 5 & 0 & 3 & 4 & 5 & 2
\end{array} \] The calculation is as follows:

0 - 8 → borrow → 10 - 8 = 2
9 - 4 = 5
9 - 5 = 4
9 - 6 = 3
7 - 7 = 0
4 - 9 -> borrow -> 14 - 9 = 5
5 becomes 4.
The rest remains: 976.
So, the result is 9764503452.

Step 4: Final Answer
The result of the multiplication is 9764503452. Therefore, option (A) is the correct answer.