Question

638 × 999 = ?

• A. 637362
• B. 637400
• C. 637962
• D. 638638

Answer 1

Answer:

A. 637362

Efficient Multiplication Technique

• For competitive exams, understanding and applying efficient calculation methods is essential for saving time. The multiplication problem involving 999 is a classic example where a simple trick can significantly speed up the calculation.

• The core principle for multiplying numbers by a sequence of nines (like 9, 99, 999, etc.) is to recognize that these numbers can be expressed as (10ⁿ - 1).

• In this specific case, 999 can be conveniently written as (1000 - 1).

• Substitute this expanded form into the original expression: 638 × 999 becomes 638 × (1000 - 1).

• Apply the distributive property of multiplication over subtraction, which states that a × (b - c) = (a × b) - (a × c).

• Following this property, the expression transforms into: (638 × 1000) - (638 × 1).

• Perform the individual multiplications:

  • 638 × 1000 is easily calculated by appending three zeros to 638, resulting in 638000.

  • 638 × 1 simply equals 638.

• The final step involves a straightforward subtraction: 638000 - 638.