Long Multiplication: A Comprehensive Guide

Long multiplication is a fundamental arithmetic procedure that is utilized to efficiently multiply multi-digit numbers. This comprehensive guide is designed to cater to the needs of both novice learners and individuals seeking to refresh their skills. It provides a step-by-step walkthrough of the long multiplication process and offers valuable insights to facilitate proficiency.

Long multiplication is a method for multiplying two numbers that involves breaking down the process into smaller, more manageable steps. It’s particularly useful when dealing with large numbers that would be challenging to multiply mentally.

The Steps of Long Multiplication

Let’s explore the steps of long multiplication with a clear and detailed explanation:

Step 1: Setup: Write the two numbers you want to multiply vertically, with the larger number on top and the smaller number below. Align them at the rightmost digit.

× 36

Step 2: Multiplication:

1- Starting with the rightmost digit of the bottom number “the ‘6’ in this example”, multiply it by each digit of the top number, one at a time.
  • Multiply 6 by 7, which equals 42.
  • Write down the 2 and carry over the 4 to the next column.
2- Move to the next digit in the bottom number “the ‘3’ in this example” and repeat the multiplication process, but this time, include the carried-over value.
  • Multiply 3 by 7, which equals 21.
  • Add the carried-over 4, resulting in 25.
3- Continue this process for each digit in the bottom number, moving from right to left.

Step 3: Addition. After completing the multiplications for all digits in the bottom number, add up all the partial products to find the final result.

427 × 36 ——- 2562

Step 4: Finalizing. The result, 2562 in this example, is the product of 427 and 36.

Common Tips for Success

  • Take your time: Long multiplication can be time-consuming, so don’t rush. Accuracy is more important than speed.
  • Practice regularly: The more you practice, the more confident you’ll become in performing long multiplication with ease.
  • Use scrap paper: When working with larger numbers, use scrap paper to perform intermediate calculations, especially for carrying over values.


This kind of multiplication is a valuable mathematical skill that finds applications in various aspects of life, from solving everyday problems to advanced mathematics arithmetic, and science. By mastering the steps outlined in this guide and practicing regularly, you’ll become proficient in performing long multiplication with confidence. So, embrace the process, stay patient, and you’ll find that long multiplication becomes a powerful tool in your mathematical toolkit.

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