Have you ever struggled with multiplication tables and wished there was an easier way to calculate? Look no further! In this step-by-step guide, we will teach you the ‘Proof of 9’ technique, a simple and effective method for mastering multiplication. Read on to unlock the secrets of this powerful technique.

Understanding the ‘Proof of 9’ Technique

The ‘Proof of 9’ technique is based on the fundamental concept that when you multiply any digit by 9 and add the resulting digits together, the sum will always equal 9 or a multiple of 9. Let’s explore this fascinating concept further with examples:

  • 9 × 1 = 9 (resulting digits: 9)
  • 9 × 2 = 18 (resulting digits: 1 + 8 = 9)
  • 9 × 3 = 27 (resulting digits: 2 + 7 = 9)
  • and so on…

As you can see, no matter which digit you multiply by 9, the sum of the resulting digits will always be 9. This forms the basis of the ‘Proof of 9’ technique.

The Step-by-Step Guide

Now that you understand the concept behind the ‘Proof of 9’ technique, let’s dive into the step-by-step process of applying it:

  1. Choose a number you want to multiply by 9.
  2. Multiply that number by 10.
  3. Subtract the original number from the result obtained in step 2.
  4. Voila! You have the multiplication result.

Let’s illustrate this technique with an example:

Suppose you want to find the product of 9 × 5.

  • Step 1: Choose the number 5.
  • Step 2: Multiply 5 by 10: 5 × 10 = 50.
  • Step 3: Subtract 5 from 50: 50 – 5 = 45.
  • Step 4: The result is 45, so 9 × 5 = 45.

Using this technique, you can quickly and accurately multiply any digit by 9 without relying on memorizing multiplication tables.

Benefits of the ‘Proof of 9’ Technique

The ‘Proof of 9’ technique offers several benefits:

  • Speed: This technique allows for faster mental calculations, saving you time and effort.
  • Accuracy: By following the step-by-step guide, you can be confident in the accuracy of your multiplication results.
  • Flexibility: The technique applies to any digit multiplied by 9, making it universally applicable.
  • Conceptual Understanding: Understanding the rationale behind the technique helps build a solid foundation in mathematics.

The ‘Proof of 9’ technique is a valuable tool for anyone seeking to improve their multiplication skills. By following the step-by-step guide, you can quickly and accurately multiply any digit by 9. So, why struggle with multiplication tables when you can master this powerful technique? Start practicing today and unlock the potential of mental calculation!

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