Mastering Multiplication Tables: A Simple Technique for Quick Calculations

Learning to perform multiplication quickly and accurately can be the key to enhancing your mathematical skills. Today, we'll explore a simple yet powerful technique to help you compute larger and more complex multiplications. Whether you're a student seeking to improve your math skills or simply curious about mental arithmetic, this method could prove to be invaluable.

What's the Trick?

Here's a trick that may surprise you: once you know the square of a two-digit number, you can find the square of the next consecutive number by following a straightforward process. For example, if you know that 82 x 82 6724, then to find 83 x 83, you can combine the two 82s and add 1 to 6724. In mathematical terms, 6724 1641 6889. Similarly, if you know that 695 x 695 483025, you can compute 696 x 696 using 483025 13901, giving you 484416.

How to Compute Without the Previous Answer?

When you don't already know the square of a number, you can still calculate it using a simple technique. Consider the example of squaring 95. We can break this down into steps:

Convert both 95s into 0s to get 6060, which equals 360000. Multiply one 95 by 600 (95 x 600 57000) and do it again (57000 x 600 114000). Multiply both 95s together (95 x 95 9025). Combine these results: 360000 114000 9025 483025.

Even for numbers that are not pairs, this logic can be generalized. For example, if you want to determine the product of 288 and 397, follow these steps:

20 x 300 60000. 88 x 300 26400. 397 x 200 79400 (using the distributive property: 397 x 200 397 x 2 x 100). 88 x 97 8536 (using the distributive property: 88 x 97 88 x 100 - 88 x 3). Combine all the results: 60000 26400 79400 8536 114336.

Four-Digit Multiplications and Beyond

Once you move beyond three-digit multiplications, the same formula can be applied. For instance, if you wish to calculate 675 x 412, follow these steps:

40 x 600 240000. 75 x 400 30000. 12 x 600 7200; use the distributive property (12 x 600 12 x 6 x 100). 12 x 75 900; use the distributive property (12 x 75 12 x 7 x 10 12 x 5). Combine all the results: 240000 30000 7200 900 278100.

Remember, the key to mastering these techniques lies in practice. Whether you need to perform quick calculations in your head or simply want to impress your friends and family, these methods will help you achieve your goals with ease.

Further Reading

For more insights into mental arithmetic, consider the following resources provided by David Frigault:

How do you do multiplication in your head? How do you compute square roots in your head? Whisper a math trick that is not very well-known

Have fun learning and exploring these techniques!