Mental Math Tricks: How To Solve 17 x 23 Quickly

Mental math is a valuable skill that can be helpful in various situations, from everyday calculations to more challenging academic tasks. One of the most common challenges people face is multiplying two-digit numbers, especially when they're not perfect squares or easily recognizable multiples. But what if I told you there's a simple trick to solve problems like 17 x 23 quickly in your head?

This article will explore a mental math trick that can help you multiply two-digit numbers close to each other with ease. This trick is based on the concept of squaring and is surprisingly efficient. Let's dive in!

The Trick: Squaring and Adjusting

The trick involves the following steps:

1. Find the average: Calculate the average of the two numbers you want to multiply. In our example, the average of 17 and 23 is (17 + 23) / 2 = 20.
2. Square the average: Square the average you just calculated. 20 squared is 20 x 20 = 400.
3. Find the difference: Determine the difference between each of the original numbers and the average. In our example, the difference between 17 and 20 is 3, and the difference between 23 and 20 is also 3.
4. Subtract the square of the difference: Square the difference you found in step 3 and subtract it from the squared average. In our case, 3 squared is 3 x 3 = 9. Subtracting 9 from 400 gives us 400 - 9 = 391.

Therefore, 17 x 23 = 391.

Why Does This Work?

This trick works because it leverages the concept of algebraic squares. Consider the following:

(a + b)(a - b) = a² - b²

In our example, let's represent 17 as (a - b) and 23 as (a + b). Here, a = 20 (the average) and b = 3 (the difference). So, we can write:

17 x 23 = (20 - 3)(20 + 3) = 20² - 3² = 400 - 9 = 391

Practice Makes Perfect

This mental math trick might seem a bit tricky at first, but with practice, you'll be able to perform these calculations quickly and efficiently. Here are a few more examples to try:

• 14 x 16: Average = 15, 15² = 225, Difference = 1, 225 - 1 = 224
• 28 x 32: Average = 30, 30² = 900, Difference = 2, 900 - 4 = 896
• 47 x 53: Average = 50, 50² = 2500, Difference = 3, 2500 - 9 = 2491

Conclusion

This mental math trick provides a simple and effective way to multiply two-digit numbers close to each other. By understanding the underlying principles and practicing regularly, you can improve your mental math skills and impress others with your quick calculations. So, next time you need to multiply two numbers close to each other, give this trick a try!