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Multiplying Numbers Ending in 5: A Simple Math Trick

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Multiplying Numbers Ending in 5: A Simple Math Trick

Have you ever struggled with multiplying numbers that end in 5? It can seem daunting, but there's a simple trick that makes it a breeze! This method is not only easy to learn but also helps you estimate answers for other multiplication problems.

The Trick

Let's say you want to multiply 15 and 25. Here's how the trick works:

  1. Step 1: Ignore the fives and multiply the remaining numbers: 1 x 2 = 2.
  2. Step 2: Multiply the last digits (5 x 5 = 25).
  3. Step 3: Combine the results from steps 1 and 2: 225.

That's it! You've successfully multiplied 15 and 25 using this simple trick.

Why Does This Work?

This trick works because of the way we represent numbers. Any number ending in 5 can be written as 10n + 5, where 'n' is any whole number. Let's see how this applies to our example:

  • 15 = (10 x 1) + 5
  • 25 = (10 x 2) + 5

Now, when we multiply 15 and 25, we get:

(10 x 1 + 5) x (10 x 2 + 5) = 100 x 1 x 2 + 10 x 5 x 2 + 10 x 1 x 5 + 5 x 5

Simplifying this expression, we get:

200 + 100 + 50 + 25 = 375

Notice that the first two terms (200 and 100) represent the product of the numbers before the fives (1 x 2 x 100), and the last term (25) is the product of the fives (5 x 5). The middle term (50) is the sum of the products of the numbers before the fives and 5 (1 x 5 x 10 + 2 x 5 x 10). This explains why the trick works!

Practice Makes Perfect

Try this trick out with different numbers ending in 5. It's a fun way to practice multiplication and impress your friends with your quick calculation skills!

Beyond Numbers Ending in 5

This trick can also be used to estimate the product of numbers that are close to multiples of 5. For example, if you need to multiply 16 and 24, you can use the trick to multiply 15 and 25 (which we know is 375) and then adjust the answer slightly. Since 16 is one more than 15 and 24 is one less than 25, the actual answer will be a little less than 375.

So, next time you encounter a multiplication problem involving numbers ending in 5, remember this simple trick and make your calculations a breeze!

Elementary Math