Now that school is back in session, it’s time to get serious about your favorite subject: Mathematics!
In the old days – before calculators and computers – people used an archaic tool to calculate mathematical equations. It was called the “brain.” And while it’s rumored that humans still possess this rusty relic, it may need some serious dusting off if they want to take it out for a spin.
In this article, you will learn that it is quite possible to add, subtract, multiple, and divide without the use of electronic aids. When you’ve finished reading, you may be tempted to toss your calculator in the trash – but we recommend that you don’t, as it is likely an app on your smartphone.
When teaching math, educators tend to do it by the book, demonstrating how tried-and-true methods should be used exclusively to solve mathematical equations. But did you know that there are sneaky shortcuts? Much to the chagrin of teachers, there are many clever little tricks and hacks you can use to circumvent the laborious tasks of multiplication and long division. Master these techniques and you can produce answers quicker than anything that has batteries.
Let’s look at a few “tricks” that will help you calculate math problems in your head and make your calculator (practically) obsolete. In this article, we will tackle the numbers 5 and 25. But fear not, as we will cover other numbers in future posts.
Multiplying By 5:
16 x 5 + ?
Of course, you choose to use the old-fashioned method of multiplying by 5. If so, it might look something like this:
5 x 10 = 50
5 x 6 = 30
50 + 30 = 80
While that gets the job done, it takes three steps to arrive at the correct answer. If you are interested in a shortcut where you can produce the answer quicker, try this handy trick:
Divide by two and then multiply by 10.
Did you get that? If you want to multiply a number by 5, start by cutting that number in half. Then simply multiply your answer by 10 (or, just add a 0 to the end if the number is even). Let’s see if it works:
We want to multiply 16 by 5. So, let’s cut 16 in half (that would be … um, let’s see: 8) and then add a 0 to the end (wait – don’t tell me! … 80?). Yes, 80. You say you could have figured that one out in your head using the traditional method? Okay, fair enough. Let’s try another one, Smart Alec:
222 x 5 = ?
What’s half of 222? Why, it’s 111, of course. Add a 0. What do you have? 1,110.
Even numbers are slightly easier than odd numbers since you can simply add a 0. For odd numbers, all you need to do in most cases is eliminate the decimal point. Example:
23 x 5 = ?
Half of 23 = 11.5. Axe the pesky decimal point and what do you have? 115.
Multiplying By 25
Now that you’ve mastered multiplying by 5, let’s kick it up a notch and multiply by 25. No biggie, right? After all, 25 is just 5 x 5. You may not multiply by 25 every day, but when you do, you’ll be happy you learned this neat little trick.
When you think about it, 25 is nothing more than 100 divided by 4. So, if you want to multiply 58 by 25, try this instead:
58 x 100 = 5800
5800 / 4 = 1450
Before you can reach into your pocket for your calculator, you have your answer.
Squaring Two-Digit Numbers that End in 5
So, you’ve just learned a cool way to multiply by 5, and then an even cooler way to multiply by 25. But, are you ready to learn some serious math tomfoolery now? Try this:
852 = ?
Let’s face it. If you tried solving 85 x 85, your brain would ache. Instead, let’s do it in two easy, breezy steps:
Step 1: When squaring a number that ends in 5, the answer will always end in 25. Examples:
15 x 15 = 225
865 x 865 = 748,225
748,225 x 748,225 = 559,840,650,625
So, when you are squaring a two-digit number that ends in 5, you know that the answer will end in 25. The other parts of this technique are as follows:
Multiply the first number by the next higher number.
Then, place that number in front of the 25.
Let’s give it a whirl:
852 = ?
Well, we know that the equation ends in 25. The next step is to simply multiply the first number (8) by the next higher number (9). So, you have: 8 x 9 = 72
Put it in front of the 25, and you get 7225.
The trick also works with three-digit, four-digit, and 80-digit numbers, but it’s not likely you will be able to make those calculations in your head. For 8652, you would need to solve 86 x 87 (7482) and then place it in front of the 25 (748,225).
Armed with these tricks, you can now give that brain a good workout, while giving your calculator a much-deserved rest!
When you're curious, you find lots of interesting things to do. ~ Walt Disney