10 Simple Arithmetic Tricks

Mathematics can be intimidating for many. This compilation aims to enhance your basic knowledge of math tricks and improve your mental calculation speed.

1. The 11 Multiplication Trick

We all know the trick for multiplying by 10—just add a 0 to the end of the number. But did you know there's a simple method to multiply a two-digit number by 11? Here's how:

Take the original number and imagine a space between its two digits (for example, let's use 52):

5_2

Now, add the two digits together and place the sum in the middle:

5_(5+2)_2

That's it – you've got the answer: 572.

If the sum of the middle numbers results in a two-digit number, simply place the second digit and add 1 to the first:

9_(9+9)_9

(9+1)_8_9

10_8_9

1089 – It works every time.

If you need to square a two-digit number ending in 5, this trick makes it a breeze. Multiply the first digit by itself plus one, then add 25 at the end. That's it!

25 = (2x(2+1)) & 25

2 x 3 = 6

625

Most people quickly memorize the 5 times table, but when you deal with larger numbers, it can get tricky – or does it? This trick is super simple.

Take any number, divide it by 2 (in other words, halve it). If the result is a whole number, add a 0 to the end. If not, ignore the remainder and add a 5. It works every time:

2682 x 5 = (2682 / 2) & 5 or 0

2682 / 2 = 1341 (whole number, so add 0)

13410

Let's try another example:

5887 x 5

294 (fractional number, ignore remainder and add 5)

29435

This one is simple – to multiply any number from 1 to 9 by 9, hold both hands in front of you. Drop the finger corresponding to the number you are multiplying (for instance, 9×3 – drop your third finger). Count the fingers before the dropped one (in the case of 9×3, it's 2) and then count the fingers after (in this case, 7). The answer is 27.

This is a very straightforward trick that might seem obvious to some, but not to everyone. The trick is to simply multiply by two, and then multiply by two again:

58 x 4 = (58 x 2) + (58 x 2) = (116) + (116) = 232

If you need to leave a 15% tip, here’s an easy method. First, calculate 10% (divide the total by 10), then add half of that number, and you’ll have the final tip amount:

15% of $25 = (10% of 25) + ((10% of 25) / 2)

$2.50 + $1.25 = $3.75

If you have a large number to multiply and one of the numbers is even, you can easily break it down into smaller steps to find the answer:

32 x 125 is the same as: 16 x 250 is the same as: 8 x 500 is the same as: 4 x 1000 = 4,000

Dividing a large number by five is actually very simple. All you need to do is multiply by 2 and then move the decimal point:

195 / 5

Step 1: 195 * 2 = 390 Step 2: Move the decimal: 39.0 or simply 39

2978 / 5

Step 1: 2978 * 2 = 5956 Step 2: 595.6

To subtract a large number from 1,000, follow this simple rule: subtract all digits except the last from 9, then subtract the last digit from 10:

1000 -648

Step 1: Subtract 6 from 9 to get 3 Step 2: Subtract 4 from 9 to get 5 Step 3: Subtract 8 from 10 to get 2

Answer: 352

Multiply by 5: Multiply by 10 and divide by 2. Multiply by 6: Multiply by 3 and then 2. Multiply by 9: Multiply by 10 and subtract the original number. Multiply by 12: Multiply by 10 and add twice the original number. Multiply by 13: Multiply by 3 and then add 10 times the original number. Multiply by 14: Multiply by 7, then by 2. Multiply by 15: Multiply by 10 and add 5 times the original number. Multiply by 16: Double four times or multiply by 8 and then by 2. Multiply by 17: Multiply by 7 and add 10 times the original number. Multiply by 18: Multiply by 20 and subtract twice the original number. Multiply by 19: Multiply by 20 and subtract the original number. Multiply by 24: Multiply by 8, then multiply by 3. Multiply by 27: Multiply by 30 and subtract 3 times the original number. Multiply by 45: Multiply by 50 and subtract 5 times the original number. Multiply by 90: Multiply by 9 and add a zero. Multiply by 98: Multiply by 100 and subtract twice the original number. Multiply by 99: Multiply by 100 and subtract the original number.

Bonus: Percentages

In comment 23, Yanni shared a fantastic tip for calculating percentages, so I thought I'd share it here:

Want to calculate 7% of 300? It might seem challenging, but is it really?

To understand percentages, let's break down the word 'Percent.' 'PER' means 'For each,' as in '10 tricks per Mytour page.' 'CENT' stands for 100, like in 'Century' meaning 100 years or 100 cents making a dollar. Therefore, 'PERCENT' means 'For Each 100.'

This leads to the idea that 7% of 100 is 7. Similarly, 8% of 100 equals 8, and 35.73% of 100 equals 35.73. But what's the significance?

Now, back to finding 7% of 300: For the first hundred, 7% equals 7. The second hundred, 7% equals another 7, and again for the third hundred, it's 7. So, 7 + 7 + 7 gives us 21.

Since 8% of 100 equals 8, it stands to reason that 8% of 50 is half of 8, which is 4.

For any number you're working with, break it down into multiples of 100. If the number is smaller than 100, simply adjust the decimal point.

EXAMPLES: 8% of 200 = ? 8 + 8 = 16. 8% of 250 = ? 8 + 8 + 4 = 20. 8% of 25 = 2.0 (move the decimal back). 15% of 300 = 15 + 15 + 15 = 45. 15% of 350 = 15 + 15 + 15 + 7.5 = 52.5

It's helpful to know that you can always reverse the percentages, such as 3% of 100 being the same as 100% of 3.

35% of 8 is equivalent to 8% of 35.

Technorati Tags: arithmetic, math