Math is seen as the realm of logic and rationality, but even so there is a lot of trickiness in the number world! From quick ways to do arithmetic to various statistical anomalies, these are 25 Easy Arithmetic Tricks You Can Start Using Right Now!
Multiply by 5
To do this quickly, divide by 2 and then multiply by 10
Multiply by 4
This may seem obvious but to do this in your head, just double twice. Some people do this intuitively and others don’t.
Start with a random number. If it is even then divide by 2. If it is odd, multiply by 3 and add 1. If you keep going you will find that no matter where you started you will eventually hit 1. Like hailstones, the number will go up, and inevitably come back down. This is an example with 7:
7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
Multiple of 3
Your math teacher may never have told you this but you can check if a number is a multiple of 3 simply by checking whether the sum of its digits is a multiple of 3.
You can't just put 10% back
If your boss ever tells you that he is going to cut your salary by 10% but let you work 10% more to make up for it, don’t do it! Let’s say you made $10 per hour. 10% off would be $9 per hour. Adding 10% back would be $9.90. Be careful what the percentage refers to!
All the squares
You can get every square number by adding up the odd numbers. Here’s the start:
1 = 1 x 1, 1 + 3 = 4 = 2 x 2, 1 + 3 + 5 = 9 = 3 x 3
Choose a single digit number. Multiply it by 9. If the result has 2 digits then add them together. Subtract 5. Change your number into a letter based on this pattern:
A=1, B=2, C=3…
Think of a country that begins with your letter. Think of an animal that begins with the last letter of that country. You most likely chose to put a kangaroo in Denmark.
Any three digit number multiplied by 1001 will give that number twice. 456 x 1001 is 456,456.
The percentage trick
x% of y = y% of x. An example:
20% of 40 = 40% of 20
If there are 23 people in a room the chance that any two of them will have the same birthday is actually higher than 50%. Now you can use statistics to impress your friends!
By reversing a number and adding it back to itself over and over you can make almost any number a palindrome. Here is an example:
525600 + 6525 = 532125
532125 + 521235 = 1053360
1053360 + 633501 = 1686861
There are some numbers you cannot do the last trick with though. At least no computer has been able to find a palindrome yet. The lowest known lychrel number is 196.
Although it seems counterintuitive it has been shown that people can add 5 to any number greater than 5 if they subtract 5 and then add 10. For example, 8 + 5 would be 8 – 5 = 3 and 3 + 10 = 13.
Multiplying by 11
To multiply a 2 digit number by 11 just take the sum of its digits. If it is a single digit number just write it between the digits. If it is greater than 2 digits, carry the 1! Here are some examples:
34 x 11 = 374
47 x 11 = 517
Multiplying by 9
When multiplying by 9 simply multiply by 10 and then subtract the other number. For example:
23 x 9 = 230 – 23 = 207
Rule of 72
In financial mathematics this is a quick way to figure out how long it will take an investment to double given a fixed annual rate of return. For example, $1 invested at 10% would take 7.2 (72/10) years to double and turn into $2.
Turn repeating decimals into fractions
This can be frustrating even with a calculator but there is a trick! Lets take 0.63636363… First, find the repeating part of the decimal (63). Divide the repeating part by a another number that has the same number of place but consists of nines (99). So 0.63636363… equals 63/99
The magic string
Imagine that you tied a string around the equator of the Earth so tight that you couldn’t even fit a razor blade underneath. Now let’s imagine that we lengthen the string by only 1 meter. Of course we would now have some slack around the equator, but how much? It’s hard to believe but the answer is that the string would now clear the Earth by 16cm all the way around! If you want a party trick just google the proof. It will fit onto a napkin.
The coin sorter
Lay out a bunch of coins on the table and tell your friend to blindfold you. Ask him how many of the coins are facing heads up. Whatever number he tells you, flip that many coins over (any coins) and move them to a separate pile. You will now have two piles with the same number of heads and tails and your friend will think you are a wizard after he counts them! To add some drama, pretend to select the coins you flip carefully. Why does this work? It’s math!
Figure out the last number of any barcode
The last digit in any barcode (the one that is apart from the rest and not under the bars) is actually used by the computer to check and make sure it read the numbers right. Impress your friends by being able to “guess” these! Starting from the right add every odd digit three times and every even digit once. Then subtract the last digit of the total from 10. Here is an example:
For 03600029145 you should calculate something like this:
5+1+2+0+6+0 = 58
10 – 8 = 2
The extra digit would be 2!
Check any multiplication problem
This makes use of a trick called digital roots. For 2878 x 4902 = 14107956 just do the following:
Find the digital roots of the first number:
2+8+7+8 = 25
2+5 = 7
Do the same for the second and third numbers. We’ll spare you the time and tell you that they are both 6. So, take 7×6 (the digital roots of the two numbers you are multiplying) which equals 42. 4+2 = 6. Since 6 = 6 the math is right!
The calendar trick
Tell your friend to select a square of 9 numbers on any calendar. For example:
14 15 16
21 22 23
28 29 30
No matter what square he chooses you can quickly tell him what they all add up to. Just multiply the middle number by 9! 22 x 9 = 198
The calendar trick on steroids
This time tell your friend to select a 5×4 box around any 20 numbers on the calendar. All you have to do to figure out what they all add up to is take the lowest number and highest number and add them together. Then multiply the answer by 10.
Calendar trick extended
The previous two tricks will actually work on any grid of numbers as long as it is continuous!
The Monty Hall Problem
First gaining public attention when it was sent to Ask Marylin (Marlylin vos Savant’s column in Parade Magazine), the answer to this statistical anomaly at first caused quite an uproar. Some Phd’s and mathematicians (even from MIT!) wrote to the magazine in disbelief. After several months though, with some scientists even designing computer simulations to prove it, the answer to the Monty Hall Problem showed itself to be correct. And here is the problem as it was written to Marylin in 1990:
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
The answer is incredibly that yes, your chances increase if you switch doors. You’ll have to google it to find all the proofs but a quick way to visualize it is to imagine not 3 doors but 1 million doors. You choose 1 door and then the game show host opens all but 1 other door. This time the answer becomes more obvious. You should definitely switch. Would your really trust yourself to have picked the right door out of 1 million? Here is another intuitive explanation offered by Matthew Carlton:
An intuitive explanation is that if the contestant picks a goat (2 of 3 doors) the contestant will win the car by switching as the other goat can no longer be picked, while if the contestant picks the car (1 of 3 doors) the contestant will not win the car by switching.