Ten Math Tricks That Will Blow Your Mind
by Anne Marie Helmenstine, Ph.D.for ThoughtCo.
Are you ready to give your mathematics skills a boost? These simple math tricks can help you perform calculations more quickly and easily. They also come in handy if you want to impress your teacher, parents, or friends.
Multiplying by 6
If you multiply 6 by an even number, the answer will end with the same digit. The number in the tens place will be half of the number in the ones place.
Example: 6 x 4 = 24
The Answer Is 2
- Think of a number.
- Multiply it by 3.
- Add 6.
- Divide this number by 3.
- Subtract the number from Step 1 from the answer in Step 4.
The answer is 2.
Same Three Digit Number
- Think of any three-digit number in which each of the digits is the same. Examples include 333, 666, 777, 999.
- Add up the digits.
- Divide the three digit number by the answer in Step 2.
The answer is 37.
Six Digits Become Three
- Take any three-digit number and write it twice to make a six digit number. Examples include 371371 or 552552.
- Divide the number by 7.
- Divide it by 11.
- Divide it by 13. (The order in which you do the division is unimportant.)
The answer is the three digit number
Examples: 371371 gives you 371 or 552552 gives you 552.
- A related trick is to take any three-digit number.
- Multiply it by 7, 11, and 13.
The result will be a six digit number that repeats the three-digit number.
Example: 456 becomes 456456.
The 11 Rule
This is a quick way to multiply two digit numbers by 11 in your head.
- Separate the two digits in your mind.
- Add the two digits together.
- Place the number from Step 2 between the two digits. If the number from Step 2 is greater than 9, put the ones digit in the space and carry the tens digit.
Examples: 72 x 11 = 792
57 x 11 = 5 _ 7, but 5 + 7 = 12, so put 2 in the space and add the 1 to the 5 to get 627
To remember the first seven digits of pi, count the number of letters in each word of the sentence:
“How I wish I could calculate pi.”
This gives 3.141592
Contains the Digits 1, 2, 4, 5, 7, 8
- Select a number from 1 to 6.
- Multiply the number by 9.
- Multiply it by 111.
- Multiply it by 1001.
- Divide the answer by 7.
The number will contain the digits 1, 2, 4, 5, 7, and 8.
Example: The number 6 yields the answer 714285.
Multiply Large Numbers in Your Head
To easily multiply two double digit numbers, use their distance from 100 to simplify the math:
- Subtract each number from 100.
- Add these values together.
- 100 minus this number is the first part of the answer.
- Multiply the digits from Step 1 to get the second part of the answer.
Super Simple Divisibility Rules
You’ve got 210 pieces of pizza and want to know whether or not you can split them evenly within your group. Rather than whip out the calculator, use these simple shortcuts to do the math in your head:
- Divisible by 2 if the last digit is a multiple of 2 (210).
- Divisible by 3 if the sum of the digits is divisible by 3 (522 because the digits add up to 9, which is divisible by 3).
- Divisible by 4 if the last two digits are divisible by 4 (2540 because 40 is divisible by 4).
- Divisible by 5 if the last digit is 0 or 5 (9905).
- Divisible by 6 if it passes the rules for both 2 and 3 (408).
- Divisible by 9 if the sum of the digits is divisible by 9 (6390 since 6 + 3 + 9 + 0 = 18, which is divisible by 9).
- Divisible by 10 if the number ends in a 0 (8910).
- Divisible by 12 if the rules for divisibility by 3 and 4 apply.
Example: The 210 slices of pizza may be evenly distributed into groups of 2, 3, 6, 10.
Finger Multiplication Tables
Everyone knows you can count on your fingers. Did you realize you can use them for multiplication? A simple way to do the “9” multiplication table is to place both hands in front of you with fingers and thumbs extended. To multiply 9 by a number, fold down that number of finger, counting from the left.
Examples: To multiply 9 by 5, fold down the fifth finger from the left. Count fingers on either side of the “fold” to get the answer. In this case, the answer is 45.
To multiply 9 times 6, fold down the sixth finger, giving an answer of 54.