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Math tricks

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Math tricks

  1. 1. Amazing Math Tricks
  2. 2. The 7-11-13 trick! Ask a friend to write down ANY three digit number such as 231 or 884. Ask them to multiply the number by: x7 x 11 x 13 ...but even if your friend has used a calculator, you will have written down the answer ages ago! Its fiendish! THE SECRET: all you do is write out the starting number twice! So 231 will become 231231 and 884 will become 884884. You dont believe it? Well try it on this calculator and see for yourself! You work this calculator by clicking the mouse on the buttons. Go on, put in ANY three digit number then x7 x11 x 13 and see what you get!
  3. 3. The 3367 trick! This trick is similar to the 7-11-13 trick. Its harder to do, but it looks far more miraculous! Get a friend to pick any 2 digit number e.g. 74 x 3367 To work out the final answer you have to imagine the original number written out three times e.g. 747474 then divide it by three. 249158 This one takes practice, but unlike the others, its very hard to see how its done!
  4. 4. The missing digit trick! Ask a friend to secretly write down ANY number (at least four digits long). e.g. 78341 Ask the friend to add up the digits... e.g. 7+8+3+4+1 = 23 ... and then subtract the answer from the first number. e.g. 78341 - 23 = 78318 Your friend then crosses out ONE digit from the answer. (It can be any digit except a zero) e.g. 7x318 Your friend then reads out what digits are left .e.g. 7-3-1-8 Even though you havent seen any numbers, you can say what the missing digit is! EIGHTTHE SECRET This great trick relies on the power of 9. After your friend has added up the digits and subtracted them, the answer will ALWAYS divide by 9. If a number divides by nine, then when you add the digits up, they will also divide by 9. If you check our example 7+8+3+1+8 = 27 which does divide by nine. When your friend crosses a digit out, he then reads out the digits that are left. You add them up. In the example we had 7+3+1+8 = 19 All you do now is see what you have to add on to your answer to get the next number that divides by nine! The next number to divide by 9 after 19 is 27. So you need to add on EIGHT. This is the number that was crossed out!
  5. 5. The "24" Mystery! A Murderous Math fan called OBAID pointed out that if you square ANY prime number bigger then 3, then subtract 1, the answer always divides by 24! E.g. 112 = 121 then 121 - 1 = 120 and yes 120 does divide by 24. WHY? If you understand algebra, (and youve read The Phantom X ) then youll know that all prime numbers can be written as (6n+1) or (6n-1). (6n+1)2 = 36n+12n+1. So (6n+1)2 -1 = 36n+12n. This factories to 12n(3n+1). Either n or (3n+1) must be even, therefore the whole expression must be divisible by 24. (6n-1)2 = 36n-12n+1. So (6n-1)2 -1 = 36n-12n. This factories to 12n(3n-1). Either n or (3n-1) must be even, therefore the whole expression must be divisible by 24.
  6. 6. The Prime Number Trick Using prime numbers, you can amaze your friends with a prime prediction... Ask your friends to pick any prime number bigger than 5, but they must not tell you what it is. Square it. (In other words multiply the prime number by itself.) Add 17 Divide by 12 Without knowing which prime number your friends picked, you can still tell them: There will be a remainder of 6. For example, if you want to try the trick with the prime number 2801, heres what to push: 2801 * 2801 = + 17 = / 12 = ...and thats the answer! Now find a new prime number and try it.
  7. 7. 5 squared shortcut Trick 1 Here is a really quick way to square any number with a 5 on the end Lets take   Ok, so what you have to do is split up the numbers, giving you and    Forget about the for the moment and do this: Always add 1, adding 1 to the 4, so we get 4 + 1 = 5 Then multiply this answer, 5, by the original first number, 4 5 X 4 = 20 So what you have is 20 and Everyone knows = 25 right? Well it does. This is what makes it easy. Put the two answers together and thats the answer! 2025
  8. 8. 5 squared shortcut Trick 2 This works for any number ending in but when the numbers get over 100 it tends to get a little trickier with the multiplication. Give it a try with another number. Try , it isnt difficult. Split the numbers apart: 8 and Again, forget about the Add 1 to 8  8+1=9 Multiply 9 by the first number, which was 8 9 X 8 =72 Now, put all the numbers together, 72 and   = 25
  9. 9. Squaring a 2-digit number beginning with 5 Take a 2-digit number beginning with 5. Square the first digit. Add this number to the second number to find the first part of the answer. Square the second digit: this is the last part of the answer.    Example: If the number is 58, multiply 5 × 5 = 25 (square the first digit). 25 + 8 = 33 (25 plus second digit). The first part of the answer is 33   3 3 _ _ 8 × 8 = 64 (square second digit). The last part of the answer is 64    _ _ 6 4 So 58 × 58 = 3364.    See the pattern? For 53 × 53, multiply 5 × 5 = 25 (square the first digit). 25 + 3 = 28 (25 plus second digit). The first part of the answer is 28   2 8 _ _ 3 × 3 = 9 (square second digit). The last part of the answer is 09    _ _ 0 9 So 53 × 53 = 2809.
  10. 10. Squaring a 2-digit number ending in 5 Choose a 2-digit number ending in 5. Multiply the first digit by the next consecutive number. The product is the first two digits: XX _ _. The last part of the answer is always 25: _ _ 2 5.    Example: If the number is 35, 3 × 4 = 12 (first digit times next number). 1 2 _ _ The last part of the answer is always 25: _ _ 2 5. So 35 × 35 = 1225.    See the pattern? For 65 × 65, 6 × 7 = 42 (first digit times next number): 4 2 _ _. The last part of the answer is always 25: _ _ 2 5. So 65 × 65 = 4225.
  11. 11. Squaring numbers made up of sixes Choose a a number made up of sixes. The square is made up of:  one fewer 4 than there are repeating 6s  3  same number of 5s as 4s  6    Example: If the number to be squared is 666 The square of the number has:  4s (one less than digits      in number)           4 4  3                             3  5s (same number as 4s)        5 5  6                                   6 So 666 × 3666333 = 443556.    See the pattern? If the number to be squared is 66666 The square of the number has:  4s (one less than digits       in number)           4 4 4 4  3                                 3  5s (same number as 4s)            5 5 5 5  6                                           6 So 66666 × 66666 = 4444355556.
  12. 12. Multiply Up to 20X20 In Your Head In just FIVE minutes you should learn to quickly multiply up to 20x20 in your head.  With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator. I will assume that you know your multiplication table reasonably well up to 10x10. Try this: Take 15 x 13 for an example. Always place the larger number of the two on top in your mind. Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need. First add 15 + 3 = 18 Add a zero behind it (multiply by 10) to get 180. Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15) Add 180 + 15 = 195. That is It! Wasnt that easy? Practice it on paper first!
  13. 13. The 11 Rule You likely all know the 10 rule (to multiply by 10, just add a 0 behind the number) but do you know the 11 rule? It is as easy! You should be able to do this one in you head for any two digit number. Practice it on paper first! To multiply any two digit number by 11: For this example we will use 54. Separate the two digits in you mind (5__4). Notice the hole between them! Add the 5 and the 4 together (5+4=9) Put the resulting 9 in the hole 594. Thats it! 11 x 54=594 The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the "ones" digit in the hole and carry the "tens" digit from the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627 Practice it on paper first!
  14. 14. Finger Math: 9X Rule To multiply by 9,try this: (1) Spread your two hands out and place them on a desk or table in front of you. (2) To multiply by 3, fold down the 3rd finger from the left. To multiply by 4, it would be the 4th finger and so on. (3) the answer is 27 ... READ it from the two fingers on the left of the folded down finger and the 7 fingers on the right of it. This works for anything up to 9x10!
  15. 15. Multiplication Tricks Multiply by 11 The eleven times table has always been very easy to learn up to 9 x 11. Heres a simple way of multiplying large numbers by 11 too. Lets try. Write down the first digit. Add the first and second digits. Write it. Add the second and third digits. Write it. Again and again do this. Write down the last digit. Example 1 - 425 x 11 First number = 4 4 + 2 = 6. 2 + 5 = 7 Last number = 5 The answer is 4675. Example 2 - 5890 x 11 First number = 5. 5 + 8 = 13. Now we cant write 13. So, add 1 into 5. Then write down 3. 8 + 9 = 17. Again add 1 into 3. Now it is 4. After that write down 7. 9 + 0 = 9. Then write down last digit. It is 0. Answer : 64790
  16. 16. Mind-Reading Number Trick Think of a number, any positive integer (but keep it small so you can do computations in your head). 1. Square it. 2. Add the result to your original number. 3. Divide by your original number. 4. Add, oh I dont know, say 17. 5. Subtract your original number. 6. Divide by 6. The number you are thinking of now is 3!

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