Street magicians like David Blaine often do amazing maths tricks. But what is the maths behind them? Learn the tricks here and improve your mental arithmetic! Ask someone to quickly think of a two-digit number between 1 and 100 with both digits odd and both digits different from each other… the answer will often be … 37. The key to learning to do arithmetic at lightning speed are techniques, borrowed from the ancient Vedics that allow us to write down the answer from LEFT to RIGHT (i.e. in the order we READ the answer). “What?!” you might ask. You may even have to read that last sentence twice before the penny drops. The reason its so strange is because the methods of arithmetic we are usually taught (like addition, subtraction, long multiplication or long division) usually involve us constructing the answer the other way round from RIGHT to LEFT! Below you will also find some other magical looking tricks for working out the answers to outrageous looking problems in seconds.
Multiplication Tricks
X x 1: X
X x 2: 2X
X x 3: work from left to right multiplying each digit by 3. If the product is more than 9 then write down the remainder and carry the 1 above the previous digit.
X x 4: times 2 then times 2 again
58 x 4 = (58 x 2) + (58 x 2) = (116) + (116) = 232
X x 5: (METHOD 1) Divide by 2, round down then suffix 0 if even or 5 if odd
2682 x 5 -> (2682/2)(0) -> 13410
5887 x 5 -> (5887/2)(5) -> 29435
X x 5: (METHOD 2) suffix 0 then divide by 2
X x 6: times 3 then times 2
X x 9: (METHOD 1 – for 1 digit numbers) hold out hands fingers open. drop down finger X. Answer: 1st digit = fingers to left of finger X. 2nd digit = fingers to right of finger X
3 × 9 –> drop finger 3 -> 27
7 x 9 -> drop finger 7 -> 63
X x 9: (METHOD 2 – general) suffix 0 then subtract X
X x 10: Suffix 0 to X
14 x 10 -> 14(0) -> 140
X x 11: Split the number and add the digits (and carry and add)
52 x 11 -> 5_2 -> 5_(5+2)_2 -> 572
99 x 11 -> 9_9 -> 9_(9+9)_9 -> (9+1)_8_9 -> 10_8_9 -> 1089
X x 12: suffix 0 then add 2X
X x 13: suffix 0 then add 3X
X x 14: times 7 then times 2
X x 15: suffix 0 then add 5X
X x 16: double 4 times
X x 17: suffix 0 then add 7X
X x 18: suffix 0, double then subtract 2X
X x 19: suffix 0, double then subtract X
X x 20: suffix 0 and then double
X x 45: suffix 00, divide by 2 then subtract 5X
X x 90: times 9 then suffix 0
X x 98: suffix 00 then subtract 2X
X x 99: suffix 00 then subtract X
X5 squared: Double (X+1) then suffix 25
25 x 25 -> 2(2+1)25 -> 625
35 x 35 -> 2(3+1)25 -> 825
X (even) x Y: keep dividing X by 2 and doubling Y until Y is a power of 10 then add zeros
32 x 125 -> 16 x 250 -> 8 x 500 -> 4 x 1000 = 4000
X x Y: draw diagonally “down” lines for each digit of X. draw diagonally “up” lines for each digit of Y. obtain the line intersection products. sum the products vertically. from right to left and carry left to get the answer.
Division Tricks
X/5: double X then move decimal 1 place to left
195 / 5 -> 195 x 2 -> 390 -> 39
2978 / 5 -> 2978 x 2 -> 5956 -> 595.6
XYZ… / 9: write down X, suffix X+Y, suffix (X+Y), remember to carry! Last digit/9 is the remainder (remember to carry)
Cube Trick
Cube Root Trick
Square Trick
Square Root Trick
Percentage Trick
Find X% of 100 then add portions of 100%
8% of 200 -> 8 + 8 -> 16.
8% of 250 -> 8 + 8 + 4 -> 20.
8% of 25 = 2% (/4) of 100 (x4) -> 2
3% of 100 = 100% of 3
