Ho ho ho.
Dec 30, 2008
Dec 10, 2008
Vedic maths, Part 2
In the last lesson we learnt the basic vedic style for multiplication and addition - going from left to right. There are a few more developments on this later - but once you've got the trick it's very handy. When I'm bored I like to double numbers in my head: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 etc. I get a lot further with this technique.
Anyway this lesson is just going to be some simple tricks you can do. Some are just common sense or you may know already.
Multiplication by 4, 8, 16, 20, 40 etc:
Doubling numbers is easy, so in multiplying a number, by say, 4, you just double the number twice (and again to multiply by 8).
In doubling, say, 152, it may be easier to split 152 into 15,2 and double 15 to 30 and 2 to 4, getting 304. This number splitting gets used a lot. Multiplying by 40, 800, you just double the right number of times and add the appropriate number of noughts. 17 x 40 = 17, 34, 68, 680.
Extending the multiplication table:
Say you want 14 x 18. You may not know this off the top of your head, but you may know that 7 x 9 = 63. Since 14 and 18 are double of 7 and 9 you can just double 63 twice: 126, 252. For 14 x 7, since 7 x 7 = 49, 14 x 7 = 98. for 17 x 14 you can either multiply 17 by 7 and double the result, or find 16 14's and add another 14 (238).
Multiplication by 5, 25, 50 etc:
Rather than multiplying a number by 5, you can just put a 0 onto the number and halve it (because half of 10 is 5). 44 x 5 = 440, 220. 27 x 50 = 2700, 1350. Using the number splitting above, an easy way to halve 2700 would be to split the number into 2,70,0 and halve the sections (1,35,0).
For multiplication by 25 you multiply by 100 and halve twice. 82 x 25 =8200, 4100, 2050. 181 x 25 = 18100 (18,10,0), 9050 (90,50), 4525.
Squaring numbers that end in 5:
Use the formula 'by one more than the one before'. For 75 squared, multiply the 7 by the next number up, 8. This gives 56 for the first part of the answer, and the last part is just 25 (5 squared). So 75 squared = 5625. 305 squared = 30 x 31 + 25 = 93025 (930,25).
Anyway this lesson is just going to be some simple tricks you can do. Some are just common sense or you may know already.
Multiplication by 4, 8, 16, 20, 40 etc:
Doubling numbers is easy, so in multiplying a number, by say, 4, you just double the number twice (and again to multiply by 8).
In doubling, say, 152, it may be easier to split 152 into 15,2 and double 15 to 30 and 2 to 4, getting 304. This number splitting gets used a lot. Multiplying by 40, 800, you just double the right number of times and add the appropriate number of noughts. 17 x 40 = 17, 34, 68, 680.
Extending the multiplication table:
Say you want 14 x 18. You may not know this off the top of your head, but you may know that 7 x 9 = 63. Since 14 and 18 are double of 7 and 9 you can just double 63 twice: 126, 252. For 14 x 7, since 7 x 7 = 49, 14 x 7 = 98. for 17 x 14 you can either multiply 17 by 7 and double the result, or find 16 14's and add another 14 (238).
Multiplication by 5, 25, 50 etc:
Rather than multiplying a number by 5, you can just put a 0 onto the number and halve it (because half of 10 is 5). 44 x 5 = 440, 220. 27 x 50 = 2700, 1350. Using the number splitting above, an easy way to halve 2700 would be to split the number into 2,70,0 and halve the sections (1,35,0).
For multiplication by 25 you multiply by 100 and halve twice. 82 x 25 =8200, 4100, 2050. 181 x 25 = 18100 (18,10,0), 9050 (90,50), 4525.
Squaring numbers that end in 5:
Use the formula 'by one more than the one before'. For 75 squared, multiply the 7 by the next number up, 8. This gives 56 for the first part of the answer, and the last part is just 25 (5 squared). So 75 squared = 5625. 305 squared = 30 x 31 + 25 = 93025 (930,25).
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