Shortcuts in Multiplications

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NOTE : These techniques are for Mental Maths. You should do calculations in your mind only. Please avoid using Pen/Pencil and Paper. 

Multiplication using multiples

Assume that we should find out the result of 12X15. 

12 x 15   (Here we can write this 15 as 5x3)

=  12 x 5 x 3 (now 12x5 becomes 60)

=  60 x 3 (For this you just calculate 3x6, that is 18 and add one Zero to it. that is 180)

=  180 (see, how simple it is?)

Multiplication by distribution 

Assume that we should find out the result of 12x17

12 x 17   (Here we can divide this 17 as 10+7. here, multiplying 12 with 17 is same as multiplying 12 with 10 and 7 separately and then adding the results)

so, we can write it as

= (12 x 10) + (12 x 7) 

= 120 + 84

= 204 

Multiplication by "giving and taking"

12 x 47  (Here its little difficult for us to calculate the multiplication of 12 and 47 mentally. so just check for the ROUNDED number nearer to 47. Yes it is 50. so.....

= 12 x (50 - 3) 

= (12 x 50) - (12 x 3)  (we have discussed this rule earlier)

= 600 - 36

= 564

Multiplication by 5

* If we have to multiply a number with 5, just divide the number with 2 and then multiply the result with 10. Confused? Its very simple step actually....

428 x 5   (Now just divide the number with 2)

= 428 x 1/2 = 214 (Now multiply it with 10. I mean just add a zero at the end :P)

= 214 x 10

= 2140 (This is our result)

Whats the logic behind this step? 

Very simple. 

* Lets say the number is X. 

* Now we are dividing the number with 2.  so here X becomes X/2. 

* And then we are multiplying it with 10.  So it will become 10x / 2  

* Now cancel it with 2. so it becomes 10x / 2 = 5X = 5 multiplied by X. Thats it ;)

Multiplication by 10  ------------  just move the decimal point one place to the right

16 x 10

= 160

15.9 = 159

169.93 = 1699.3   (Need an explnation for this too??? :P)

Multiplication by 50 ------ divide with 2 and then multiply by 100

Well, this is also same process as we did for 5. Here we should add an extra zero. Thats it

18 x 50

= (18/2)  = 9

= 9 x 100

= 900

Multiplication by 100 -------- move the decimal point two places to the right

45 x 100

= 4500  

Multiplication by 500-------- divide with two and multiply with 1000 

21 x 500

= 21/2 x 1000

= 10.5 x 1000

= 10500

Multiplication by 25 ---------- use the analogy Rs 1 = 4 x 25 Paise

25 x 14 (just divide the 14 as 10+4)

= (25 x 10) + (25 x 4) 

= 250 + 100 --->  Rs2.50 + Rs1

= 350

Hey one more thing. Here you can use another technique too. Which we have used for multiplication with 5.

Multiplication by 25 -----------  Divide by 4 and multiply by 100 

36 x 25

= (36/4) x 100

= 9 x 100

= 900  

Multiplication by 11 (if sum of digits is less than 10)

72 x 11

= 7+2 =9, it is Less than 10. so,

= place this term 9 between 7 &2

= 792 (That's the answer)

Multiplication by 11 (if sum of digits is greater than 10)

87 x 11

=>  8 + 7 = 15 

because here 15 is greater than 10, first use 5 and then add 1 to the first term 8, 

which gives you the answer

= 957 

Multiplication of numbers ending in 5 with the same first terms (square of a number)

25 x 25 

first term = (2 + 1) x 2 = 6

last term = 25

answer = 625 ---> square of 25

75 x 75 

first term = (7 + 1) x 7 = 56

last term = 25

answer = 5625 ---> 75 squared

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