Shortcuts in Multiplications
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
5.9 = 159
169.93 = 169.3 (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
