Calculation Tricks : Multiplication

I write this article today amidst the excitement of release of my first ever compiled ebook on parajumbles. Visit the FB page : https://www.facebook.com/mbadecoded for more on that. Today we look at the calculation tricks for multiplication. First we start with the specific tricks that pertain to multiplication by a specified number. Then eventually we look at how multiplication can be done faster in general.

Multiplication by 11

Step 1 : Put the right most digit of number being multiplied as the right most digit of your answer.
Step 2 : Each successive digit of number being multiplied is added to the digit next to it and put as the next digit moving right to left. If the sum is of two digits the ten's place digit is carried over to the left.


example : 5892 * 11
Step 1 : Answer : -----2 which is nothing but 2 + 0(as no right hand side neighbour)
Step 2 : 9 + 2 = 11. Carry over 1. Put 1 beside 2. Answer : ----12
Step 2(Contd) : 8 + 9 + 1(carry) = 18. Carry over 1. Put 8 beside 12. Answer : ----812
Step 2(Contd) : 5 + 8 + 1(carry) = 14. Carry over 1. Put 4 beside 812. Answer : ---4812
Step 2(Final) : 5 + 1(carry) = 6. Put 6 beside 4812 to get your final answer : 64812

How about multiplication by 12 or 13 or ..?
Before adding the right hand neighbour you double each digit first in each step.
5324 * 12 = Written as : 05324 * 12
4*2 = 8. Answer : ----8
2*2 + 4 = 8. Answer : ----88
3*2 + 2 = 8. Answer : ----888
5*2 + 3 = 13.Add 3 to the left and carry over 1. Answer : --3888
0*2 + 5 + 1(carry) = 6. Final answer : 63888
Try figuring out the logic and you will be able to generalize multiplication for more numbers..For now moving onto other special cases.


Multiplication by 25

As simple as it can get. 25 = 100/4. You add two zeroes to your number and divide it by 4. Just an alternative to your usual calculation.

example : 1761253 * 25 = 176125300/4 = 44031325

Multiplication by 111

To multiply a two-digit number by 111, add the two digits and if the sum is a single digit, write this digit twice  in between the original digits of the number.

example : 35x111= 3885 ; 63x111= 6993

The same idea works if the sum of the two digits is not a single digit, but you need to take the carry over to the left.

example : 57x111= 6(5 + 1) | 3(=2 + 1) | 2 | 7 = 6327
because 5+7=12

For 3 digit numbers,
Carry if any of these sums is more than one digit.

example :
123x111 = 1 | 3 (=1+2) | 6 (=1+2+3) | 5 (=2+3) | 3 = 13653
241x111 = 2 | 6(=2 + 4)| 7(=2 + 4 + 1) | 5(=4 + 1) | 1 = 26751

352x111=3 | 9 (=3+5 + 1) | 10 (=3+5+2)| 7 (=5+2)| 2 = 39072



Multiplication of numbers close to 100(called the "base")

Case 1 : 102*106 i.e both numbers greater than 100.

Left part of the answer will be : (102 + (106 - 100)) = 108 OR (106 + (102 - 100) = 108

Right part of the answer will be : A two digit multiplication of surplus from both numbers = 2*6 = 12. Carry the left most digits of this right part if the answer is more than two digits.

Answer : 10812


Case 2 : 95*97 i.e both numbers are less than 100
Similar approach. Just surplus replaced with deficits. Left part : (95 - 3) = (97 - 5) = 92
Right part : 3*5 = 15. Carry if required.

Answer : 9215


Case 3 : 104*95 i.e one number is less and other greater than 100

Again the similar approach. Left part will be : (104 + (-5)) = (95 + 4) = 99

Right part = 4*(-5) = -20.

Answer : 99 | -20 <- Does that look right to you? I hope so no. Let's look at how to make it look right.

Removing the negative sign
You borrow a 1 from the neighbouring 9 which by value is a 100. So your answer will become :
99 - 1 | 100 - 20 = 9880

Another example for such a kind where you need to borrow again but this time something different. Idea is to bring down the right hand side to a positive two digit number.

91*112 = (91 + 12) | -9*12 = 103|-108 = 103 - 2 | 200 - 108 = 101|92 = 10192

Let's end this one here today. Practice a lot on these techniques(Squares one earlier as well) if you want them to actually save your time in calculations. Solve at least 15-20 questions on each type by constructing various number combination. Like and share if you like the content on Lagom.
Next time we ll discuss the general multiplication techniques as well as when the base is changed from 100 i.e to say the numbers are close to say 50 or 400 or 1000 or anything like that. Keep following..Till then..



Cheers!
AS