1) The document teaches a method for multiplying multi-digit numbers mentally in a step-by-step fashion by breaking the problem down into multiplying individual digits. 2) Key steps include multiplying the nearer digits first, then the more extreme digits, and carrying digits to the left. 3) Practice problems of increasing difficulty are provided, from 2-digit to 4-digit multipliers, to demonstrate applying the method. The reader is encouraged to time themselves and check their work.

1. Multiplication Part I
Let us see one example first:-
4156 × 5679 = 23367011189924 (Subscripts are the margins and carried
forward)
Do you know, how much time did this multiplication take? I say – only 10 seconds.
Can you believe it?
Yes, you have to believe it, because you will be learning the same trick here with
me. So, take a deep breath and concentrate.
Let us start.
Q1. 8 × 6 = ?
Q2. 7 × 9 = ?
You can easily tell Q1. = 48 and Q2. = 63
Q3. 56 × 45 = ?
5 6
×4 5
------------
2 8 0
2 2 4
------------------
2 5 2 0
Ok, you got your answer. So, how much time have you taken? Do not worry, I tell
you something new but much established.
Q3. 56 × 45 =
Step (a) = 6 × 5 = 30
Step (b) = 56 × 45 = (6 × 4) + (5 × 5) = 49 = 49 + 3 = 52
Step (c) = 5 × 4 = 20 = 20 + 5 = 25
Answer = 2520

2. Please note that youhave to carry the margins to the left and add them. Ihave marked
them knowingly in bold letters.
So, what I did? In step (a) and (c), there is no need for explanation. But watch
step (b) again.
Step (b) = (closer ones multiplied) + (extreme ones multiplied)
So, there is nothing new. In step (b) only, you have to practice a little. Do it fast.
Multiply the inner digits + multiply the extreme digits. You should take a note
that you have to do it mentally.
Now you solve:-
Q4. 79 × 83 = 65 9 57
What were your steps?
Step (a) = 9 × 3
Step (b) = (9 × 8) + (7 × 3)
Step (c) = 7 × 8
Good, you are fine now, solve the following questions. Do it fast. Do not write the
steps.
Q5. 89 × 54 = 48 8 0 3 6
Q6. 73 × 69 = 50 8 3 2 7
Q7. 59 × 87 = 51 11 3 6 3
Q8. 49 × 65 = 31 7 8 4 5
I think you do not have any problems with two digits multiplication. Now let us
see, when the multiplicand has more digits.
Q9. 529 × 64 = 33 3 8 6 5 3 6
Step (a) = 9 × 4
Step (b) = (9 × 6) + (2 × 4) (Same nearer to nearer and extreme to extreme)

3. Step (c) = (2 × 6) + (5 × 4) (Same nearer to nearer and extreme to extreme)
Step (d) = 5 × 6
Note – never forget to carry the margins.
So, what is the new in it?
Up to step(b), it was like before. Youknow that the multiplier has two digits. Once
you have completed02 digits of multiplicand × 02 digits of multiplier , move to
next digit leftward in multiplicand. That is why step (c) = 52 × 64 ( Here also do
not forget nearer to …….. old story)
Now you try yourself:-
Q10. 58514 × 67 = 39 9 2 9 0 4 4 3 3 2 8
Step (a) = 4 × 7
Step (b) = (4 × 6) + (1 × 7)
Step (c) = (1 × 6) + (5 × 7)
Step (d) = (5 × 6) + (8 × 7)
Step (e) = (8 × 6) + (5 × 7)
Step (f) = 5 × 6
My friend, please do not be afraid from so many steps. Steps are bound to be
eliminated. Finally, what you did in the above problem? You shifted to left side of
the multiplicand, once you were over with 02 digits of multiplicand × 02 digits of
multiplier.(Because the multiplier has only two digits.)
Now, let us go to see some three digits multiplier problems:-
Multiplication part II
Now, let us go to see some three digits multiplier problems:-
Q 12. 2859 × 654
Step (a) = 9 × 4 (As usual)
Step (b) = (9 × 5) + (5 × 4) (As usual)
Step(c) = (9 × 6) + (5 × 5) + (8 × 4) (Nearerto nearer, middle to middle, extreme
to extreme)

4. Step (d) = (5 × 6) + (8 × 5) + (2 × 4) (Once you are finishing the three digits of
multiplier, move to leftward in multiplicand, as what we did in 02-digits cases)
Step (e) = (8 × 6) + (2 × 5) (It is a new step, we will see in details)
Step (f) = 2 × 6
Hey, I am writing again and again to carry the margins. You do not forget to
do it.
Details of Step (e) – We have seen that there are three digits in multiplier. You
covered the entire left digits in step (d). So, now you have to retreat. Use two digits
of left side of the multiplier and as well as of multiplicand.
Try yourself:-
Q13. 756462 × 543 = ?
Step (a) = 2 × 3 = 6
Step (b) = (2 × 4) + (6 × 3) = 26
Step (c) = (2 × 5) + (6 × 4) + (4 × 3) = 48
Step(d) = (6 × 5) + (4 × 4) + (6 × 3) = 68 (Completed three of multiplier in previous
step, move leftward in multiplicand, till the time it is finished)
Step (e) = (4 × 5) + (6 × 4) + (5 × 3) = 65
Step (f) = (6 × 5) + (5 × 4) + (7 × 3) = 77
Step (g) = (5 × 5) + (7 × 4) = 60 (completed all 03 digits of both in previous step,
so, involve 02 digits of both.)
Last step = 7 × 5 = 41
Answer = 410758866 (In bold letters, I have shown the margins.)
Confident, good.
Let us move to four digits of multiplier. I would like to tell you one thing that there
will not be anything special, let it be of 50 digits of multiplier. You have to learn
the basics, and for that no problem, I have already guided you.
Q14. 5436 × 4214 = 22907304

5. Step (a) = 6 × 4 = 24
Step (b) = (6 × 1) + (3 × 4) = 20
Step (c) = (6 × 2) + (3 × 1) + (4 × 4) = 33
Step (d) = (6 × 4) + (3 × 2) + (4 × 1) + (5 × 4) = 57(In step (c) only, you have
completedthree digits, so use four digits of both. Here you should not break the
oath, that you took. Nearer to nearer + ……………..+ ………… + extreme to
extreme.)
Step (e) = (4 × 3) + ( 4 × 2) + (5 × 1) = 30 (As you have touched the 04 digits in
last step, now recede)
Step (f) = (4 × 4) + (5 × 2) = 29
Last step = 5 × 4 = 22
Now, I need to take a deep breath. To take rest, I need to give you some tasks.
Q15. 76 × 56
Q16. 89 × 59
Q17. 467 × 46
Q18. 5874 × 54
Q19. 675 × 894
Q20. 4786 × 457
Q21. 8236 × 4873
Q22. 54763 × 4356
Do it fast. Calculate the time. Match your answer with the calculator. If there is any
doubt, read this topic twice, thrice and so on. Please e-mailme through contactus
section of the site. I will be more than happy.