Quicker Maths

## Shortcut Method for Multiplication

Posted on June 9, 2010

A guest post by Nandeesh H.N. of Kolkata

Shortcut multiplication for approximate numbers

When applying the rules of multiplication of exact numbers to approximate numbers we waste time and effort in the computation of digits that will be dropped at a later stage. The computation can be made more efficient if we are guided by the following rules:

1.      Equalize the number of significant digits of multiplicand and multiplier. In case of 6.7428 * 23.45, round off 6.7428 as 6.743 to make four significant digits as in 23.45.

2.      Start the multiplication with the higher digit places of the multiplier (not the lower digit places).  In case of 6.743 * 23.45, the multiplier is 23.45 and we have to start the multiplication with 2 and not 5.

3.      Before multiplication by the next place of the multiplier, cross-line the last digit of the multiplicand. (i.e.  3 of 6.743). That is, multiply 6.74 with 3 of 23.45. However, add to the result the rounded product of 3 of 23.45 by the discarded digit 3 of 6.743.

4.      Before multiplication by the next place of the multiplier, cross-line the last digit of the multiplicand. (i.e.  4 of 6.74). That is, multiply 6.7 with 4 of 23.45. However, add to the result the rounded product of 4 of 23.45 by the discarded digit 4 of 6.74. And so on.

5.      The resulting products are arranged so that all lower order digits are arranged one under another.

6.      Place the decimal point as per the rough estimate of the result.

Example:
6.7428 * 23.45
6.743 * 23.45  (Round off 6.7428 as 6.743)
----------------
13486   (6743 * 2 = 13486. Strike out 3 of 6.743)
2023  ( 6743 * 3 = 20229 which is written as 2023 for 674 * 3. Strike out 4 of 674)
270 ( 674 * 4 = 2696 which is written as 270 for 67 * 4. Strike out 7 of 67)
34        ( 67 * 5 = 334 which is written as 34 for 6 * 5.)
----------
158.13  (Place the decimal considering 7 * 23 is about 158)
158.1   (Rounding off the result to four significant digits)
---------

Example:
96.538 * 73.64
96.54 * 73.65   (Round off 96.538 as 96.54)
----------------
67578   (9654 * 7 = 67578. Strike out 4 of 9654)
2896  ( 9654 * 3 = 28962 which is written as 2896 for 965 * 3. Strike out 5 of 965)
579 ( 965 * 6 = 5790 which is written as 579 for 96 * 6. Strike out 6 of 96)
48        ( 96 * 5 = 480 which is written as 48 for 9 * 5.)
----------
7110.1  (Place the decimal considering 97 * 74 is about 7110)
7110    (Rounding off the result to four significant digits)
----------

This post is contributed by Nandeesh Nagarajaia. He is a Chemical Engineer who did his B.Tech from NIT Suratkal.  He is now in IT field as Assistant General Manager(Systems) in Hindustan Copper Limited. He love Maths and enjoy teaching Maths to his sons.

On behalf of all the QuickerMaths.com users, I  am highly grateful for his contribution.

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1. very nice awesome trick to multiply by 101.

2. Multiply any number with 5
Step 1: Just Add 0 (Zero) After given number.

Example: 38*5
Step 1: 380
Step 2: 380/2 = 190

Multiply any number with 15
Step 1: Just Add 0 (Zero) After given number.
Step 2: Half the Result Number.

Example: 38*15
Step 1: 380
Step 2: 380/2 = 190
Step 3: 380+190 = 570

3. sir——-this is not clear. please elaborate
1.However, add to the result the rounded product of 3 of 23.45 by the discarded digit 3 of 6.743.–
2. However, add to the result the rounded product of 4 of 23.45 by the discarded digit 4 of 6.74.
3.158.13 (Place the decimal considering 7 * 23 is about 158)
4. (Place the decimal considering 97 * 74 is about 7110)

4. what is the short cut of 16.45*5.2*2.8
for bank exams with in 1sec

what is the short cut for 2.25%640-1.5%of480

5. hello sir , i like ur shortcuts very much .but plz tell me how to find unit’s digit in numbers like 7 raise to power 205 ,19^239 and also sir problems like if a number divided by 13 gives remainder 4 and when divided by 17 it gives remainder 11 plz sir m pissed off in solving dese typo problems

6. sir i want to know 4 digit multificaation shotcut method like 1984895*9856
or 8957*8965
plz any one send some shor method

7. I Saw this multiplication, but I will share one very easiest multiplication.
Any 2 digit number which is multiplied by 101. It is the very easy multiplication
for example 63*101=6363, 78*101=7878, 95*101=9595, etc..
i.e. just we write the number 2 times that is the exact multiplication of 101.
but this is only applicable for 2 digits.
try it and tell ur opinion.

8. thankx for this!

9. Hello Vineet,

First Thanks for your tremendous works towards providing such kind of great knowledge that you have.keep it up

and Second shame on some selfish persons like Mr Evan Mendis who’s nature is only running behind money .
my only suggestions to such kind of person is, that not make yourself selfish everytime in life.think over it

“KNOWLEDGE IS INCREASED, WHEN YOU DISTRIBUTE TO OTHERS”

Thanks & Regards
Sandeep Rajput

• Thanks Sandy, for such kind words. However, we may not demean anyone because they also have good intentions of distributing their knowledge. Moreover, they might be forced to charge, as it is their bread and butter and creating & maintaining a website is really not cheap these days.

10. sorry,it look like regular multiflication.Because we got 4 steps for multiplicand

11. I’m aware about this previously, but still there was clearly a few helpful pieces that completed the image for me personally, thank you so much!

12. thanks for this tip it helps full me

13. super tip thanx sir

14. This is such a great resource that you are providing and you give it away for free. I enjoy seeing websites that understand the value of providing a prime resource for free. I truly loved reading your post. Thanks!

15. Keep posting stuff like this i really like it

16. Hi Vineet,

I own a site where i sell ebooks related to vedic maths and other fast calculation methods.

I am amazed to see that you are giving all this content for free. You could easily write a ebook and start selling. Even I could help you in that. But what you are doing is hampering my business and I am sure of other similar sites. Hope you will make better use of your knowledge.