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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)

= 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 ~~10~~x / ~~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

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not clear the meaning of last term.if we take an example of 75*75 than 7+1*7=56 than if we take a last term ie. 75 than the answer is 5675 but that is wrong .right answer is 5625 plz clear it

ReplyDeleteLook if we need to find square of any no ending with 5 like 175*175

Deletewrite 25 at the unit and tenth place blindfoldly then for the later part just find 17*(17+1)= 17*18=306. so the ans will be 30625 rather 30675.

The correct ans is 30625, you can check it out.

other example 195*195= 19*20=380 & 25 at ones & tenth place so ans is 38025.

It's handy concept for finding square of the no ending with 5.

Hope you concept is clear now:)

@ Anonymous : The last term is not 75. Its 25 (5 X 5). Please do check it...

Deleteits always 25 at the last for any suares like 25, 35,45....check once

Deleteex: 75*75

7(7+1)=7*8=56 and last is 25

it is 5625

gr8ambitionz is really providing gr8 tips,.,.

Deletethanks a lot

nice tricks..thankx....you can also do this:

Delete75*75=7*8=56(7 multiply by its next digit)

5*5=25

you can use this method till 10 coz its difficult sometime to multiply 13*14 etc...after 10 you can follow above mention method.

thanks all the best folks

thanks once again admin :)

thnks for ur grt work !! really halpful tips !

Deletefor square we can use a(square)+2ab+b(square) formula as below:

Deletesuppose 75*75

take a=7, b=5

so a*a=49 and b*b=25 and 2ab=2*7*5=70

now put from last as 5 of b*b, in hand=2, put (2*a*b+in hand)=2, in hand=7, now (a*a+in hand)=49+7=56......so the result is 75*75=5625

yes mam, it's really helpful

Deleteshort cut for square of the number which ends with 5

Deleteexample: square of 65

first step 5*5= 25

second step 6*next number(7)= 42

so answer is 4225

dude listen clearly ;) 7+1*7 =56

Deleteu have to square the last digit of 75 and 5 square is 25 ;)

so that answer is 5625 ;) got it?

Hi dude normally, square the numbers ending with 5 the last two digits must be 25.take some example 5*5=25

Delete15*15=225

25*25=625

35*35=1225

45*45=2025

55*55=3025

65*65=4225

75*75=5625

85*85=7225

vice versa

thnks....!! its helpful..! :)

ReplyDeletethanks a lot :)

ReplyDeletecan u plz tell how to find cube roots apart frm factor method

ReplyDeleteWe are going to post the procedure in a few days Friend. Keep Checking :)

DeleteIts so helpful.

ReplyDeleteAwsum work.Thank u so much

last term will be always 25 only

ReplyDelete75*75=

f.t=(7+1)*7=56

L.T=25(fix for all)

answer=5625

thanks for all the stuff provuded by this webpage .....................

ReplyDeletevery useful

ReplyDeleteReally gud nd usefull

ReplyDeleteThanks a lot for providing such a useful website for us......

ReplyDeletegud tricks.......

ReplyDeletesuper like.......

THANKS ..REALLY GUD TRICKS ......APPRECIABLE WORK.......

ReplyDeleteits really good

ReplyDeleteGreat work..thanks...

ReplyDeleteThanking for all of u, who are involved in this creation. Thanks again. I didn't open my institute books to prepare for IBPS as you have provided all subjects.

ReplyDeletere -exam is going to tough ah

ReplyDeleteanother method:multiplication of no. ending in 5with same first term

ReplyDelete25*25

first term is 2

next number is 3

2*3=6

squre of 5=25

so ans is 625

more e.g.35*35=1225

45*45=2025

115*115=12125

Thanks for the update Tina

DeleteGood Day

@tina your last answar is wrong.Correct answer is 115*115=13225(trick: 5*5=25; and 11*12=132)

Deleteanother method:multiplication of number ending in 5 with same first term

ReplyDelete25*25

2 is first term and 5 is second term

cosecutive no. of first term is 3

multiply both no.2*3=6

squre of second term =25

so ans is 625

more e.g.35*35=1225

45*45=2025

any short cut for 45*55

ReplyDeleteyou can double any of the number and then multiply Aman. At last you simply should divide the number with 2.

DeleteSee you can do the above calculation as

90*55 = 4950/2 = 2475

or

45*110 = 4950/2 = 2475

Hope it helps

90/2*110/2=9900/4=2475

Delete90/2*110/2=9900/4=2475

Deleteapplying ......(a+b)(a-b) i.e (50+5)*(50-5)=2500-25=2475

DeleteThank you so much...you helped me a lot

ReplyDeleteThanks a lot...

ReplyDeletethank u....

ReplyDeletevery gud stuff i

ReplyDeleteIts superb....................thank you

ReplyDeleteIts gr8...it will helps a lot... but need more and difficult sums with shortcuts....

ReplyDeletethanks a lot sir

ReplyDeletethx a lot frds.... these tricks are very useful:)

ReplyDeleteAwesome work

ReplyDeletethnq gaining shrtcut n easyway

ReplyDeletethanks it helpful

ReplyDeletemam will u publish quick reference guide for ibps po exam it will be very usefull if u do so

ReplyDeletemam will u help us by publishing quick reference guide for ibps po exam

ReplyDeleteMultiplication by 11 (sum of no. less than 10)

ReplyDeleteshortcut not working for 53*11

According to shortcut it should be 593 but right ans is 583.

Please help

53*11

DeleteSTEP 1= 5_3 (LEAVE ONE DIGIT SPACE IN BETWEEN THE SQUARING DIGITS...)

STEP 2= 5+3=8 (FILL 8 IN BETWEEN THEM...)

NOW THE ANS IS 583...:)

53*11

Delete5_3 (leave one digit space in between them.)

then 5+3=8

fill 8 in between the squaring digit...

ans is 538

@anonymous yes its working ..without any problem

Delete53*11 -----> using shortcut 5+3=8(8<10) so place 8 b/w 5 & 3 which is 583

For multiplication by 11 , if the number is a 4 digit number or more like 1234 or so?

ReplyDeletehie everybody, a very chilly mrng to all my fellows.

ReplyDeletecan any 1 tell me a simple trick to solve 55*11.

advance tnx to the buddy

simple yaar 5_5 leave one place gap as usual and now 5+5=10 which is not less than 10 right ....so now add that borrowed one to first digit i.e 5+1=6 so answer is 605 hope you understood but there is other simple method i.e55*(10+1)=550+55=605 this one is better one for such multiplication

Deletesimple yaar 5_5 leave one place gap as usual and now 5+5=10 which is not less than 10 right ....so now add that borrowed one to first digit i.e 5+1=6 so answer is 605 hope you understood but there is other simple method i.e55*(10+1)=550+55=605 this one is better one for such multiplication

Deletehie everybody, a chilly mrng to all of my fellows

ReplyDeletethanks to the blog admin, fro sharing their idea with us.

please if any 1 could give me a trick to solve 55*11.

APPLY >10 FORMULA... 5+5=10 SO ADD 0 FIRST and THEN ADD 1 TO FIRST TERM.. ie 605

ReplyDeletegreat tips

ReplyDeleteits an wonderfull tricks , it helps me a lot , thanks for providing such good things

ReplyDeletethese type of tricks i have not seen any where..thank u so much...great job u had done..

ReplyDeletewhat is the multiplication rule for 11 if the number to be multiplied is greater than 99 ?

ReplyDeleteI don't think this is helpful . Its time taking more than normal calculation.

ReplyDeleteOSM tips...

ReplyDeletecould u plz clarify the multiplication of 3 or more digits number with 11?

Eg:-

11*151 = ?

11*9563= ?

etc...

REALLY APPRECUABLE TECHNIQUES OF LEARNING :)

ReplyDeleteappreciable techniques of learning (Y)

ReplyDeleteIs there any shortcuts for multiplying prime with prime number? eg. 17*23*19*29=?

ReplyDeletecould u plz clarify the multiplication of 10

ReplyDeletehere 16*10=160 this is correct

how 5.9=159

the correct one is 59 right?

&

169.93=169.3

the answer is 1699.3

how 169.3?

clarify it. mam/sir

gr8 trick...

ReplyDeletehow to solve this Q

ReplyDeletehow many six letter word can be formed with the letters of word POLICY such that the vowels occur only at even places.

i never find multiplication much easier before.. thanks for posting this :-)

ReplyDeletecan u tel any short cut for 44*44

ReplyDelete4*4*11*11

ReplyDeleteI came across this post just now...and i really regret that i had not found this earlier....have been wasting so much time doing calculations in bank exams :((

ReplyDeletebut thank u sooooo much for making things easier for us....God bless ur whole team...pls keep up this amazing work...thanks again :D

mam/sir

ReplyDeletepls explain hw 5.9*10 has been solved???

169.93*10 has been solved???