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*. We are very thankful to him for his great support and efforts.*

**Mr. Hareesh Kumar**
EXAMPLES: 123458 * 5 = ?

Solution : 123458*5 = (123458/2) * 10 = 61729*10 =
617290

Example: 224569*5 = ?

Solution: 224569*5 = (224569/2) * 10 = 112284.5 * 10 =
1122845

Hence the pattern becomes:

**X * 5 = (X/2) * 10**

**Multiplication with 15:**

Example: 124*15 =?

Solution: 124*15 = (124 + (124/2)) * 10

= (124 + 62) * 10 = 1860

Hence the pattern becomes:

**X*15 = (X + X/2) * 10**

**è**

**X*15 = (3X/2) * 10**

**Multiplication with 25:**

Example: 2264 * 25 =?

Solution: 2264*25 = (2264/4) * 100 = 566 * 100 = 56600

Hence the pattern is:

**X*25 = (X/4)*100**

**Multiplication with**35:
Example: 127*35 =?

Solution: 127*35 = (3*127 + (127/2)) * 10

= (381 + 63.5) * 10 = 4445

Hence the pattern is:

**X*35 = (3*X + X/2) * 10**

**è**

**X*35 = (7X/2) * 10**

Note : The above shown patterns will continue for all the
numbers ending with 5. In general we can write this as:

**X*n5 = (n*X + X/2) * 10**

Where, n = 0,1,2,3, ………………………………

**Some more examples :**

- 136 * 65 = (6*136 + 136/2) * 10 = (816+68)*10 = 8840
- 132*105 = (10*132 + 132/2) * 10 = (1320 + 66)*10 = 13860
- 123*55 = (5*123 + 123/2)*10 = (615+61.5)*10 = 6765

**Multiplication of Numbers Ending with 5 and having the difference of 10 :**

Let us assume that there are two numbers X5 and Y5, and the difference between the two numbers is 10.

(Larger number of X and Y)

^{2}– 1 | 75**Note :**X and Y may be single digit or 2-digit or 3-digit numbers!

EXAMPLES:

1) 35*45 =?

Sol: 35*45 = (4

^{2}– 1) |75 = 1575

2) 75*85 = ?

Sol: 75*85 = (8

^{2}– 1)|75 = 6375

3) 105*115 = ?

Sol: 105*115 = (11

^{2}– 1)|75 = 12075

4) 235*245 = ?

Sol: 235*245 = (24

^{2}– 1)|75 = 57575

5) 255*245 = ?

Sol: 255*245 = (25

^{2}– 1)|75 = 62475

6) 1055*1045 = ?

Sol: 1055*1045 = (105

^{2}– 1)|75 = 1102475

7) 1125*1135 = ?

Sol: 1125*1135 = (113

^{2}– 1)|75 = 1276875

awesomeeeeeee!!!!!! thanks a ton hareesh kumar.. grt work....

ReplyDeletereally superr...

Thank you Shakthi

Deleteexcellant, thanq for ur guidence...

ReplyDeleteVery nice

ReplyDeleteExcellent thanQ mam...

ReplyDeleteawesome

ReplyDeletethere is another trick to multiply

ReplyDeleteif you have two no in which total of unit is 10 and rest of the rest digits are same eg.23*27 =? find out their mid term ie 25

then subtract the difference bitween mid term and digit square from square of mid term

23*27=square(25)-square(2)=625-4 =621

92*98=7225-9=7216

104*106=11025-1=11024

112*118=13225-9=13216

Multipication by 11: xy*11=x(x+y)y if x+y<10

ReplyDeleteif x+y>10 add carry to x

ex:34*11=3(3+4)4=374

38*11=3(3+8)8=(3+1)18=418

good

Deletegood............thanq

Deletethank u so much

ReplyDeletegood

ReplyDeletesuperb.....superb....and....superb.........thanks....

ReplyDeleteSuperb!!

ReplyDeleteSUPERB TECHNIQUES.........THANK U SOOO MUCH AND TELL US THE SHORT CUT FOR FOUR DIGIT MULTIPLICATION...

ReplyDeletesuperb................

ReplyDeletegreat technique...

ReplyDeleteThanks for guidance

ReplyDeletethis site will really go on the top, one day... .. .

ReplyDeletethank u for ur valuable information

ReplyDeletey cant u provide online exams

hope u will definetly start online exams

thanks and please post some shortcut techniques for the peoblems on ages

ReplyDeletethank u very much for ur support...

ReplyDeletethanks

ReplyDeleteAwesome...thanx a lot...

ReplyDeleteThankyou chooooooo much......... it was really helpful :-)

ReplyDeletewhat about 35*75 if the nos are ending with 5 technique? Math is wrong here...

ReplyDeletewhat about 35*75 in multiplication of nos ending with 5 technique? solve this right now...? trick fails here...

ReplyDeleteThanks hareesh kumar...

ReplyDeletethanks for guidance

ReplyDeletethanks for this.this very helpful in competitive exams

ReplyDeleteHi kresz T, you are asking the multiplication of 2 numbers where both the numbers are ending with 5 but their difference is not 10. That is why above rule fails. Please check again what Hareesh Kumar has mentioned.

ReplyDelete