# Shortcut Techniques for multiplication with the numbers ending with 5

Friends, here are some shortcut techniques for multiplicating with the numbers ending with 5 shared by Mr. Hareesh Kumar. We are very thankful to him for his great support and efforts.

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 = (42 – 1) |75 = 1575

2)    75*85 = ?
Sol: 75*85 = (82 – 1)|75 = 6375

3)    105*115 = ?
Sol: 105*115 = (112 – 1)|75 = 12075

4)    235*245 = ?
Sol: 235*245 = (242 – 1)|75 = 57575

5)    255*245 = ?
Sol: 255*245 = (252 – 1)|75 = 62475

6)    1055*1045 = ?
Sol: 1055*1045 = (1052 – 1)|75 = 1102475

7)    1125*1135 = ?
Sol: 1125*1135 = (1132– 1)|75 = 1276875

1. awesomeeeeeee!!!!!! thanks a ton hareesh kumar.. grt work....
really superr...

1. Thank you Shakthi

2. excellant, thanq for ur guidence...

3. 4. Excellent thanQ mam...

5. 6. there is another trick to multiply
if 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

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

1. 2. good............thanq

8. thank u so much

9. 10. superb.....superb....and....superb.........thanks....

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

13. superb................

14. great technique...

15. Thanks for guidance

16. this site will really go on the top, one day... .. .

17. thank u for ur valuable information
y cant u provide online exams
hope u will definetly start online exams

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

19. thank u very much for ur support...

20. 21. Awesome...thanx a lot...

22. Thankyou chooooooo much......... it was really helpful :-)

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

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

25. Thanks hareesh kumar...

26. thanks for guidance

27. thanks for this.this very helpful in competitive exams

28. Hi 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.