Multiplication using Split and Merge Method
This method is the most effective method for multiplication. We usually don’t
do mistakes when we multiply a number with less than 10. We do mistakes
only when the number is big. Let’s go to the technique.
a) What is 63 x 15?
63 x
15
—-
315
63
—-
= 945 //
This is the usual method we follow. It took 20 seconds for me. For you it may
take less than that.
Here is the simpler method.
= 63 (10 + 5) = 630 + 315 = 945. (Hardly takes 10 seconds).
In competitive exams, every second counts and even a 0.1 mark can change
your future.
b) What is 81 x 19?
= 81 (20 – 1). It don’t need to be only addition. It can be subtraction also. The
ultimate aim is to reduce the time by using simple calculation.
= 1620 – 81 = 1539
c) What is 131 x 26
= 26 (100 + 30 + 1) = 2600 + 780 + 26 = 3406. (You can split the number to n
number of times)
d) What is 147 x 150
You can split this to 150 (100 + 40 + 4 + 3) OR 147 (100 + 50) = 14700 + 7350
NOTE: Always use the simple way to find the answer
Traditional Method will surely take 30 plus seconds.
= 106 (1000 + 2 + 2 + 1)
106000 x
212
212
106
——–
106530
(I have split the number to many numbers for your understanding. It can be just
106 (1000 + 5)).
f) What is 1256 x 516
= 1256 (500 + 10 + 3 + 3)
628000 x
12560
3768
3768
——
648096
(It may look big. But once you practice this method, you will understand how
simple and effective it is)
Multiplication with 5 – Into 10 By 2 Method (x 10/2)
When you have to multiply any number with 5, First multiply with 10 and
divide by 2.
• 2 x 5 = 20 /2 = 10
• 77 x 5 = 770/2 = 385
• 1876 x 5 = 18760/2 = 9380
• 978672 x 5 = 9786720/2 = 4893360 (You can directly write the answer)
g) What is 1082 x 107
= 1082 (100 + 5 + 2)
= 108200 + [10820/2] + 2164
= 108200 + 5410 + 2164
= 115774
(Note that I write this many steps only for your understanding)
h) What is 103 x 97
Here rather than using split and merge method, we can apply another 7th std
Formula.
(a + b) (a – b) = a2
– b2
(100 + 3) (100 – 3) = 1002
– 32 = 10000 – 9 = 9991.
i) What is 53 x 47
= (50 + 3) (50 – 3) = 2500 – 9 = 2491. (It just took 5 seconds).
j) What is 163 x 157
= (160 + 3) (160 – 3) = 25600 – 9 = 25591
Multiplication with 11
a) 21 x 11 = ?
Leave the traditional method. Shortcut method is write 2 and 1 at the first and
last position. (Always add from the left)
i.e. 2___1 Now add 2 and 1. That is 3. Answer is 231. (You got answer in one
second).
b) 25 x 11 = 2 ___ 5 = 275
c) 32 x 11 = 3 ___2 = 352
d) 253 x 11 = 2 _______ 3 = 2783 (Just adding the adjacent numbers).
e) 531 x 11 = 5 ____1 = 5841
f) 277 x 11 = 2____7
Here 2 followed by (2 + 7) then (7 + 7) then 7
= 29 (14) 7
(Carry the 1 to the left)
= 3047
g) 9879 x 11 = 9_____9
= 9 (9 + 8) (8 + 7) (7 + 9) 9
= 9 (17) (15) (16) (9) (Add the carry over number to the left)
= (9+1) (7+1) (5+1) (6)(9)
= 108669
i) 1387 x 11 = 1 ______ 7
= 1 (1+3) (3+8) (8+7) 7
= 1 (4) (11) (15) 7
= 1(4 +1) (1+1) (5) (7)
= 15257
j) 2587 x 11 = 2______7 = 27(13)(15)7 = 28457
k) 3768912 x 11 = 3_______2 = 3(10)(13)(14)(17)(10)(3)2 = 41458032
Practice Problems
