Multiplication without paper
Multiplication can be made an
interesting exercise by learning some tricks.Don’t you think that you should have knowledge of some super-duper
trick which could have been saved your time and multiplication could have been
done mentally without using pen and paper?
There are hundreds of such magical trick
which help to do calculation mentally and without pen and paper. Do you know
what is more interesting here that there are absolutely no chance of
mistake? Let me ask you a simple
question first: -
What is 100 times 456789?
I am really in a serious mood and not
joking guys despite the fact that I know you can do this multiplication in
fraction of second by just putting two zeros after 456789 and you will return
back with your answer 4567890. The fact of the matter is that when you are
asked to multiply a number by the multiple of 10, like 10, 100, 1000, 10000…
you just put the number of zeros in front of the number to be multiplied by
noticing how many numbers of zeros are in multiplier which is the multiple of
10’s. Likewise, the method discussed here will let you get the answer in
seconds.
Hey guys, are you ready for the journey
of multiplication fantasy? If your answer is a big YES, then here I begin.
1. When
the sum of unit digit is 10 and ten’s digit are same
Rule: - a) The answer will have two parts. Multiply the unit
parts. The product should have exactly two digits. If you get the lesser digit
put a zero before.
b) Second Part = Ten’s digit x
(Ten’s digit + 1)
Example:
- 42 × 48 =?
Solution:
- Here the sum of unit digit is 10 (2 + 8 = 10) and ten’s digit in both
multiplicand and multiplier are same.
Unit
Part = 2 × 8 = 16
Second
Part = 4 × 5 = 20
Hence,
42 × 48 = 2016
Example: - 74
× 76 =?
Solution:
- Sum of unit digit = 10 (4+ 6 = 10) and ten’s digit in both multiplicand and
multiplier are same (7).
Unit
Part = 4 × 6 = 24
Second
Part = 7 × 8 = 56
Hence,
74 × 76 = 5624
Example: - 99
× 91 =?
Solution:
- Sum of unit digit = 10 (9+ 1= 10) and ten’s digit in both multiplicand and
multiplier are same (9).
Unit
Part = 9 × 1 = 09 (In order to fulfill the condition of two digits in the
product 0 is put before 9)
Second
Part = 9 ×10 = 90
Hence,
99 × 91 = 9009
2.
Sum of ten’s digit is 10 and unit digit
are same
Rule:-The
answer will have two parts
a) LHS = Product of ten’s digit + Unit digit
RHS = Product of Unit
digits
Always remember there
should be exactly two digits in the RHS. In case there is a single digit in RHS,
put a zero before the product you get
Example:
- 84 × 24 =?
Solution: - Sum of ten’s digit = 10 (8+2 = 10) and Unit digit in multiplicand and
multiplier are same (4)
LHS = Product of ten’s digit + Unit digit = 8×2 + 4
= 20
RHS
= Product of Unit digit = 4 × 4 = 16 Hence,
84 × 24 = 2016
Example:
- 93 × 13 =?
Solution: - Sum of ten’s digit = 10 (9+1 = 10) and
Unit digit in multiplicand and
multiplier are same (3)
LHS = Product of ten’s digit + Unit digit = 9 × 1 +
3 = 12
RHS
= Product of Unit digit = 3 × 3 = 09
(one
Zero is put due to less number of digit in the product)
Hence, 93 × 13 = 1209
Example:
- 75 × 35 =?
Solution: - Sum of ten’s digit = 10 (7+3 = 10) and
Unit digit in multiplicand and
multiplier are same (5)
LHS = Product of ten’s digit + Unit digit = 7× 3 + 5
= 26
RHS
= Product of Unit digit = 5 × 5 = 25
Hence,
75 × 35 = 2625
3.
When the difference between the digits to be multiplied is 1
When two consecutive numbers are to be multiplied,
follow this technique for quicker multiplication.
a)
Square the
smaller/ greater number.
b) Add / subtract the smaller/ larger
number to the previous result
Example: - Multiply 23 by 24
Solution: -
a) Square the smaller number = 23 x 23 =
529
b) Add the smaller number to the previous result =529 + 23 = 552 Hence, 23 × 24 = 552
Example: - Multiply 75 by 76
Solution: -
a) Square the smaller number = 75 x 75 =
5625
b) Add the smaller number to the previous result =5625 + 75 = 5700 Hence, 75 × 76 = 5700
4. When
the difference between the digits to be multiplied is 2
a)
Find the mean
and square it. The mean of two numbers a and b = a + b / 2
b)
Subtract 1
Example: - Multiply 25 by 27
Solution: - a) Mean = 25 + 27 / 2 = 26. (Mean can be
found by adding 1 to smaller or subtracting 1 from the larger number in this
case.)
b) Square the mean = 26 2 = 676
c)
Subtract 1 from the last result = 676 – 1 = 675
Hence, 25 x 27 = 675
Example: - Multiply 74 by76
Solution: - a) Mean = (74 + 76)/ 2 =
75. (Mean can be found by adding 1 to smaller or subtracting 1 from the larger
number in this case.)
b) Square the mean = 75 2 = 5625
c)
Subtract 1 from the last result = 5625 – 1 = 5624
Hence, 74 x 76 = 5624
5. When the difference
between the digits to be multiplied is 3
Rule:
-
a) Add 1 to the smaller
number and square it
b)
Subtract 1 from the smaller number and add to the previous result
Example: - Multiply 28 by 31
Solution: -
Here the smaller number is 28.
a)
Add 1 to it = 28 + 1 = 29 b)
Square it = 292 = 841
c)
Subtract 1 from the smaller number and add to the previous result = 841 + 28 –
1 = 868
Hence, 28 × 31 = 868
Example: - Multiply 24 by 27
Solution: -
Here the smaller number is 24.
a)
Add 1 to it = 24 + 1 = 25 b)
Square it = 252 = 625
c)
Subtract 1 from the smaller number and add to the previous result = 625 + 24 –
1 = 648
Hence, 24 × 27 = 648
6. When the difference between the two numbers to be multiplied
is 4
Rule:
a)
Take the mean of numbers. If the numbers are a and b; where a >b then mean
is either a – 2 or b + 2 b)
Take the square of mean number.
c)
Subtract 4 from the result.
Example: - Multiply 65 by 69?
Solution: Here the difference between the numbers to
be multiplied is 4. Take its mean.
a)
Mean = 65 + 2 = 67 b)
Square it = 672 = 4489
c)
Subtract 4 from the previous result = 4489 – 4 = 4485
Hence, 65 × 69
= 4485
Example: - Multiply 84 by 88?
Solution: Here the difference between the numbers to
be multiplied is 4. Take its mean.
a)
Mean = 84 + 2 = 86 b)
Square it = 862 = 7396
c)
Subtract 4 from the previous result = 7396 – 4 = 7392
Hence, 84 × 88
= 7392
7. When the difference between the two numbers to be multiplied
is 6
Rule: a)
Take the mean of numbers.
b)
Take the square of mean number. c)
Subtract 9 from the result.
Example: - Multiply 42 by 48?
Solution: Here the difference between the numbers to
be multiplied is 6. Take its mean.
a)
Mean = 42 +3 = 45 b)
Square it = 452 = 2025
c)
Subtract 9 from the previous result = 2025 – 9 = 2016
Hence, 42 × 48
= 2016
8. When the difference between the two numbers to be multiplied
is 8
Rule: a)
Take the mean of numbers. If the numbers are a and b; where a >b then mean
is either a – 4 orb+4
b)
Take the square of mean number. c)
Subtract 16 from the result.
Example: - Multiply 64 by 72?
Solution: Here the difference between the numbers to
be multiplied is 8. Take its mean.
a)
Mean = 64 + 4 = 68 b)
Square it = 682 = 4624
c)
Subtract 16 from the previous result = 4624 – 16 = 4608
Hence, 64 × 72 =
4608
9. When the difference between the two numbers to be multiplied
is 10
Rule: a)
Take the mean of numbers. If the numbers are a and b; where a >b then
mean
is either a – 5 or b + 5
b)
Take the square of mean number. c)
Subtract 25 from the result.
Example: - Multiply 84 by 94?
Solution: Here the difference between the numbers to
be multiplied is 10. Take its mean.
a)
Mean = 84 + 5 = 89 b) Square it = 892 = 7921
c) Subtract 25 from the previous result = 7921 – 25 = 7896
Hence, 84 × 94 = 7896
Courtesy :- From Maths made Easy - Rupa Publication by Rajesh Kumar Thakur
(Book available on different website / e- books also available)
Rajesh Kumar Thakur
rkthakur1974@gmail.com
