Multiplication without tears

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?

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

Example: - Multiply 95 by 94
Solution: - a) Square the Larger number = 95 x 95 = 9025 b) Subtract the larger number to the previous result = 9025 −95 = 8930
Hence, 95 × 94 = 8930

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

Example: - Multiply 82 by 84
Solution: - a) Mean = (82 + 84)/ 2 = 83. (Mean can be found by adding 1 to smaller or subtracting 1 from the larger number in this case.)
b) Square the mean = 83 2 = 6889
c) Subtract 1 from the last result = 6889 – 1 = 6888

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 = 29^2 = 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 = 25^2 = 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



For More on Multiplication without Tears you can buy MATHS MADE EASY published by Rupa Publication

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com