Multiplying Two Numbers when Sum of their Unit Digits is 10

Vedic Multiplication Trick

This method of multiplication from Vedic Maths will make it very easy to multiply two numbers when sum of the last digits is 10 and previous parts are the same. For example multiplications like

23x27 :  Sum of Unit digits i.e. 3+7 = 10; Remaining number i.e. 2 is same in both numbers

46x44:  Sum of Unit digits i.e. 6+4 = 10; Remaining number i.e. 4 is same in both numbers

112x118:  Sum of Unit digits i.e. 2+8 = 10; Remaining number i.e. 11 is same in both numbers

291x299:  Sum of Unit digits i.e. 1+9 = 10; Remaining number i.e. 29 is same in both numbers

135x135:  Sum of Unit digits i.e. 5+5 = 10; Remaining number i.e. 13 is same in both numbers

Solving 46 x 44

You will get the answer in two parts.

First part, to get left hand side of the answer: multiply the left most digit(s), i.e. 4 by its successor 5

Second part, to get right hand side of the answer: multiply the right most digits of both the numbers i.e. 4 and 6.

Example

First part: 4 x (4+1)

Second part: (4 x 6)

Combined effect:  (4 x 5)  | (4 x 6) = 2024

*| is just a separator. Left hand side denotes tens place, right hand side denotes units place

 

More Examples

37 x 33 = (3 x (3+1)) |  (7 x 3) = (3 x 4) | (7 x 3) = 1221

11 x 19 = (1 x (1+1)) |  (1 x 9) = (1 x 2)  | (1 x 9) = 209

As you can see this method is corollary of  "Squaring number ending in 5"

It can also be extended to three digit numbers like :

E.g. 1: 292 x 208.

Here 92 + 08 = 100, L.H.S portion is same i.e. 2

292 x 208 = (2 x 3) x 10 | 92 x 8  (Note: if 3 digit numbers are multiplied, L.H.S has to be multiplied by 10)

60 | 736 (for 100 raise the L.H.S. product by 0) = 60736.

E.g. 2: 848 X 852

Here 48 + 52 = 100,

L.H.S portion is 8 and its next number is 9.

848 x 852 = 8 x 9 x 10 | 48 x 52 (Note: For 48 x 52, use methods shown above)

720 | ₂496

= 722496.

[L.H.S product is to be multiplied by 10 and 2 to be carried over because the base is 100].

Eg. 3: 693 x 607

693 x 607 = 6 x 7 x 10 | 93 x 7 = 420 / 651 = 420651.

Note: This Vedic Maths method can also be used to multiply any two different numbers, but it requires several more steps and is sometimes no faster than any other method. Thus try to use it where it is most effective

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