Multiplication of two digits can be easily done if we learn the following concept.

__Case 1__

When the given two numbers have same digit in their ten’s places.

Example : 11&17, 90&99, 57&53 have same digits in their ten’s places.

__Concept __

- Take the example 13×19. Here the base is 10. (Base is obtained by multiplying the digit in ten’s place with 10.) Now take one number and subtract base number from it, (13-10=3) and add it to the other number (19).

Simply put, add units digit of one number to another. 3+19.

- 3+19=22, then multiply the resultant number with the base number 22×10=220.
- Now multiply the units digits (3 & 9) of both the given numbers (19,13),

3x 9=27.

- Now add the obtained product (27) with 220 ie 247
- 13×19 = 247.

Take another example 55×56

Base =50, 55+6=61, 61×50 (base) =3050, 5×6=30 (product of digits in unit places). Adding 3050 an 30 we get 3080.

55×56=3080.

This method will be very useful to calculate squares of numbers very easily.

1) **75×75**

75+5=80, 80×70=5600 (Base 80), 5×5=25, 5600+25=5625.

Implies 75×75 = **5625**.

2) **48×48**

(56×40)+64 = **2304**. (Base 40)

3) **81×81**

6560+ (1X1) = **6561**

** **

__Case 2__

When the two numbers have adjacent digits in ten’s place.

Example : 23&35 (2,3 in ten’s place), 46&59 (4,5 in ten’s place), 88&74 etc.

In this case base number will be the number which is a multiple of 10 and as well as closer to both the numbers. Base no. for 78&87 is 80.

__Concept__

- Take the example 29×32. Here the base is 30. Now take one number and subtract base number from it .29-30= (-1).
- Now add this number (-1) with other number (32).
- 32+ (-1)=31.
- 31 x base no. = 31×30=930.
- 32-30=2, multiply this no. with (-1), 2x(-1)=-2.
- Add this product with 930. That is 930+(-2)=928
- 29×38 =928.

**Examples**

**1) 76 x 85**

76 85

76-80=(-4) 85-80 =5. (Base 80)

85+(-4)=81

81 x 80 =6480

(-4)x5= (-20).

Now, 6480-20=6460.

76×85=6460.

**2) 54×66**

Base 60.

54-60=(-6) 66-6=6

66+(-6)=60.

60×60=3600

(-6)x6=(-36)

3600+(-36)=3564

**3) 81×91**

Base 90.

81-90=(-9) 91-90=1

91+(-9)=82

82×90=7380

(-9)x1=(-9)

7380+(-9) = 7371

__Case 3__

When the numbers are not in any of the above cases case 3 metod is used.

Example 57×74, 68×81,18×93.

__Concept__

42×71 .

First multiply the digits on units digits and put the product on units digit of answer.

42×71 = ____2

Then multiply the digit in units place of first number with the digit in tens place of second number and vice versa, and add these two numbers.

Hope you find these methods to be helpful, keeping practicing them with your own examples to improve your speed and accuracy.