Using the Average to Multiply

When multiplying numbers, sometimes the average method is quite useful to determine their product.

Vedic Sutra: Vyastisamastih (Specific and General)

The rule is very simple: square the average of 2 numbers and subtract the square of the difference of average from either number.

Let us understand this with an example:

41 x 39 = ?

Average of 41 and 39 is 40.

So, answer = ((41+39)/2)^2 – (41-40)^2 = 40^2 – 1^2 = 1600 – 1 =1599.

Another example:

32 x 28 = ?

This method can be applied across various products.  Let us practice more:

a 69 × 71                              b 37 × 43                                 c 87 × 93

d 24 × 26                              e 85 × 65                                 f 75 × 95

g 133 × 147                           h 91 × 99