It's fairly easy to multiply two numbers that are close to the same multiple of 10.
The algorithm for doing it is called “Nikhilam Navatascaramam Dasata.” It is part of a system of algorithms and mnemonics to remember them, collectively known as “Vedic Math”, that was developed by Jagadguru Swami Bharati Krishna Tirthaji Maharaj in the early 20th century.
The easiest way to explain the algorithm is to give examples, and explain the algorithm along the way.
First find a suitable “base”. Since 7 and 8 are both close to 10, we'll use 10. Write the difference between the numbers to be muliplied, and the base, off to the right:
Now add the difference between the one number to be multiplied and 10, to the other number to be multiplied. Pick either combination, because you will get the same result
Put the result on the left side of the answer:
Now let's try it with significantly bigger numbers, to see why this is such an advantage.
Since both numbers are close to 100, we will use 100 as our base. Write the difference between the numbers to be muliplied, and the base, off to the right. Because 100 has two zeroes, we need two digits on the right hand side.
The 87 comes from either 89 + (-2), or 98 + (-11). The 22 comes from (-2) x (-11). You can do this problem in your head. Let's try another one, to show when you need to pad the right side with leading zeroes:
The 95 comes from either 97 + (-2) or 98 + (-3). The 06 comes from (-2) x (-3). We need to pad it with a zero, because the base is 100 so we need two digits on the right-hand side.
Let's try an example where the numbers to be multiplied are a little bigger than a multiple of 10:
The 107 comes from either 102 + 5 or 105 + 2. The 10 comes from 5 x 2 (the product of the differences on the right).
Let's try another example where the numbers to be multiplied are on either side of a multiple of 10:
Uh oh, we have a negative on the right! Add it to the left hand side:
Let's try bigger numbers.
993 = 995 + (-2) OR 993 = 998 + (-5). 010 comes from (-5) x (-2) = 10, then padded with one leading zero because we need 3 digits because our base is 1000.
The method also works with multiples of powers of 10:
because we had to multiply 10 by 2 to get to the base, we need to multiply the LEFT SIDE ONLY of the answer by 2
