Checking our calculations
For the past few weeks we have studied basic calculations like addition, subtraction, multiplication and division. Now let us take a break and see how to check our calculations. We have already learned the digital root or Beejank methods, which are very useful to check our calculations. Here is a recap.
Beejank (in vedic math terminology) or digital root is the sum of all the digits of a number. We add the digits repeatedly till we are down to a single digit. This single digit is the digital root of the given number.
Example: Finding the digital root of 67459
6 + 7 + 4 + 5 + 9Â = 31
3 + 1 = 4
So the digital root of 67459 is 4
There is a technique to make this addition simpler. To make it easy we need not add all the digits every time. We can cast out 9s and only add the other digits to find the digital root.
Let me show that in the same problem. We have the digits 6,7,4,5,9 in the given number. Leave out the 9. Then leave out any set of numbers that add up to 9. That leaves us with 6 and 7 to add. 6 + 7 = 13 = 4.
Do you remember the 9-point circle?
This 9-point circle clearly shows that the digital sum of any number is between 1 and 9 and adding a 9 does not alter the digital sum of any number.
Notice here that on any branch the digit sum of every number is the same. For example on the 1-branch we get 1, 10, 19, 28, all of which have a digit sum of 1. This shows that adding 9 to a number does not affect its digit sum. And in fact it follows that adding any number of 9s, or subtracting any number of 9s will not affect the digit sum of a number.
To find the digit sum of 73201: We have 2 and 7 that add up to 9 and can therefore be left out. This leaves 3 and 1, which add up to 4.
So the digit sum of 73201 is 4.
The digital sum of 53012: We know that 1, 3 and 5 add up to 9 and so can be left out. This leaves only 2, so this is the answer.
The digit sum of 53012 is 2.
Now can we try with some riddles in digital sum,
1. The digit sum of a 2-digit number is 8 and the digits are the same. What is the number?
This is clearly 44
2. The digit sum of a 2-digit number is 9 and the first figure is twice the second. What is it?
This must be 63
3. Give three 2-digit numbers that have a digit sum of 3.
12, 21, 30
4. The digit sum is 7 and the difference between the digits is 3.
The answer can be 25 or 52
5. The digit sum is 7 and one digit is 4.
34 or 43
6. A 2-digit number has a digital sum of 5 and the figures are the same. What is the number?
5 is an odd number, but looking at the 9-point circle we see that 14, which is also on the 5-branch can be split into 7+7. So the number must be 77