Checking of Calculations: Casting Out Nines

While doing arithmetic calculations, we should normally check our calculation. But the checking should not be as tedious as the original problem. To solve this problem I am explaining below a very frequently used method which is discussed in Vedic Mathematics as well as by many other mathematicians.

Vedic Sutra: Vedic Mathematics Technique

Beejank: The Sum of the digits of a number is called Beejank. If the addition is a two digit number, then these two digits are also to be added up to get a single digit.

Find the Beejank of 632174.

As above we have to follow

632174  –> 6 + 3 + 2 + 1 + 7 + 4 –> 23 –> 2 + 3 –> 5

But a quick look gives 6 & 3 ; 2 & 7 are to be ignored because 6+3=9,2+7=9.

Hence remaining 1 + 4 –> 5 is the beejank of 632174.

Checking of Addition

Thumb Rule: Whatever we do to the number, we also do to their digit sum: then the result                 we get from the digit sum of the number must be equal to the digit sum of the answer.

For example: The number: 12+45+96+75+25 =253

The digit sum = 3+9+6+3+7 =28=10=1

Answer’s digit sum: 2+5+3 =10=1 (verified)

Another example:  3.5+23.4+17.5 = 44.4

The digit sum: 8+9+13=8+9+4=21=3

Answer’s digit sum: 12=3 (verified)

Casting Out Nines

This method is also known as “casting-out-nines“. The method involves converting each number into its “casting-out-nines” equivalent, and then redoing the arithmetic. The casting-out-nines answer should equal the casting-out-nines version of the original answer. Below are examples for using casting out nines to check addition.

We get the casting-out-nines equivalent of a number by adding up its digits, and then adding up those digits, until you get a one digit number. If our answer is 9, then that becomes 0. As a short cut, we don’t have to add in any of the 9′s in our work, as these are the equivalent of 0. We can just “cast out” those 9′s. For example, 19 becomes 1, without even adding 1 and 9 and getting 10, and then adding 1 and 0 and getting 1. As a further short cut, we can group numbers together which add up to 9, and replace them with 0. 2974 becomes 4, because we can cast out the 9 and the 2+7 (which is also 9 or 0). Well, let’s try an arithmetic problem:

137892     3

+ 92743   + 7

——    –

230635     1

3+7=10, casting out 9 we get 1.

This rule is also applicable to subtraction, multiplication and up to some extent to division also

In the next post I will explain the use of this method for all of them.

Concept: CHECKING OF CALCULATIONS
Beejank: The Sum of the digits of a number is called Beejank. If the addition is a two digit number, then these two digits are also to be added up to get a single digit.
Find the Beejank of 632174.
As above we have to follow
632174  –> 6 + 3 + 2 + 1 + 7 + 4 –> 23 –> 2 + 3 –> 5
But a quick look gives 6 & 3 ; 2 & 7 are to be ignored because 6+3=9,2+7=9.
Hence remaining 1 + 4 –> 5 is the beejank of 632174.
Checking of Addition
Thumb Rule: Whatever we do to the number, we also do to their digit sum: then the result                 we get from the digit sum of the number must be equal to the digit sum of the answer.
For example: The number: 12+45+96+75+25 =253
The digit sum = 3+9+6+3+7 =28=10=1
Answer’s digit sum: 2+5+3 =10=1 (verified)
Another example:  3.5+23.4+17.5 = 44.4
The digit sum: 8+9+13=8+9+4=21=3
Answer’s digit sum: 12=3 (verified)
This method is also known as “casting-out-nines”. The method involves converting each number into its “casting-out-nines” equivalent, and then redoing the arithmetic. The casting-out-nines answer should equal the casting-out-nines version of the original answer. Below are examples for using casting out nines to check addition.
We get the casting-out-nines equivalent of a number by adding up its digits, and then adding up those digits, until you get a one digit number. If our answer is 9, then that becomes 0. As a short cut, we don’t have to add in any of the 9′s in our work, as these are the equivalent of 0. We can just “cast out” those 9′s. For example, 19 becomes 1, without even adding 1 and 9 and getting 10, and then adding 1 and 0 and getting 1. As a further short cut, we can group numbers together which add up to 9, and replace them with 0. 2974 becomes 4, because we can cast out the 9 and the 2+7 (which is also 9 or 0). Well, let’s try an arithmetic problem:
137892     3
+ 92743   + 7
——    –
230635     1
3+7=10, casting out 9 we get 1.
This rule is also applicable to subtraction, multiplication and up to some extent to division also
In the next post I will explain the use of this method for all of them.
Concept: CHECKING OF CALCULATIONS
Beejank: The Sum of the digits of a number is called Beejank. If the addition is a two digit number, then these two digits are also to be added up to get a single digit.
Find the Beejank of 632174.
As above we have to follow
632174  –> 6 + 3 + 2 + 1 + 7 + 4 –> 23 –> 2 + 3 –> 5
But a quick look gives 6 & 3 ; 2 & 7 are to be ignored because 6+3=9,2+7=9.
Hence remaining 1 + 4 –> 5 is the beejank of 632174.
Checking of Addition
Thumb Rule: Whatever we do to the number, we also do to their digit sum: then the result                 we get from the digit sum of the number must be equal to the digit sum of the answer.
For example: The number: 12+45+96+75+25 =253
The digit sum = 3+9+6+3+7 =28=10=1
Answer’s digit sum: 2+5+3 =10=1 (verified)
Another example:  3.5+23.4+17.5 = 44.4
The digit sum: 8+9+13=8+9+4=21=3
Answer’s digit sum: 12=3 (verified)
This method is also known as “casting-out-nines”. The method involves converting each number into its “casting-out-nines” equivalent, and then redoing the arithmetic. The casting-out-nines answer should equal the casting-out-nines version of the original answer. Below are examples for using casting out nines to check addition.
We get the casting-out-nines equivalent of a number by adding up its digits, and then adding up those digits, until you get a one digit number. If our answer is 9, then that becomes 0. As a short cut, we don’t have to add in any of the 9′s in our work, as these are the equivalent of 0. We can just “cast out” those 9′s. For example, 19 becomes 1, without even adding 1 and 9 and getting 10, and then adding 1 and 0 and getting 1. As a further short cut, we can group numbers together which add up to 9, and replace them with 0. 2974 becomes 4, because we can cast out the 9 and the 2+7 (which is also 9 or 0). Well, let’s try an arithmetic problem:
137892     3
+ 92743   + 7
——    –
230635     1
3+7=10, casting out 9 we get 1.
This rule is also applicable to subtraction, multiplication and up to some extent to division also
In the next post I will explain the use of this method for all of them.
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