We all make mistakes when doing calculations. However, there is a simple way of checking a calculation operation which is rarely taught to children.
This method of checking is based on substituting the values involved in the operation with other values which we will call substitutes. We then perform the operation for the substitutes to check its validity.
The substitute for a number is determined by the sum of the digits of that number. For the number, 7492 for example, the sum of the digits is
7+4+9+2=22
But as long as we have a number with more than one digit, then we calculate the sum of its digits. That is, for 22 it is
2+2=4.
The substitute for the number 7 492 is therefore 4.
There is a way to simplify. We can ignore the digits 9 when determining the substitute for a number. We can also ignore two or more digits whose sum is 9 or a multiple of 9. And we will get the same result.
For our value 7492, I can ignore the 9 and I can ignore the 7 with the 2, then I will only have 4 which is the substitute.
For example, the operation :
7492 x 365 = 2734580
1st verification step
Determine the substitutes for the two values as well as that of the product found:
For the 1st value 7492, I ignore the 9 and ignore the 7 with the 2, the substitute for the 1st value is 4.
For the 2nd value 365, I ignore the 3 with the 6, so the substitute is 5.
For the product found 2734580, I ignore the 2 with the 7 and the 4 with the 5, so I have 3+8=11 and 1+1=2. The substitute for the product found is 2.
2nd verification step
Draw a cross as in the picture below. Write the substitute for the 1st value at the top, the substitute for the 2nd value at the bottom and the substitute for the result found on the left.
3rd verification step
Multiply the substitute for the 1st value by the substitute for the 2nd value. This is 4x5=20. And as long as we have a number with more than one digit, then we calculate the sum of its digits. That is 2+0=2. Finally write this number on the right.
Checking rule
If the number written on the right is equal to the number written on the left, then the result is probably correct. This is the case now where both numbers are equal to 2.
If the number written on the right is different from the number written on the left, then the result is 100% incorrect. Look for the error in your calculation of the operation and then check again.
An addition operation can be checked in the same way, except that in the 3rd step, the substitute numbers of the two values must be added instead of multiplied.
For example, the operation :
7292 + 362 = 7654
Up is 2. I ignored the 9 and also the 7 with the 2.
Below is 2. I ignored the 3 with the 6.
On the left is 4. I ignored the 5 with the 4. I calculated 7+6=13. And 1+3=4
On the right, it is 2 + 2 = 4. That is, the sum of the substitute numbers of the two values.
To check a subtraction operation, I always prefer to check the corresponding addition operation.
The equivalent of the operation: 7 - 4 = 3, is the addition operation: 7 = 4 + 3.
That is, the first value of the subtraction operation is the sum of the subtracted value and the result value.
A division operation is verified by the corresponding multiplication operation.
The equivalent of the operation: 12 : 4 = 3, is the multiplication operation: 12 = 4 x 3.
That is, the dividend of the division operation is the product of the divisor and the quotient.
And if there is a remainder of the division, it must be added as follows:
14 : 4 = 3 (r = 2) is equivalent to : 14 = (4 x 3) +2
So, to check a division operation, in the 3rd step, multiply the quotient by the divisor and then add the remainder.
Let's give an example: 3454 : 15 = 230 and remainder = 4.
At the top is the sum of the digits of the divisor. That is, 1+5=6.
At the bottom is the sum of the digits of the quotient. That is 2+3=5.
On the left is the sum of the digits of the dividend. That is 3+4=7.
On the right it is (5x6)+4=34. And 3+4=7.
We have the same number on the right and on the left. The result of the check is positive.
