# Math – Subtraction Formula

Before going into the description of my formula for a subtraction Equation, I would first give the summary description of the general formula for a subtraction equation that would most likely be used on a daily basis.

**Note: Before publishing the infinity formula, this formula is published for the purpose of explaining another version of the formula for a subtraction equation. This formula is used as the subtraction equation for the infinity formula. This paragraph will be removed one the infinity formula is published.**

# General Mathematical Subtraction Formula

When it come to a subtraction equation, the general knowledge formula is the borrowing method. The borrowing method is applied when subtracting two number to each other at the rate of a specified amount of digit at a time. A specified amount of digit in most case for an explanation of the formula would most likely to be one digit at a time. In my explanation, the specified amount of digit the equation is applying to at a time can also be called the set of Digits or the digits set.

In the general formula, the subtraction equation alway started from the digits on the right side of the numbers and then process to the digits in the beginning of the numbers. Before applying the subtraction to any digits set, if the digit value of the digits set in the first number is lower than the digit value of the digits set of the second number, a value has to be borrow from the next digits set of the first number and the borrowing value for a subtraction equation that only involve two numbers would always be a digit one is then added to the beginning of the current set of digits from the first number. The digits set that the current set of digits would always borrow from if needed, would always be the next left digits set from the current digits set. The borrowing digit value would be subtracted from the digits set where the borrowing value borrowed from. The borrowing value would most often be called the borrowing/regrouping value. In my opinion, the coined term borrowing/regrouping is because the digit that was borrowed from the next set of digits would be placed at the beginning of the current digits set. Thus, what borrowed from the next set of digits is regrouped with the current digits set by placing the borrowed value at the beginning of the current digits set.

That is if the value of the first digits set is lower than the value of the second set of digits. If the value of the first sets of digits is higher than the value of the second set of digits, there would not be a borrowing value and a normal subtraction equation would be applied to the set of digits from both numbers.

To demonstrate the general formula, I would apply the formula to a couple of examples and we are subtracting one digit at a time.

```Example 1: 25
-17

Step 1: 5 can't subtract to 7, therefore, we have to borrow a value of one from the next set of digits which is the digit two.
Thus, the equation for the first digits set is: 15 - 7 = 8

Step 2: Since we borrowed a value of one from the digit two, we reduce the digit two by a value of one.
The equation for the second set of digits is: 1 - 1 = 0

-17
--
08 or 8 is the answer of 25 - 17
```
```Example 2: 851
-758

Step 1: 1 can't subtract to 8, therefore, borrow a value of 1 from five.
current equation: 11 - 8 = 3

Step 2: a value of 1 was borrowed from 5, therefore, the digit 5 would now become the digit 4.
4 can't subtract to 5, therefore, borrow a value of 1 from 8.
current equation: 14 - 5 = 9

Step 3: a value of 1 was borrowed from 8, therefore, the digit 8 would now become the digit 7.
It is possible to subtract seven to seven, hence, no need to borrow.
Note: We can never borrow from the last set of digits because there is nothing to borrow from.
current equation: 7 - 7 = 0

-758
-----
093 or 93 is the answer of 851 - 758.
```

The general formula works perfectly fine when the first number is the number with the larger value, nevertheless, the general formula would not be able to produce an answer if the first number is smaller than the second number. When applying the general formula and the second number is the bigger number, we would have to place the second number on top and subtract to the first number. When this happen, the result value of the equation would be in the opposite negative or positive base from the two numbers. For example, when positive A is smaller than positive B and we are subtracting A to B, the result value would be a negative result value. Another example is when negative A is smaller than negative B and we are subtracting A to B, the result value would be a positive result value.

The reason of why we can’t subtract a smaller number to a larger number without a reversal of the equation is because, in the last set of digits, there isn’t another digits set for the equation to borrow from. The equation neither can borrow from a zero value. If we were to borrow from a zero value or a nil value then, in fact, we are producing an additional value that is not supposed to be there. Which would obviously render the equation to produce an incorrect answer. The reason for why reversing or swapping the position between the larger number and the smaller number would work is because of absolute values. For example, the equation of 5 – 2 would produce the result value of 3 and the equation 2 – 5 would produce a result value of -3. The absolute value of the result value from both equations is 3. Thus we can say that the equation of 5 – 2 and 2 – 5 would produce the same absolute value as the result value. Thus, if our equation was 78 – 98, the result value would be the negative value of the result value of the equation of 98 – 78. In another explanation, the result value of the equation 78 – 98 would be the negative value of the absolute value of either equation 78 – 98 or 98 – 78.

One property of borrowing a value of one from the next set of digits is that, if we are borrowing from the next set of digits and the next set of digits is a value of zero, the next set of digits would automatically become the largest value that can be contained within the digits set and the equation would also automatically borrow a value of one from the next digits set after the digits set that just been borrowed from. For example, if we were to process the equation at the rate of one digit at a time and a value of one would be borrowed from a zero digit, the set of digits we just borrowed from would become the digit nine and we are automatically borrowing a value of one from the digits set after the digits set of zero. For another example, if the equation were to be processed at the rate of two digits at a time and a value of one would be borrowed from the set of digits that contained two zeroes. Then the set of digits that contained the two zeroes digit would become 99 and we are automatically borrowing a value of one from the next set of digits after the set of digits that we just borrowed from. In this explanation, at first glimpse, it may seem that we might eventually borrow twice from the last digits set that we borrowed from. However, double borrowing can never occur because after borrowing a value, the zero set of digits would contain the highest value, therefore, there isn’t a possibility that the once was a zero set of digits would require any additional value to be able to subtract to another set of digits that is the same size by the amount of digit.

One shortcut to a subtraction equation is when both numbers are equal in digit value, a zero result value would be produced. This is because when a number reduce to a value of itself then there would not be a value left.
The full article can be found @ http://kevinhng86.iblog.website/2017/04/10/math-subtraction-formula/
This article was written by Kevin Ng @ http://kevinhng86.iblog.website.

This post first appeared on Programming With Kevin, please read the originial post: here

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