This page extends the subtraction in first principles into a simplified procedure for subtraction of integers, which is called *sign property of integer subtraction*.

The procedure is summarized as -- subtraction is addition of additive inverse.

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**Subtraction by Place-value with de-grouping** -- Simplified Procedure : A number is subtracted from another as per the following procedure:

• the place-value positions are arranged units under units, `10`s under `10`s, etc.

• the units are subtracted and if the minuend digit is smaller than the subtrahend digit, then one ten's place is borrowed to make the minuend at the position larger. Then subtraction is carried out.

• continue to the higher place-value position. The "borrow" is the simplification of taking `1` from a place value to `10` pieces of a lower place value.

What is the difference `4 - 3`?

By first principles, `text(received:)3` is taken away from `text(received:)4`.

- `43`
- `1`
- `1`

The answer is "`1`"

What is the difference `4 - (-3)`?

By first principles, `text(given:)3` is taken away from `text(received:)4`.

- `1`
- `7`
- `7`

The answer is "`7`".

What is the difference `-4 - (-3)`?

By first principles, `text(given:)3` is taken away from `text(given:)4`.

- `-1`
- `-1`
- `7`

The answer is "`-1`".

What is the difference `-4 - (-5)`?

By first principles, `text(given:)3` is taken away from `text(given:)4`.

- `-1`
- `+1`
- `+1`

The answer is, "`+1`".

Note the following

• `4 - 3 = 4 + (-3) = 1`

• `4-(-3) = 4 + (+3) =1`

• `-4-(-3) = -4 + (+3) = -1`

• `-4-(-5) = -4 + (+5) = 1`

Based on this, the subtraction is simplified and handed as addition of negative of subtrahend. That is,

`text(minuend ) - text( subtrahend )` `= text(minuend ) + (-text(subtrahend))`

**Integer Subtraction Simplified Procedure** : **Sign-Property of Integer Subtraction:**

Integer subtraction is handled as integer addition with addends (a) minuend and (b) the negative of subtrahend.

`text(minuend )-text( subtrahend )`

` = text( minuend as addend )``+ text( negative of subtrahend as addend)`

*Solved Exercise Problem: *

Find the result of `(-6)-0`.

- `-6`
- `-6`
- `6`

The answer is "`-6`"

*Solved Exercise Problem: *

Find the result of `-140` subtracted from `11`.

- `151`
- `151`
- `-129`

The answer is "`151`"

*Solved Exercise Problem: *

Find the result of `2` subtracted from`-2`

- `0`
- `-4`
- `-4`

The answer is "`-4`"

*Solved Exercise Problem: *

Find the result of `-2345` subtracted from `-889`

- `-3234`
- `-3234`
- `1456`

The answer is "`1456`"

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