__maths__>__Whole Numbers__>__Whole numbers addition and subtraction__### Subtraction: Simplified Procedure for Large Numbers

This page extends the subtraction in first principle into a simplified procedure for subtraction of large numbers, which is called as *subtraction by place value with de-grouping*.

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Consider the subtraction `15-12`. Which of the following step helps in the subtraction?

- take-away `12` from `15` and count the remaining quantity
- take-away `12` from `15` and count the remaining quantity
- two digit number subtraction is not possible

The answer is 'take-away `12` from `15` and count the remaining quantity'.

Considering the subtraction `15-12`. Taking away `12` from `15` is shown in the figure. The dotted lines cross the equal amount from the numbers `12` and `15`. The remaining quantity is shown in the dotted ellipse.

What is the count shown in the remaining quantity?

- `3`
- `3`
- `27`

The answer is '`3`'.

Consider the subtraction `23-8`. The quantities are shown in the figure. Taking away `8` from `23` is to be done.

Which of the following step help in this subtraction?

- subtraction is not possible as `8` cannot be taken away from `3` units
- the tens bar is made of `10` units, so that can be split into units
- the tens bar is made of `10` units, so that can be split into units

The answer is 'the tens bar is made of `10` units, so that can be split into units'.

Considering the subtraction `23-8`. The subtraction is illustrated in the figure. Note that `1` ten is broken-down into `10` units.

The subtrahend `8` is taken away from the `23` and the remaining is `1` ten and `5` units. The difference is `15`.

A tens block is split into `10` units blocks. This is referred as **de-grouping**. The grouped place-value is degrouped into lower place-value.

**De-grouping**: When handling grouped numbers, at a place-value, `1` of a higher place-value can be de-grouped into `10` of the next lower place-value.

Considering the subtraction `23-8`. A simplified procedure, **Subtraction by Place-value with de-grouping** is shown in the figure.

`23-8` is considered.

In the units place minuend `3` is smaller than subtrahend `8`. So, one ten is broken into `10` units. The units place subtraction is `13-8 = 5`.

In the tens place, the subtraction is with remaining `1` ten in minuend as `1-0 =0`.

The difference is calculated as `15`.

Consider the subtraction of `274-132`. We can quickly carryout the subtraction by the quantities in the figure.

What is the difference?

- `216`
- `142`
- `142`

The answer is '`142`'.

Consider the subtraction `274-132`. The numbers are given in place value in the figure.

What is the difference?

- `216`
- `142`
- `142`

The answer is '`142`'.

Considering the subtraction `274-132`. A simplified procedure, **Subtraction by Place-value with de-grouping** is given in the figure.

The digits in the units place are subtracted,

Then the digits in the tens place are subtracted.

Then the digits in the hundreds place are subtracted.

The difference is `142`.

Consider the subtraction `156 - 11`. Which of the following is correct? `156-11=046` or `156-11 = 145`.

- `046`
- `145`
- `145`

The answer is '`145`'. Note that the units are subtracted from units, and the tens are subtracted from the tens.

Consider the subtraction `156-88`. The simplified procedure, **Subtraction by Place-value with de-grouping** is given in the figure.

• The digits in units place are subtracted. Since `6` minuend is smaller than `8` subtrahend, the one ten from tens place is *borrowed* as `10` units into units place. The borrowed `10` units and the units in the minuend `6` together make `16`. Subtraction at the units place is `16-8 = 8`.

• The digits in the tens place are subtracted. Since one ten was borrowed into units place, the tens place of minuend is revised to `4`. The `4` is less than the subtrahend `8`. So, One hundred from hundreds place is borrowed as `10` tens. The borrowed `10` tens and the `4` tens in the minuend together make `14`. Subtraction at the tens place is `14-8 = 6`.

• Subtraction in the hundreds place is `0-0=0`.

What is the difference?

- `8+6+0=14`
- `68`
- `68`

The answer is '`68`'.

Consider the subtraction `675-396`. The simplified procedure is given in the figure. Note: the subtraction of place values and the borrow are highlighted in color.

What is the difference?

- `279`
- `279`
- `1751`

The answer is '`279`'.

**Subtraction by Place-value with de-grouping** -- Simplified Procedure : Two numbers are subtracted as follows:

• 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. Note: The "borrow" is the simplification of taking `1` from a place value to `10` pieces of a lower place value.

*Solved Exercise Problem: *

What is the difference `2332-1297`

- `1145`
- `1035`
- `1035`

The answer is "`1035`"

*Solved Exercise Problem: *

What is the difference `122-99`

- `23`
- `23`
- `33`

The answer is "`23`"

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