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

This page extends the addition in first principles into a simplified procedure for addition of large numbers, which is called as *addition by place value with regrouping*.

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Consider addition of `12` and `15`. Which of the following step helps in the addition?

- Combine `12` and `15` together and count the combined quantity
- Combine `12` and `15` together and count the combined quantity
- two digit number addition is not possible

The answer is 'Combine `12` and `15` together and count the combined quantity'.

Considering addition of `12` and `15`. Combining `12` and `15` is shown in the figure. The top shaded portion shows the numbers `12` and `15`. The combined quantity is shown in the lower half.

What is the count shown in the combined quantity?

- `1215`
- `27`
- `27`

The answer is '`27`'.

Consider the addition of `19` and `17`. The quantities are illustrated in the figure. Counting the two quantities together, there are `2` tens and `16` units.

What is the sum?

- `216`
- `36`
- `36`

The answer is '`36`'.

Considering the addition of `19` and `17`. The combined sum is illustrated in the lower portion of the figure. Note that `10` units are combined together to form the `1` ten. So the result of the addition is `36`.

`10` units blocks are grouped into `1` ten. This is referred as **regrouping**.

Note that, the two numbers `19` and `17` were grouped already and when combined, the number representing the sum is regrouped.

**Regrouping**: In a place value position, when combining grouped numbers, `10` of a lower place-value can be regrouped into `1` of the next higher place-value.

Considering the addition of `19` and `17`. A simplified procedure for addition is shown in the figure.

`9` and `7` are added to `16`. The `10` units are converted to `1` ten and moved to the tens position.

The sum is calculated as `36`.

Consider the addition of `214` and `132`. We can quickly count the combined quantity in the figure.

What is the sum?

- `216`
- `346`
- `346`

The answer is '`346`'.

Considering the addition of `214` and `132`. The numbers are given in the place-value form in the figure.

What is the sum?

- `216`
- `346`
- `346`

The answer is '`346`'.

Considering the addition of `214` and `132`. A simplified procedure **Addition by Place-value** is given in the figure.

The digits in the units place are added,

Then the digits in the tens place are added.

Then the digits in the hundreds place are added.

What is the sum as given in the figure?

- `216`
- `346`
- `346`

The answer is '`346`'.

Consider the addition of `156` and `11`. Which of the following is correct?

`156+11=266` or

`156+11 = 167`.

- `266`
- `167`
- `167`

The answer is '`167`'. The units are added with units, and tens are added with tens.

Consider the addition of `156` and `88`. The simplified procedure **Addition by Place-value with regrouping** is given in the figure.

• The digits in units place are added. `6+8=14`. `14` units is modified as `1` ten and `4` units. The `1` ten is moved to the tens place as carry over. The `4` units is placed in the units place of sum.

• The tens place is modified `1+5+8 = 14`. `14` tens is modified as `1` hundred and `4` tens. The `1` hundred is moved to the hundreds place as carry over. The `4` tens is placed in the tens place of sum.

• The hundreds place is modified `1+1 = 2`. `2` hundreds is placed in the hundreds place of the sum.

What is the sum?

- `244`
- `244`
- `2+4+4 = 10`

The answer is '`244`'.

Consider the addition of `675` and `896`. The simplified procedure **Addition by Place-value with regrouping** is given in the figure. Note: the addition of place values and the carry over are highlighted in color.

What is the sum?

- `1571`
- `1571`
- `1751`

The answer is '`1571`'.

**Addition by Place-value with regrouping** -- simplified procedure : Two numbers are added as follows:

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

• the units are added and if the result has `10` numbers, then it is carried to the `10`s place.

• The addition is continued to the higher place-value position. Note: The carry over is the simplification of combining `10` of a place value to a higher place value.

*Solved Exercise Problem: *

What is the sum of `2314+2883`?

- `4197`
- `5297`
- `5297`

The answer is "`5297`"

*Solved Exercise Problem: *

What is the sum of `34+66`?

- `100`
- `100`
- `910`

The answer is "`100`"

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