__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`. The quantities are combined together and the combined quantity is counted.

Combining `12` and `15` is shown in the figure. The combined quantity is shown in the lower half. The combined quantity is:

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. The units can be

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 count the combined quantity in the figure. The combined quantity is counted as,

`4` units and `2` units together is `6` units,

`1` tens and `3` tens together is `4` tens,

`2` hundreds and

`1` hundred together is `3` hundreds.

So the combined count is `346`.

The numbers `214` and `132` are given in the place-value form. Addition is carried out and

The result if `346`.

The simplified procedure 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.

Considering the addition of `156` and `11`. The result is `167`, and not 266. The place value positions should be

Considering the addition of `156` and `88`. The simplified procedure,

The digits in units place are added. 6 plus 8 equals 14. 14 units is modified to 1 ten and 4 units. The 1 ten is moved to the tens place as

The tens place is modified 1 plus 5 plus 8 ;; equals 14. 14 tens is modified as 1 hundred and 4 tens. The 1 hundred is moved to the hundreds place as

Consider the addition of two numbers. 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.

The result of addition 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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