Home » Math Theory » Operations of Numbers » Multi-Digit Addition

Addition is one of the four fundamental operations of arithmetic. It is usually denoted by the plus symbol +. The result of every addition process is called the sum, and the numbers being added are called the addends. In a nutshell, addition is a process in which two or more numbers are combined together.

Multi-digit, from the word itself, is a number having more than one digit. This means that multi-digit addition is simply the addition of any number having more than one digit.

When adding multi-digit numbers, we usually see use the vertical method and the terms as shown in the figure:

• The addends are the numbers to which the addition process will be applied.
• The carry over is the single-digit that is regrouped from one column of digits to the column of a higher place value.
• The plus sign is the symbol that denotes the addition process.

## How to do the multi-digit addition?

While one-digit numbers can be easily added, larger numbers or multi-digit numbers require us to split them into columns according to their respective place values. We always begin addition on the right side, in accordance with the place value system.

### Adding multi-digit numbers without regrouping

1. Write the numbers with the place values lines up.
2. Add the digits in the ones place.
3. Add the digits in the tens place.
4. Continue doing these steps until you have added all the place values.

Example #1

What is the sum of 135 and 23?

Solution

Example #2

What is the sum of 4381 and 418?

Solution

Example #3

Find the sum of 2048 and 2021.

Solution

Example #4

What will be the result of 15 346 + 12 631?

Solution

Example #5

Determine the sum of 194 765 and 304 212.

Solution

### Adding multi-digit numbers with regrouping

1. Write the numbers with the place values lines up.
2. Add the digits in the ones place. If the sum exceeds 10, then carry over the digit to the tens place.
3. Add the digits in the tens place. If the sum exceeds 10, then carry over the digit to the hundreds place.
4. Continue doing these steps until you have added all the place values. If there is a need to regroup, carry over to the next higher place value.

Example #1

What is the sum of 821 and 98?

Therefore, the sum of 821 and 98 is 919

Example #2

Determine the sum of 999 and 23.

Solution

Example #3

What will be the result of 1995 + 345?

Solution

Example #4

Determine the sum of 4875 and 3249.

Solution

Example #5

What is the sum of 23 765 and 87 845?

Solution

## How to solve problems involving multi-digit addition?

1. List all the information given in the problem.
2. Analyze the problem.
3. Apply the rules of adding multi-digit numbers.

Example #1

A flower store sells roses and sunflowers only. Based on their inventory, they have 3546 roses and 4582 sunflowers. How many flowers does the flower store have?

Solution

The problem states that there are 3546 roses and 4582 sunflowers. Since we are asked to get the total number of flowers in the store, then we will use the addition operation.

Example #2

Venus has saved up $30,465 in the last 4 years. This year, she was able to save$2,975. How much is the total savings of Venus?

Solution

In the problem, it is stated that Venus was able to saved up $30, 465 and$2,975. Thus, using the rules of multi-digit addition,

Example #3

An Asian restaurant earned $15, 365 last week. This week, they earn$23, 499. How much did they earn in two weeks?

Solution

Given the problem, we can note that the Asian earned $15, 365 and$23, 499 for the past two weeks. Thus, using the rules of multi-digit addition,

Therefore, the Asian restaurant earned \$38,864 in the last two weeks.