Addition

The addition is a process of adding two or more items together. In math, addition is the method of calculating the total of two or more numbers to know the sum of the numbers. It is a primary arithmetic operation. We use addition more often in real life. One of the most common everyday uses for addition is while we work with money or calculating our grocery bills.

The addition is an operation used in math to add the numbers. The obtained result or answer after addition is known as a sum. For example, if we add 2 and 3, (2 + 3) we get the sum as 5. Here we performed the addition operation on two numbers 2 and 3 to get the sum i.e. 5.

Addition Symbol (+)

In mathematics, we have different symbols. The addition symbol is one of the majorly used math symbols we use while performing addition. In the above definition of addition, we read about adding two numbers 2 and 3. If we observe the pattern of addition (2 + 3 = 5) the symbol (+) is connecting the two numbers and completes the given expression. An addition symbol is consists of one horizontal line and one vertical line. The addition symbol is also known as the addition sign or plus sign.

The addition formula we used to write any addition fact is addend + addend = sum. While performing addition we use some terms which are:

• Addends: Numbers on which addition operation is to be performed. 
• Sum: Final answer of the addition.
• Symbols: We use two symbols while performing addition, one is a plus sign (+) and the other one is 'equal to' sign (=)

There can be multiple addends in an addition fact. The basic addition formula or the mathematical equation of addition can be explained as: 

Here, 5 and 3 are addends and 8 is a sum. To learn more about the addition formula click here.

While solving addition problems, one-digit numbers can be added in a simple way, but for larger numbers, we split the numbers into columns using their respective place values, like ones, tens, hundreds, thousands, and so on. We always start doing addition from the right side as per the place value system. While solving such problems we may encounter some cases having carryover and some without carryover. Let us understand the two processes with help of examples.

Addition Without Regrouping

The addition that involves the sum of digits less than or equals to 9 at each place value is called addition without regrouping. Let us understand how to add two or more numbers without regrouping with the help of an example.

Example: Help James in adding 11234 and 21123

Solution: Follow the given steps and try to relate them with the image given below the steps.

Step 1: Start with ones place digits. (4 + 3 = 7)
Step 2: Move to tens place digits. (3 + 2 = 5)
Step 3: Now add the digit of hundreds place. (2 + 1 = 3)
Step 4: Now add digits of thousands place. (1 + 1 = 2)
Step 5: Lastly add digits of ten thousands place. (1 + 2 = 3)
Step 6: 11234 + 21123 = 32357.

In addition without regrouping, we simply add digits at each place value and write the respective sum to get the answer.

Addition With Regrouping

The addition that involves the sum of digits greater than 9 at any of the place values is called addition with regrouping. To add two numbers with regrouping, we find the sum of the digits and then write only the unit place digit in the respective column, while taking the tens place digit with the column to the immediate left. Let us understand how to add two or more numbers with regrouping with the help of an example.

Example: Help Jack in adding 3475 and 2865

Solution: Follow the given steps and try to relate them with the image given below the steps.

Step 1: Start with ones place digits.
= 5 + 5 = 10.
Here the sum is 10. The tens digit of a sum (i.e., 1) will be carried to the tens place. 
Step 2: Add tens place digits along with the carryover 1.
= 1(carry) + 7 + 6 = 14.
Here the sum is 14. The tens digit of a sum (i.e., 1) will be carried to the hundreds place.
Step 3: Now add the digit of hundreds place along with the carryover digit 1.
= 1(carry) + 4 + 8 = 13.
Here the sum is 13. The tens digit of a sum (i.e., 1) will be carried to the thousands place.
Step 4: Now add digits of thousands place along with the carryover digit 1.
= 1(carry) + 3 + 2 = 6
Step 5: 3475 + 2865 = 6340

Note: There is an important property of addition which states that changing the order of numbers does not change the answer. For example, if we reverse the addends of the above illustration we will get the same sum as a result (2865 + 3475 = 6340).

Another way to add numbers is with the help of number lines. Let us understand the addition using the number line with the help of an example. If we need to solve 10 + 3 we start by marking the number 10 on the number line. When we add using a number line, we count by moving one number at a time to the right of the number. Since we are adding 10 and 3, we will move 3 steps to the right. This brings us to 13. Hence, 10 + 3 = 13.

The concept of the addition operation is used in our day-to-day activities. We should carefully observe the situation and identify the solution using the tips and tricks that follows addition. Let us understand the theory behind the real life addition word problems with the help of an interesting example.

Example: A soccer match had 4535 spectators in the first row and 2332 spectators in the second row. Using addition theory find the total number of spectators present in the match.

Solution: 

The number of spectators in the first row = 4535
The number of spectators in the second row = 2332
Here 4535 and 2332 are addends. Let us apply the place value theory we read in the above section to find the total number of spectators.

Step 1: Adding ones place digits. (5 + 2 = 7)
Step 2: Adding tens place digits. (3 + 3 = 6)
Step 3: Adding the digits of hundreds place. (5 + 3 = 8)
Step 4: Now add digits of thousands place. (4 + 2 = 6)
Step 5: 4535 + 2332 = 6867.
Therefore, the total number of spectators present in the match = 6867.

Below are a few tips and tricks that you can follow while performing addition in your everyday life.

Tips and Tricks on Addition

• Words like 'put together, 'in all', 'altogether', 'total' give a clue that you need to add the given numbers.
• Start with the larger number and add the smaller number to it. For example, adding 12 to 43 is easier than adding 43 to 12.
• Break numbers according to their place values to make addition easier. For example, 22 + 64 can be split as 20 + 2 + 60 + 4. While this looks difficult, it makes mental addition easier.

Important Notes:

• When adding different digit numbers, make sure to place the numbers one below the other in the correct column of their place value
• Adding zero to any number gives the number itself.
• When 1 is added to any number, the sum is the successor of that number.
• The sign used to denote an addition is '+'.
• The order in which you add a group of numbers doesn't matter, the answer is the same. For example, 2 + 5 + 3= 10; and 5 + 3 + 2= 10. It is called the associative property of addition.

Topics Related to Addition

Check out these interesting articles to know about addition and its related topics.

• Addition Formula
• What is regrouping in math addition?
• Addition Calculator
• Addition of Algebraic Expressions
• Associative Property of Addition
• Addition of Fractions

Where do We Use Addition?

We use addition in our everyday situations. For example, if you want to know how much money you spent on the items you bought, or you want to calculate the time you will take to finish a task, or you want to know the number of ingredients used in cooking something, you need to perform addition operation.

What are the Types of Addition?

The types of addition mean the various methods used in addition. For example, vertical addition, addition using number charts, the addition of small numbers using your fingers, addition using number line, etc.

What are Addition Strategies?

Addition strategies are the different ways in which addition can be learned. For example, using a number line, with the help of a place value chart, separating the tens and ones and then adding them separately, and many others.

What are the Real-Life Examples of Addition?

Suppose you have 5 apples, and your friend gave you 3 more,  after adding 5 + 3, we get 8. So, you have 8 apples altogether. Similarly, suppose there are 16 girls and 13 boys in a class, if we add the numbers 16 + 13, we get total number of students in the class, which is 29. These are two of the real-life addition examples. There are an infinite number of examples that you can think of related to adiditon

What are the Three Parts of Addition?

The 3 parts of addition are the addends, the two signs (plus sign and equal to sign), and the sum.

• The Addend: In addition, the numbers or terms being added together are known as addends.
• The 'equal to' sign and plus sign: While performing addition, we use two symbols one is a plus sign (+) other is equal to sign (=).
• The Sum: The final result obtained after performing addition is known as the sum.