Addition

Addition is the process of adding two or more items together. In math, addition is the method of calculating the sum of two or more numbers. It is a primary arithmetic operation that is used commonly in our day-to-day life. One of the most common uses of addition is when we work with money, calculate our grocery bills, or calculate the time.

Addition is an operation used in math to add numbers. The result that is obtained after addition is known as the sum of the given numbers. 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 widely used math symbols. 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 (+) connects the two numbers and completes the given expression. The addition symbol consists of one horizontal line and one vertical line. It is also known as the addition sign or the plus sign (+).

Addition Formula

The addition formula that we use to write an addition fact is addend + addend = sum; where:

• Addends are the numbers that are added, i. e., on which the addition operation is performed.
• Sum is the final answer that we get after the addition.
• Symbols: We use two symbols while performing addition, one is a plus sign (+) and the other is the '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 the addends and 8 is the sum.

How to Solve Addition Problems?

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 come across some cases with carry-overs and some without carry-overs. Let us understand the two processes with help of examples.

Addition Without Regrouping

The addition in which the sum of the digits is less than or equal to 9 in each column is called addition without regrouping. Let us understand how to add two or more numbers without regrouping with the help of an example.

Example: Add 11234 and 21123

Solution: We will follow the given steps and try to relate them with the following figure.

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

In addition without regrouping, we simply add digits in each place value column and read the respective sums together to get the answer.

Addition With Regrouping

While adding numbers, if the sum of the addends is greater than 9 in any of the columns, we regroup it by carrying over the extra digit to the preceding column. In other words, we write only the number in 'ones place digit' in that particular column, while taking the 'tens place digit' to the column to the immediate left. Let us understand how to add two or more numbers by regrouping with the help of an example.

Example: Add 3475 and 2865.

Solution: Let us follow the given steps and try to relate them with the following figure.

• Step 1: Start with the digits in ones place. (5 + 5 = 10). Here the sum is 10. The tens digit of the sum, that is, 1, will be carried to the preceding column.
• Step 2: Add the digits in the tens column along with the carryover 1. This means, 1(carry-over) + 7 + 6 = 14. Here the sum is 14. The tens digit of the sum, that is, 1, will be carried to the hundreds place.
• Step 3: Now, add the digits in the hundreds place along with the carryover digit 1. This means, 1(carry-over) + 4 + 8 = 13. Here the sum is 13. The tens digit of the sum, that is, 1, will be carried to the thousands place.
• Step 4: Now, add the digits in the thousands place along with the carryover digit 1, that is, 1(carry-over) + 3 + 2 = 6
• Step 5: Therefore, the sum of 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). This is known as the commutative property of addition.

Another way to add numbers is with the help of number lines. Let us understand the addition on a number line with the help of an example and the number line given below. 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.

Addition Properties

While performing addition we commonly use the properties listed below:

• Commutative Property: According to this property, the sum of two or more addends remains the same irrespective of the order of the addends. For example, 8 + 7 = 7 + 8 = 15
• Associative Property: According to this property, the sum of three or more addends remains the same irrespective of the grouping of the addends. For example, (5 + 7) + 3 = (5 + 3) + 7 = 15
• Additive Identity Property: According to this property of addition, if we add 0 to any number, the resultant sum is always the actual number. For example, 0 + 7 = 7.

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 how to solve 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 the concept of addition 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; We can get the total number of spectators if we add the given number of spectators in the two rows.
Here 4535 and 2332 are the addends. Let us find the total number of spectators by adding these two numbers.

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

Here 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.
• 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 set of numbers doesn't matter, the sum remains the same. For example, 2 + 5 + 3 = 10; and 5 + 3 + 2 = 10. It is called the associative property of addition.

☛Related Links

• What is regrouping in math addition?
• Addition Calculator
• Addition of Algebraic Expressions
• Addition of Fractions
• Adding Decimals

What is Addition in Math?

Addition is the process of adding two or more numbers together to get their sum. Addition in math is a primary arithmetic operation, used for calculating the total of two or more numbers. For example, 7 + 7 = 14.

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?

There are many addition examples that we come across in our day-to-day lives. 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 the total number of students in the class, which is 29.

What are the Properties of Addition?

The basic properties of addition are given below. Each property has its individual significance based on addition.

• Commutative Property: According to this property, the sum of two or more addends remains the same even if the order of the addends changes. For example, 3 + 7 = 7 + 3 = 10
• Associative Property: According to this property, the sum of three or more addends remains the same irrespective of the grouping of the addends. For example, (8 + 7) + 2 = (8 + 7) + 2 = 17
• Additive Identity Property: According to this property of addition, if we add 0 to any number, the resultant sum is always the actual number. For example, 0 + 16 = 16.

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.

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

What is the Identity Property of Addition?

According to the identity property of addition, if 0 is added to any number, the resultant sum is always the actual number. For example, 0 + 16 = 16.

What is the Difference Between Addition and Subtraction?

Addition is a math operation in which we add the numbers together to get their sum. It is denoted by the addition symbol (+). For example, on adding 5 and 7 we get 12. This is represented as, 5 + 7 = 12. Subtraction is the arithmetic operation of calculating the difference between two numbers. It is denoted by the subtraction symbol (-). For example, if we subtract 8 from 19, we get 11. This is represented as 19 - 8 = 11.