Formula, Definition, Examples | Parts Of Addition - Cuemath

Addition

Addition is the process of adding two or more items together. Addition in Maths 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 time. In this article, let us learn more about the addition definition, the addition symbol, addition sums, the parts of addition, addition with regrouping, and number line addition, along with some addition examples.

1.	What is Addition in Maths?
2.	Parts of Addition
3.	Addition Word Problems
4.	FAQs on Addition

What is Addition in Maths?

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 Definition

Addition is defined as the process of calculating the total of two or more numbers. This calculation can be a simple one or a process that involves regrouping and carrying over of numbers.

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 (+)

Parts of Addition

An addition statement can be split into the following parts.

• Addend: The numbers that are added are known as the addends.
• Addition Symbol: There is the addition symbol (+) which is placed in between the addends. If the statement is written horizontally as shown below, then we place an equal to sign (=) just before the sum is written.
• Sum: The final result obtained after adding the addends is known as the sum.

Addition Formula

The addition formula is the statement that shows an addition fact and is expressed as, addend + addend = sum. This can be understood with the help of the example shown in the figure given below. The basic addition formula or the mathematical equation of addition can be explained as follows. Let us see how to write an addition sentence in the following way.

Here, 5 and 3 are the addends and 8 is the sum. It should be noted that there can be multiple addends in an addition fact. For example, 5 + 7 + 9 + 3 = 24.

How to Solve Addition Sums?

While solving addition sums, 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. This means we start from the ones column, then move on to the tens column, then to the hundreds column, and so on. While solving such problems we may come across some cases with carry-overs and some without carry-overs. Let us understand addition with regrouping and addition without regrouping in the following sections.

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 use the following given steps and try to relate them with the following figure.

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

In addition without regrouping, we simply add the digits in each place value column and combine the respective sums together to get the answer. Now, let us understand addition with regrouping.

Addition With Regrouping

While adding numbers, if the sum of the addends is greater than 9 in any of the columns, we regroup this sum into tens and ones. Then we carry over the tens digit of the sum to the preceding column and write the ones digit of the sum in that particular 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 column.
• 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 column.
• 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.

Number Line 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.

Example: Add 10 + 3 using a number line

Solution: 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 + 7) + 3 = 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.

Addition Word Problems

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 using the following steps.

• 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 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.

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