Addition

Addition

If we talk about addition, it is defined as the process of adding two or multiple items together. The discussion on introduction to addition starts with math addition, which is the general method of calculating the sum of minimum two and more than two numbers.

Math Addition

The concept of Math Addition is defined as the process of calculating the total of two or more numbers. This calculation can be a simpler one that is not much time taking when we have small numbers like one digit numbers. For example, adding 1 and 2 gives us 3. So this can be called as simple addition whereas adding 1224 and 1339 could be time taking since it is not simple addition.

When we discuss about addition, the result that obtained at the end is termed as 'sum'. For example, if we add 5 and $10,(5+10)$ we get the sum as 15 . So the result comes out to be 15. Another example could be adding 2 digit numbers like 10 and 20. When we perform math addition on them, we get the output as 10+20=30.

Addition Symbol

Addition symbol is one of the widely used symbols in mathematics. When we carefully observe, $(5+10=15)$ the symbol $(+)$ helps to connect the two numbers and hence completes the given expression. The addition symbol can be observed as consisting of one horizontal line and one vertical line. So, we can say that the addition sign is represented by a '+' in the expression of math addition. It is also known as addition symbol and is of prime importance.

Parts of Addition

There are numerous terms that we may come across when we perform addition. Various parts of addition are discused as below:

• Addend: The numbers which are visible in the expresssion are known as addends. That are added to give the final result or sum.
• Addition Symbol: There is the addition symbol (+) which is placed in between the addends and is representative of performing addition.
• Sum: The final result or output obtained after addition of the addends is known as the sum.

Formula of Addition

Formula of addition is the statement that shows an addition fact which shows that the numbers are added with the help of addition symbol to give a sum at the end, and is expressed as, addend + addend = sum. This is the most general representation of the addition expression.

Here, as we can see that 5 and 3 are the addends and 8 is the sum. Together they constitute the parts of addition.

Addition Table

How to do addition?

While solving addition sums, one-digit numbers can be added in a simple way, but for larger numbers, we split or divide the numbers into columns using their respective place values, like ones, tens, hundreds, thousands, and the process goes on furthur. We should always remember that we start 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. The process can be extended according to the numbers given for addition.

Addition Without Regrouping

The addition in which the sum of the digits is less than or equal to 9 in each column is known as addition without regrouping.

Example: Add 11000 and 21153

Solution:

We follow the steps as:
Step 1: Initially we start with the digits in ones column. $(0+3=3)$
Step 2: Next we move to the digits in tens column. $(0+5=5)$
Step 3: In the process next, now we add the digits in hundreds column. $(0+1=1)$
Step 4: After this, we add the digits in thousands column. $(1+1=2)$
Step 5: Finally, we add the digits in ten thousands column. $(1+2=3)$
Step 6: $11000+21153=32153$

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. Or the other way round, 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.

Example: Add 3475 and 2888.

Solution:

We follow the steps as:
Step 1: We start with the digits in ones place. $(5+8=13)$. Here the sum is 13. The tens digit of the sum, that is, 1 , will be carried to the preceding column.
Step 2: Next, we add the digits in the tens column along with the carryover 1. This means, 1 (carry-over) $+7+8=16$. Here the sum is 16 . The tens digit of the sum, that is, 1 , will be carried to the hundreds column.
Step 3: Now, we 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: Next, we 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 $3475+2888=6363$

Note: There exists 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 example we will get the same sum as a result ($888 + 3475=6363$ ). This is known as the commutative property.

Number Line Addition

We understand the addition on a number line with the help of an example and the number line given below with the help of illustration and addition images.

For example: Add 20 + 3 using a number line
Solution: We initially 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 20 and 3 , we will move 3 steps to the right. This finally brings us to 23 . Hence, $20+3=$ 23 as the sum is the result at the end.

Addition Properties

Some of the most common properties of addition are 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, $6+7=7+6=13$.
- 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, $2+(7+3)=(2+7)+3=12$
- 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, $0+$ $9=9$.

Addition Examples

The concept of the addition operation is used in our day-to-day activities. We should develop the habbit of carefully seeing the situation and then apply the necessary addition skills whereever applicable.

Example 1: 9 birds set off to see some flowers. After that , 6 more came. Find the total number of birds.

Solution:
Number of birds who came initially $=9$
Number of birds who came afterwards $=6$
Hence, according to formula of addition, total number of birds: $9+6=$ 15

Example 2: Using formula of addition, solve the addition word problem.
Henry collected 80 balls and Evan collected 55 balls. What is the total number of balls they collected in all?

Solution:
Balls collected by Herry $=80$
Balls collected by Evan $=55$
Total balls collected $=80+55=135$

Example 3: During a treasure hunt, students found 2460 coins in house, 50 coins in the park, and 10 coins in haunted palace. How many total coins did they collect ? Use concept of addition to solve problem.

Solution:
Number of coins found in the house $=2460$
Number of coins found in the park $=50$
Number of coins found in the haunted palace = 10
Hence, according to formula of addition, total coins found in that day's hunt is 2520.

Example 4: In a musical show, 1200 girls and 1380 boys participated. What is the total number of participants?Use concept of addition to solve.

Solution:
Number of girl participants $=1200$
Number of boys who participated in the show $=1380$
Total number of participants $=1200+1380$
Hence, final number of participants calculated by formula of addition is 2580.

Example 5: In a school, there are 120 students in section A, 160 students in section B and 140 students in section C of class XII. Find the total number of students of class XII using formula of addition.

Solution:
Number of students in section $\mathrm{A}=120$
Number of students in section $B=160$
Number of students in section $\mathrm{C}=140$
Total number of students $=120+160+140$
Therefore, total number of students found out using concept of aaddition is 420 .

Example 6: A football match had 4000 audience in the first row and 2500 audience in the second row. Using the concept of addition find the total number of audience present in the match.

Solution:
The number of audience in the first row $=4000$; the number of audience in the second row $=2500$.
Here 4000 and 2500 are the addends. We use the following steps:
- Step 1: First we add the digits in the ones place. $(0+0=0)$
- Step 2: Next we add the digits in the tens place. $(0+0=0)$
- Step 3: Now, we add the digits in the hundreds place. $(5+0=5)$
- Step 4: Lastly, we now add digits in the thousands place. $(4+2=6)$
- Step 5: $4000+2500=6500$

Therefore, the total number of audience present in the match $=6500$

List of Topics Related to Addition