## What is Add?

The first mathematical operation that students are introduced to in elementary mathematics is addition. To add means to bring together or combine two objects. Students then build over this understanding to learn how to add more than two numbers. In higher grades, addition is the basic element to understand more complex operations like multiplication and division. The addition has an infinite number of applications in our day-to-day life. We use addition while cooking food while calculating bills at supermarkets while calculating distances, and much more.

## Basics of Addition

Let’s look at this with the help of an example.

Let’s say we have two yellow stars,

And three purple stars,

In order to find the total number of stars we have, we count all the stars together. That is, together we have 5 stars.

Mathematically, we write this as

**2 + 3 = 5**

Here, “+” denotes addition. The total that we get on adding two or more numbers is also called the **sum**. Therefore in this example, 5 is the sum of 2 and 3.

Considering one more example, if we add the numbers 6 and 4, we get the sum 10; and we write this as**6 + 4 = 10**

**Addition Methodologies**

In their quest to master addition, students start by learning how to add one-digit numbers using their fingers or the number line and then move on to adding bigger numbers using the place value or column method. Let’s take a look at how these methods work:

**Add Using fingers:**

Let’s say we have to add the numbers 5 and 3.

Step 1: Show 5 fingers on one hand and 3 on the other.

Step 2: Start counting the fingers together like this to find the total.

And we have our total

5 + 3 = 8.

**Add by Counting forward:**

Let’s use another example to see how this strategy works, Let’s say we have to add the numbers 5 and 4.

Step 1: Keep the bigger number in mind. In this case, 5.

Step 2: Count forward as many times as the second number i.e., 4 times.

Like this: 6 – 7 – 8 – 9. We get 9.

So, 4 added to 5 is 9 or the sum of 5 and 4 is 9.

**Using number line:**

Let’s see how we can add the numbers 11 and 3 using a number line.

Step 1: Mark the bigger number on the number line.

Step 2: Jump forward as many times as the second number.

And so we have

11 + 3 = 14.

**Using Column Method:**

This method is most commonly used to add 2-digit or greater numbers using their place value. This method has two aspects to itself, one where we need regrouping and one where we add without having to regroup. Let’s look at the latter one first.

**Without Regrouping:**

Let’s add the numbers 34 and 52.

Step 1: Write the numbers one below the other as per their place value like this:

Step 2: Start from the right and add the digits in the ones column first.

Step 3: Move on to the next column and add the digits in the tens column.

And so we have our answer:

34 + 52 = 86

**With Regrouping:**

This is the aspect that comes into play when the sum of the digits in any column exceeds 10.

Let’s try adding the numbers 29 and 46 using this method.

Step 1: Write the numbers one below the other as per their place value like this:

Step 2: As done previously, start from the right and add the digits in the ones column first. Here the sum of 9 and 6 will be 15. We think of 15 as 10 + 5; keep the 5 in the ones column, and give the 10 as 1 ten to the tens column as a carryover.

Step 3: Move on to the tens column and add the digits in this column along with the carryover digit to find the answer.

And so we have our sum: 29 + 46 = 75

## Properties of Addition

**Commutative Property of Addition**

We can swap the numbers in an addition equation and the sum will remain the same.

19 + 14 = 33

14 + 19 = 33

**Identity Property of Addition**

When zero is added to a number or a number is added to zero, the sum is the number itself.

15 + 0 = 15

0 + 15 = 15

**Associative Property of Addition**

While adding three or more numbers, the sum of the numbers does not depend on the order in which the numbers are added. For example, we could add the numbers 5, 8 and 6 in different ways like this:

(5 + 8) + 6 = 13 + 6 = 19

5 + (8 + 6) = 5 + 14 = 19

8 + (5 + 6) = 8 + 11 = 19

## Solved Examples in Addition:

**Example 1: Add 56 and 11 using column method.**

**Solution**

**Example 2: Add 4 and 6 on number line.**

**Solution:**

4 + 6 = 10

**Example 3: Find the missing number in 7 + ___ = 9**

**Solution: **7 + 2 = 9.

**Example 4: Add and write the total number of fingers.**

**Solution: **2 + 5 = 7.

## Practice Problems

## Add## 1Which property is shown by the addition sentence 11 + 0 = 11Associative property Identity property Additive property Destributive property CorrectIncorrect Correct answer is: Identity property The sum of any number and zero is the number itself. ## 2Add: 5 + 7 + 9.20 12 14 21 CorrectIncorrect Correct answer is: 21 5 + 7 + 9 = (5 + 7) + 9 = 12 + 9 =21 ## 3A bouquet has 36 red roses and 18 white roses. How many roses does the bouquet have in all?54 72 36 108 CorrectIncorrect Correct answer is: 54 Number of red roses = 36 Number of white roses = 18 Total number of roses = 36 + 18 = 54 ## 4Bus A has 45 passengers, Bus B has 56 passengers and Bus C has 32 passengers. How many passengers are on Bus A and Bus C?101 88 77 133 CorrectIncorrect Correct answer is: 77 Number of passengers in Bus A = 45 Number of passengers in Bus C = 32 Number of passengers on Bus A and Bus C = 45 + 32 = 77 |

**F**requently Asked Question

**Where do we use addition in our day-to-day life?**

To find the total number of objects, bill amount, and total distance traveled.

**What is addition?**

Addition is one of the basic arithmetic operations. Addition means to combine different objects and find the total.

**What number should be added to a number to get its successor?**

1 added to a number gives the successor of the number.

**If we subtract 1 from a number what number we will we get?**

When 1 is subtracted from a number we get a predecessor of the number.

**What is skip counting?**

The method of counting forward by numbers other than 1 is defined as skip counting.

For example, starting from 10 and skip counting would mean adding 5 to each new number we get like this: 10, 15, 20, 25, 30….