## What Is Addition?

Addition is a way of combining things and counting them together as one large group.

**Addition **in math is a process of combining two or more numbers. **Addends **are the numbers added**, **and the result or the final answer we get after the process is called the **sum**. It is one of the essential mathematical functions we use in our everyday activities. There are many situations in which we use to add numbers. One of the most common everyday uses for adding numbers is when we work with time or money—for example, adding up bills and receipts.

The addition symbol used to indicate adding numbers is “+” (also called the plus symbol). For example, we read $5 + 3$ as “5 plus 3”.

An addition sentence is a mathematical expression that shows two or more values added together and their sum. The two or more values that are added are called addends. The parts of an addition sentence are two or more addends, plus symbol(s), equal sign, and the sum.

## Solve Addition Problem

To add small numbers can be done using your fingers.

Example:

### Using The Number Line

We can use the number line to add. Let us look at the following addition example.

To add 5 and 7, we can count forward 7 steps from 5, as shown below.

### Using The Number Grid

Number chart is another way to add numbers.

Example: Add 57 and 16 using a hundred grid.

Step 1: Locate the bigger number $(57)$.Step 2: If the number to be added $(16)$ is more than 10, break it into tens and ones. $16 = 10 + 6$.Step 3: Jump as many 10s as in the second number.$57 + 10 = 67$ Step 4: Move forward as many ones as in the second number.$67 + 6 = 73$. The number reached is the answer. So, $57 + 16 = 73$ |

## Vertical Addition

While solving the problem, we can add the numbers vertically. Here, we arrange the numbers vertically using their respective place values, like ones, tens, hundreds, thousands, etc. We start adding from the right side (or digit at ones or unit place). While solving such problems, we may come across some cases with regrouping and some without regrouping. Let us understand with the help of examples.

### Addition without Regrouping

Example: Add 41 and 26.

Step 1: Write the numbers one below the other as per the places of the digits. | |

Step 2: Start adding from the digits in ones place $(1 + 6 = 7)$. Write the sum under the ones digit. | |

Step 3: Add the tens digits $(4 + 2 = 6)$. |

### Addition with Regrouping

Example: Add 57 and 16

Step 1: Write the numbers below the other as per the places of the digits. | |

Step 2: Start adding from the digits in ones place $(7 + 6 = 13)$. If the sum of the ones digit is greater than 9, write the ones digit of the sum under the ones and carry forward its tens digit to the tens column. | |

Step 3: Add the tens digits. If there was a carry-forward digit, add it along. $5 + 1 + 1 $(carry$-$over) $= 7$ |

## Fun Fact

- Adding zero to a number gives the number itself.
- Adding 1 to a number gives the successor of that number.
- Changing the order of the addends does not change the sum. For example, $5 + 3 + 2 = 5 + 2 + 3 = 10$

## Solved Examples

**Question 1: What is the sum of the first 10 odd numbers?**

**Answer: **

The first ten odd numbers are $1, 3, 5, 7, 9, 11, 13, 15, 17, 19$.

The sum of the first ten odd numbers

$= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19$

$= 100$

**Question 2: If a bag has 5 balls and 4 more balls are added to it, how many balls are there in the bag?**

**Answer:**

Originally, there were 5 balls in the bag. Now 4 more balls have been added.

The number of balls in this bag is now $5 + 4 = 9$.

Therefore, the bag has 9 balls.

**Question 3: The present age of Manny is 7 years. What will be his age after 10 years?**

**Answer:**

Current age of Manny is 7 years.

To find Manny’s age after 10 years, add 10 to his current age.

After 10 years, his age would be $7 + 10$ or 17 years old.

**Question 4: Samantha bought a bag for **$\$$214** and some books for **$\$$149**. How much did she spend on both?**

**Answer:**

To find the total cost, add 214 and 149.

Thus, Samantha spent $\$$363 in all.

## Conclusion

Adding numbers is a fundamental mathematical process that combines two or more numerical values. We use this operation in our daily lives; some easy examples are calculating money, calculating time, counting students in a class, etc. The symbol of this operation is a ‘+’ (plus sign). Visit SplashLearn to learn more math facts.

## Practice Problems

## Addition

### Which of the following equations represents the total number of circles in the figure below?

There are 8 green circles and 7 blue circles, So, there are $8 + 7 = 15$ circles in all.

### What is the sum of 700 and 136?

Sum of 700 and 136 is $700 + 136$ or 836.

### Find the value of 4 hundreds $+ 26$ tens?

4 hundreds $+ 26$ tens $= 400 + 260 = 660$

### Which of the following is the sum of the smallest and the greatest two-digit numbers?

Which of the following is the sum of the smallest and the greatest two-digit numbers?

## Frequently Asked Questions

**Why is addition important?**

Adding numbers is a fundamental mathematical concept, essential for the simplest problems in our daily activities. One of the most common applications is when we work with money—for example, adding up bills and receipts.

**What is addend?**

Addend is the part of the statement where we add two numbers; an addend is defined as the value that is to be added to find a sum.

**What is a sum?**

A sum is a result when we add two or more numbers.

**What is meant by addition with and without regrouping?**

Addition without regrouping is when the sum of the digits in each place value column is less than or equal to 9. Addition with regrouping is when the sum of the digits in at least one of the place value columns is greater than 9.