Addition is defined as the arithmetic operation in which we add one number to another number and obtain a sum. In this article, we will learn methods of addition, examples and applications in detail.

Addition in Maths

Addition is defined as the operation in which we combine two or more quantities to find the combined value of the quantity. We use the symbol plus (+) for performing addition operations.

For example, adding 5 and 6 we write it as 4 + 5 and their sum is 9.

If a person knows addition, he can perform other operations such as multiplication and subtraction easily.

Let us understand addition by a real life example. When you go grocery shopping, you add up the prices of the items you select to find the total cost of your groceries.

Addition Definition

Addition is defined as the process that gives the output as the total of two or more numbers or quantities.

For example, find the total marks scored by Kabir if he scored 98 in half yearly and 96 marks in the final examination. Then the total marks scored by him in a year is (98+96) 194.

Addition Symbol

“+” is used as a Symbol of Addition. Other than that, there are different symbols used in mathematics that are used for various purposes such as multiplication, subtraction or division. 

For a series of addition we also use symbol of greek alphabet sigma i.e., “Σ”. For example, adding 2 and 6 is represented as, 2 + 6 and its result is 8.

Parts of Addition

There are various parts of addition. While performing addition the parts of addiction are,

• Addend
• Addition Symbol
• Sum

Let’s learn about the same in detail.

Addend

In addition operation, the numbers that are added are called the addends. For example in the addition of 2 and 3, (2 + 3), 2 and 3 are addends.

Addition Symbol

In addition operation, the symbol that represents the addition is the plus sign (+). For example in the addition of 2 and 3, (2 + 3) and (+) represent addition.

Sum

In addition operation, the result of the addition operation is called the sum. For example in the addition of 2 and 3, (2 + 3 = 5), 5 is the sum.

Addition Formula

Addition formula is the basic formula of mathematics that gives the sum of two or more numbers.

The addition formula is,

Addend + Addend = Sum

Let’s try to understand the addition formula better with the help of an example.

For example, find the sum of 3 and 4.

Solution:

3 + 4 = 7

Addition Table

The table that gives the sum of the first ten natural numbers is called the addition table. The table added below shows the same,

The addition table is used to find the addition of two numbers quickly.

Addition Methods

We have various methods for finding the sum of two numbers or solving addition. They are

• Using Fingers
• Using Number Lines
• By Regrouping

Let’s learn the same in detail.

Addition On Fingers

Addition operation can be easily performed by using fingers. We use our fingers for finding the sum of two numbers.

Suppose we have two to find the sum of 3 and 5 then we count, till three using our fingers of one hand and then continue to count five fingers using the second hand to find the sum of both. We count all the fingers to find the sum (3 + 5 = 8).

Addition on Number Line

A number line is a line that represents numbers (Integers) and we can easily add two or more numbers with the use of a number line.

Suppose we have to find the sum of 6 and 5. Then we must follow the steps added below to find their sum,

Step 1: Mark 6 on a number line.

Step 2: We have to add 5 to 6 so we jump five places in the right direction from 6.

Step 3: Mark the final position(here 11). Thus, we get the sum of 6 and 5 to be 11.

Read more: Representation of Rational Numbers on Number Line.

Addition By Regrouping

For numbers with only one’s digit, we can add them using a number line but the addition of two digits or three digits number using a number line is not feasible as drawing number lines gets bigger and bigger. Then we use addition by regrouping to find the sum of two or more numbers.

• In this method, we write the number in H T O (Hundreds Tens Ones) format and then add one with one, ten with ten and hundred with hundred and so on.
• One thing in this method that we have to remember is if by adding any pair we came across the sum to be greater than 10 then the one’s digit is written and the tenth part is carried forward.

Suppose we have to find the sum of 234 and add 349 by regrouping they are added as

Addition Properties

Addition is one of the fundamental mathematical operations and adding two numbers gives their combined value.

There are various properties associated with addiction, which are:

Closure Property of Addition

According to closure property of addition, “adding two real numbers the result is always a real number.”

For example, if we add 2 and √2, we will get 2 + √2, which is a real number as well.

Commutative Property of Addition

According to the Commutative Property of Addition, for any two real numbers p and q, their sum is always commutative, i.e. ,

a + b = b + c.

For example, if we add 2 and 3 or 3 and 2, in both cases we will get 5 as answer.

Associative property of Addition

According to Associative property of Addition, for three real numbers a, b, and c their sum in any order is equal, i.e.,

The sum of (a + b) + c = a + (b + c).

Identity Property of Addition

According to the Identity Property of Addition, for real numbers, we have an identity element in addition that always give the original number as a result of addition, i.e. the sum of any real number say p, and the identity element zero (0) is the number p.

a + 0 = a

Inverse Property of Addition

According to the Inverse Property of Addition, for real numbers, we have an inverse element of each element such that the addition of these two elements always gives the result to be zero. i.e.

a + (-a) = 0

Addition Real life Applications

These are some of the real-life applications of addition:

• Grocery Shopping: When you go grocery shopping, you add up the prices of the items you select to find the total cost of your groceries.
• Budgeting: In personal finance, you add up your income and subtract your expenses to determine your budget or available funds.
• Cooking: In recipes, you might need to add specific quantities of ingredients together to make a dish, such as adding 2 cups of flour and 1 cup of sugar.
• Construction: Builders add measurements to determine the total length of a wall, the amount of material needed, or the dimensions of a room.
• Sports Scores: In sports like basketball, the scores of each team are added to determine the winner of the game.
• Travel: When planning a trip, you add the distances between destinations to find the total travel distance.

Addition Word Problems

These word problems on addition will help you understand how to solve questions better.

Addition Problem 1: In a class test the marks scored, by Anatika out of 20 are 10, 8, 6, and 11 in English, Maths, Science and Computers respectively. Then find the total marks scored by Anatika.

Solution:

Marks scored by Anatika

• In English = 10
• In Maths = 8
• In Science = 6
• In Computer = 11

Total marks scored by Anatika = 10 + 8 + 6 + 11 = 35

Addition Problem 2: Rakesh earns 2000, 2230, 1789, 2341, 1890, 1678, and 2318 rupees in different days of the week chronologically. Then find its total earning.

Solution:

Rakesh earns in each day of week,

• On Monday = Rs 2000
• On Tuesday = Rs 2230
• On Wednesday = Rs 1789
• On Thursday = Rs 2341
• On Friday = Rs 1890
• On Saturday = Rs 1678
• On Sunday = Rs 2318

Total money earned by Rakesh in a week = 2000 + 2230 + 1789 + 2341 + 1890 + 1678 + 2318 = Rs 14246

Addition Practice Questions

We have provided you with some questions on addition for your practice.

Addition Example 1: Find the sum of 34 and 56.

Solution:

Addition Example 2: If Ashna writes 3 pages on Saturday and 2 pages on Sunday then total pages written by him.

Solution:

• Ashna writes pages on Saturday = 3 Pages
• Ashna writes pages on Sunday = 2 Pages

Total pages written by Ashna = 3 + 2 = 5 Pages

Addition Example 3: Find how many eggs Chris eats in three days if he eats 2 eggs on the first day, 4 eggs on the second day, and 3 eggs on the third day.

Solution:

• Chris eats eggs on first day = 2 eggs
• Chris eats eggs on second day = 3 eggs
• Chris eats eggs on third day = 4 eggs

Total eggs eaten by Chris = 2 + 3 + 4 = 9 eggs

Articles Related to Addition:

• Mathematical Concepts for Beginners
• Basic Arithmetic Operations
• Addition of Fractions

Addition in Maths- FAQs

1. What is Addition in Maths?

Addition is the fundamental operation of mathematics that is used to find the sum of two or more quantities of numbers.

2. How many basic types of operations are there in Math?

There are four types of fundamental operations in Math, which include,

• Addition
• Subtraction
• Multiplication
• Division

3. How is Addition represented?

Addition is represented using the “+” symbol. For example, the addition of numbers a and b is written as a + b.

4. What are the terms used in Addition?

In an addition operation, the numbers being added are called “addends,” and the result is called the “sum.”

5. Can you add more than two numbers at a time?

Yes, we can add more than two numbers at a time. This is explained as, suppose if we have to add 3 + 4 + 5 then we first add 3 + 4, i.e. 7 and then simultaneously add 5 to 7 to get the answer as 12.

6. How to Add Fraction?

To add fraction follow the following step

Step 1: Check weather the given fractions are like fractions or unlike fractions.

Step 2: For like fraction directly add their numerator by simply taking their denominator the same.

Step 3: For unlike fraction first convert the unlike fraction to like fraction by taking the LCM of their denominator and then add the same.

7. What is zero Property of Addition?

According to zero property of addition, the sum of any number with zero is always the number itself. i.e. a + 0 = 0

8. What is the commutative property of addition?

The commutative property of addition states that the order in which you add numbers does not affect the result. In other words, a + b = b + a for any numbers a and b.

9. What is additive inverse of a number?

Additive inverse of a number is a number that on adding with the numbers gives the sum as zero(identity element) i.e., a + (-a) = 0. Thus, additive inverse of a is (-a).

10. Can decimals and fractions be added?

Yes, decimals and fractions can be added as decimal can be converted into fractions or fractions can be converted into decimals.