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# Addition|Definition & Meaning

## Definition

The act of **adding** two or more numbers together is defined as **addition** or an **arithmetic operation** that is applied to acquire the **total or sum** of desired **numbers/items**. When the addition operation is applied to two **whole numbers**, their **combined value** is the **total amount** or **sum**.

In simple words, addition is the process of **adding something** to **get** the total **sum**. Out of four **fundamental arithmetic operations** (addition, subtraction, multiplication, division) in mathematics, the **addition operator** is the most basic one.

**Graphical Demonstration**

Figure 1 – Adding Sector of a Circle

Consider the above figure which represents the **addition of sectors** the pie is divided into two portions, the first portion represents** 50%** and the second portion represents **50%** as well. Upon **adding** both we get a total of **100%**.

Figure 2 – Addition of Circles

Consider the above figure the first addend is **3 circles**, and the second addend is **2 circles **when the addition operation is applied, it **results** in **5 circles** as shown

Figure 3 – Summing Triangles

Consider the above figure. The first addend is **3 triangles**, and the second addend is **3 triangles,** when the addition operation is applied it results in a sum of **6 triangles**.

**Structure of Addition**

The addition structure can be broken down as follows

**Addend**

** **The desired **terms or numbers** that are **required to be added** are known as an addend.

**Sum**

The result of addition or the **result** after **applying the addition** operator between the addend is known as the **sum**.

**Symbol**

**Two lines** are drawn **horizontally and vertically **to **represent **the addition symbol. Additionally, it has been referred to as the **plus sign (+)**.

**Mathematical Representation**

**Addend + Addend = Sum**

An Additional symbol **(+) **is placed between the addend and equal to symbol **(=) **is placed before the sum.

**Properties of Addition**

There are **three **main properties of addition are:

**Commutative Property**

It states that **changing the order** of addend does **not affect** the **sum** or result of addition for example: if there are two addends let’s say x and y and we apply the addition operation on it then the following **equation holds** which **shows **the **commutative property **of addition.

**X + Y = Y + X**

**Verify**

**Let X=4, Y=2**

**4+2=2+4**

**5=5**

This shows that addition **holds the commutative property**.

**Additive Identity Property**

It states that when** zero (additive identity)** is added to any other addend the result or sum which we get will be **equal to **the addend to which we have added zero in other words adding zero to the addend **gives** the **addend itself**. Consider the following equation:

0** + X = X**

**Verify**

**Let X=8**

**0 + 8 = 8**

Which shows that addition **holds additive identity property.**

**Associative Property**

It states that a sum of **at least three **or more than three addends results in the same sum **irrespective** of the fact that how these addends are **grouped** in other words we can say the grouping of addends is independent of the sum. Consider the following equation:

**X + (Y + Z) = (X+ Y) + Z**

**Verify**

**Let X=9, Y=5, Z=3**

**9 +(5+3) = (9+5) +3**

**17=17**

Which shows that addition holds the associative property.

**Brief Description**

While countering problems of addition, the addition operator can be applied easily on **single-digit numbers**, but for numbers greater than single-digit numbers, we have to break the numbers like **units, tens, hundreds,** and so on. As per the place value system, we always start adding from the right-hand side. Starting with one (units), we move to tens, then hundreds, and then so on. There **may be carry** in some cases while we are solving such problems and there **may be none.**

Let’s take different examples to understand the concept of addition.

Suppose there are **three students**, the first student has **5 apples**, the second student has **3 apples**, and the third student has **9 apples**, and we are required to apply the concept of addition to this scenario then we will take these apples simply as addends 5, 3 and 9 and apply the addition operator as **5+3+9** that will give the sum **equal to 17.**

Let’s take another example: suppose we go to a grocery store, and we buy **5 bottles of juice** and **1 bottle** of milk. **5 packets of biscuits** and we want to know the **total quantity **of items we purchased so we will add all the items as

5 (bottles of juice) + 1 (bottle of milk), + 5 (packets of biscuits) = **11 items**

Suppose you have **10 dresses** and your friend gifted you **2 dresses** then the **total dresses **you have will be equal to **12 dresses** after applying the addition operation.

**A Few Examples of Addition**

**Example 1**

Consider there are **two classrooms**, students present in the first classroom are **20, **and students present in the second classroom are **30.** Find the number of students present in both classes.

**Solution**

First, convert descriptive data into a compact form.

Students in the first classroom=20

Students in the second classroom=30

The total number of students in both classrooms=?

Total number of students in both classrooms = Students in the first classroom + Students in the second classroom

Total number of students in both classroom = **20 + 30**

**Total number of students in both classrooms = 50**

**Example 2**

Your mom went to a vegetable shop, and she bought **2kg** of onions, **3kg** of tomatoes, and **1kg of **carrots. Find the total weight of the vegetables your mom bought.

**Solution**

Weight of onions= 2kg

Weight of tomatoes=3kg

Weight of carrots =1kg

Total weight = Weight of onions + Weight of tomatoes Weight of carrots

Total weight =**2kg + 3kg + 1kg**

**Total weight=6kg**

**Example 3**

Messi read **30 pages **of a book in **50 minutes **on Monday, the next day (Tuesday) he read **25 pages** of books in **90 minutes,** and on Wednesday he read **13 pages **of a book in **30 minutes.** How many pages of books did he read in three days? and how much time did he read in three days?

**Solution**

Pages read on Monday=30

Pages read on Tuesday=25

Pages read on Wednesday=13

**Total pages read in three days= 30+25+13=68**

Time spent on reading on Monday=50

Time spent on reading on Tuesday=90

Time spent on reading on Wednesday=30

**Total time spent on reading in three days= 50 + 90 +30=170**

**Example 4**

Apply the addition operator on two numbers **150,30 **and show the results.

**Solution**

*All mathematical drawings and images were created with GeoGebra.*