Addition

In math, addition is one of the basic arithmetic operations that we use to combine two or more numbers to find their total or sum.

For example, if you have $16 with you, and your friend gives you $12 more, you would have a total of $28. In math, we represent addition with a plus sign (+). So this example in arithmetic form would be,


$16  + $12  = $28. Here 16 and 12 are the addends and 28 is the sum of the total addends.

Addition is one of the few mathematical operations that have been around for thousands of years, as humans always needed to combine and count things. The ancient people used fingers and pebbles or marks to combine quantities. Around 3000 BCE, the Mesopotamians used a counting system to perform simple addition. Similarly, the Egyptians used hieroglyphs to represent numbers.

The Greeks used the counting system as a foundation and explored the properties of numbers and formalized mathematical concepts, including addition. By the 7th century, Indian mathematicians had developed the modern decimal system, which made addition much simpler.  

Overtime, we have used addition, and it has become a fundamental concept in mathematics. We use it and is taught worldwide. 
 

Addition has a few key properties that make solving problems related to addition easier. Here are a few of the main properties -

• Commutative property: When we perform addition, the order of the numbers does not matter. For example: 3 + 5 = 8 and 5 + 3 = 8.

• Associative property: If we group numbers together and then change the order of the grouped numbers, the sum will not change. For example: (2 + 3) + 4 = 2 + (3 + 4) = 9

• Identity Property: When we add a 0 with any number, the sum of 0 and that number is always itself.  For example, 3 + 0 = 3, 1999 + 0 = 1999

We categorize addition based on the way we apply it in different contexts. Here are some of the different types of addition:

Simple Addition

Simple addition is the adding of small numbers or things together.

Example: 4 + 5 = 9

Addition of Large Numbers

Adding large numbers with many digits is what we call addition of large numbers. 

Example: 1990 + 2167 = 4157

Addition of Fractions

We add fractions by first finding a common denominator, and then we add the numerators.

For example: 13 + 12 = 36+ 26 = 56

In the first set of fractions, the denominators are not the same. To get a common denominator, we multiply both the numerator and denominator of each fraction by the denominator of the other fraction. For example, 1 × 2 and 3 × 2, and 1 × 3 and 2 × 3. This gives us a common denominator of 6. Then, we add the two numerators.

Addition of Decimals 

We add numbers with decimal points by aligning the decimal places with each other.

Example: 12.5 + 3.75 = 16.25

Addition of Negative Numbers

We can add numbers with a negative sign as well. This can involve subtracting or a number line, wherein the negative numbers fall behind 0.

Example: -3 + (-2) = -5

Addition of Algebraic Expressions

Addition of algebraic expressions involves adding terms with variables by combining the like terms.

Example: 2x + 3x = 5x
 

Addition is the most basic concept in mathematics and is very important for students to understand how the concept is used in other fields as well. 

• It is one of the basic arithmetic operations.
   
• It is the foundation for most advanced topics like algebra, fractions, etc.
   
• It helps in the improvement of mental math, allowing for students to perform calculations quickly and accurately.
   
• Addition is also used in various other fields like science, geography, even in economics.
   

When solving problems involving addition, there are a few techniques and methods that we can use. These techniques and methods are useful for quick and accurate calculations, where the concept of addition is used .

Some methods are 

• Mental Math for Addition: Mental math involves solving additional issues in our heads without the need of using a pen and paper or any other tool. 

Example: If we want to add 35 and 25
First, we break the number into tens and ones.
Then, we add 30 + 20 = 50, and 5 + 5 = 10
Combine the results: 50 + 10 = 60

• Column addition: This method involves writing numbers one below the other. We align their place values and then add them step by step.

• Using a Number Line: A number line helps the students to visualize the addition method. The students start at one number, and then they move forward by the value of the second number.

Example: Add 6 and 3
First, we start at 6 on the number line.
Then, we move 3 steps to the right.
We will land on the number 9, so 6 + 3 = 9.

• Addition Using Blocks or Objects: In this method we will use actual objects like beads, pebbles, or blocks to represent numbers and then combine them.

Example: To add 2 and 3 
First we take 2 blocks and another set of 3 blocks.
Combine them and count the total number of blocks. We would get 5 blocks.
So 2 + 3 = 5.

• Addition by grouping: To solve problems that are related to addition we use this method to break down the bigger numbers to smaller number and then add them to make solving the problems easier .

Example: Adding 56 and 34
First, we break the numbers into tens and ones (50 + 30) + (6 + 4).
Now add the grouped numbers: (50 + 30) = 80 and (6 + 4) = 10
Combine the numbers and we 80 + 10 = 90
 

Solving addition is easy, but there are times when we wonder if there are much easier ways to solve problems involving addition. So in this section, we are going to look into a few tips and tricks to master addition.
 

• Keep practicing mental math, as it can help solve problems much quickly. By breaking numbers into smaller parts we can perform calculations accurately and efficiently.
   
• Start adding smaller numbers and once you’re confident enough you can start to slowly move on to larger numbers. 
   
• Use a number line to visualize addition of two or more numbers. This is especially useful for beginners
   

Addition is used in the real world almost on a daily basis. Whether it is to count how much money you have left, or how many total days of holidays you are going to have in school. Addition is used everywhere, and here are some examples of addition being used in important situations.

• Cooking: Most of the time we use addition to see how many ingredients or the specific amounts needed in recipes.
   
• Budgeting: When we want to manage our finances, we ensure to stay within a certain budget. So to know how much money we have used, we add up all the expenses to know much money was used up.
   
• Shopping: While shopping, we add prices of items to find the total cost of the amount of items and to also ensure we are within budget.