3-Digit Addition

There are four basic arithmetic operations in math:

• Addition
• Subtraction
• Multiplication
• Division.

Addition is a mathematical operation where we add two or more numbers together to find the result. The result of adding numbers is known as the sum. The symbol used to represent addition is ‘+’. 

In our daily life, we use addition to calculate quantities and measure values. For example, to calculate the daily income, scores on exams, or to calculate the score in games.

3-digit addition is simply defined as the addition of numbers that consists of three digits. Two parts of addition are addends and the sum. The numbers that are added are the addends, and the result is the sum.

To add numbers, we first arrange the numbers based on the place values, and then add the digits having the same place values. In 3-digit addition, the numbers range from 100 to 999 and can be done with or without regrouping. Moreover, we have to follow some steps to perform this type of addition. They are: 

• Step 1: According to the place values - ones, tens, and hundreds - arrange the numbers one below the other.

• Step 2: Start adding from right to left, so we start from the one place, then the tens, then the hundreds.

• Step 3: After finishing the addition, write the result as the sum. 

The 3-digit addition without regrouping is used when the sum of the digits in each place value is less than or equal to 9. The numbers in the same place columns will be added, and then the result is written under the corresponding column. We can learn this using an example: 

Let us add 257 and 432. 

• Step 1: First, add the numbers under the ones column. 
  7 + 2 = 9
  
  Write 9 in the ones column. 

• Step 2: Add the numbers in the tens column.
  5 + 3 = 8 
  
  Put 8 in the tens column. 

• Step 3: Finally, add the numbers in the hundreds column.
  2 + 4 = 6
  
  Write 6 in the hundreds' column.

Therefore, the sum of 257 and 432 is 689.

Addition with regrouping is done when the sum of digits in any place column is greater than 9. The extra value is carried over to the next column on the left. For instance, we can learn 3-digit addition with regrouping by adding 671 and 154. 

• Step 1: To begin, add the numbers in the ones column.
  1 + 4 = 5
  
  Write 5 in the ones column. 

• Step 2: Add the numbers in the tens column. 
  7 + 5 = 12
  
  Write 2 in the tens column and carry 1 to the hundreds' column. 

• Step 3: Finally, add the numbers in the hundreds' column. This means 6 + 1 + 1 (carry over).
  6 + 1 + 1 = 8
  
  Write 8 in the hundreds' column. 

Therefore, the sum of 671 and 154 is 825.

3-digit addition is the same as 2-digit addition. Using few tips and tricks can help you effectively add 3-digit numbers. The tips and tricks are as follows:

1. Vertically align digits with digits having same place value.
    
2. Always start adding from right to left.
    
3. Break the number according to place values and add digits separately. 
   Example: 722 + 536
   
   • Hundreds: 600 + 500 = 1100
   • Tens: 20 + 30 = 50
   • Ones: 2 + 6 = 8 
   
   = 722 + 536 = 1158
    
4. Remember, carry always goes to the next digit ones on the left side.
    
5. Use a place value chart to visualize alignment of numbers.

In our daily lives, we use 3-digit addition in various situations, from counting to planning events for a large group. Here are some real-world applications of this type of addition.

• Shopping: While shopping, we need to calculate the total cost of multiple items to know the total expenditure. If the prices are larger than 100 and less than 999, we can use the 3-digit addition.
  
  For example, if we buy 3 pieces of furniture for $321, $542, and $873, then the total price will be:
  $321 + $542 + $873 = $1736

• Travelling: When we go on a tour or travel long distances, we can use 3-digit addition to calculate the distance we cover.
  
  For example, if we drive 130 km to Georgia, then 432 to Washington, the total distance we cover is: 130 + 432 = 562 km

• Planning events: If we plan a function, events or conferences, we must calculate the number of guests who will attend the event to provide essential items.
  
  For instance, if we are planning an event and need to invite 200 relatives, 100 friends, and 200 others, then the total number of guests will be:
  200 + 100 + 200 = 500 guests.

• Banking and Finance: When we invest in banks, we must calculate our savings to know the balance.
  
  For instance, if we invest $100 in January and $650 in April, then the total balance is:
  100 + 650 = $750 

• Counting population: 3-digit additions are used to count the total number of individuals for making records.
  
  For example, if a hospital has 102 patients in ICU and 210 patients in general ward, then the total number of patients are 102 + 210 = 312