Addition — Definition, Formula & Examples
Addition is the operation of combining two or more numbers to find their total. The result of addition is called the sum.
Addition is a binary arithmetic operation, denoted by the symbol , that maps two numbers (called addends) to a unique number (called their sum), satisfying the commutative property and the associative property .
Key Formula
Where:
- = The first addend (a number being added)
- = The second addend (a number being added)
- = The sum (the result of the addition)
How It Works
To add two numbers, combine their values into a single total. Start with one number and count up by the amount of the second number. When adding numbers with more than one digit, line them up by place value and add each column from right to left, carrying over to the next column when a sum reaches 10 or more.
Worked Example
Problem: Find the sum of 27 and 15.
Add the ones: Add the digits in the ones place: 7 + 5 = 12. Write down 2 and carry 1 to the tens place.
Add the tens: Add the digits in the tens place, including the carried 1: 2 + 1 + 1 = 4.
Write the sum: Combine the results to get the final answer.
Answer:
Why It Matters
Addition is the foundation for nearly every other math operation you will learn, from subtraction (which reverses it) to multiplication (which repeats it). Everyday tasks like counting money, measuring ingredients, and keeping score all rely on addition.
Common Mistakes
Mistake: Forgetting to carry when digits in a column add up to 10 or more.
Correction: Always check each column's total. If it is 10 or greater, write the ones digit and carry the tens digit to the next column to the left.