Addition is a fundamental mathematical operation that combines two or more numbers to produce a total, known as the sum. It is symbolized by the plus sign (+) and is one of the core concepts taught in early mathematics education, essential for understanding more advanced topics.
- Combines numbers to find a total
- Represented by the plus sign (+)
- Produces a sum as the result
How Addition Works
When you add, you join values together. For example, if you have 3 apples and someone gives you 2 more, you add 3 + 2 to find out you now have 5 apples. The numbers you start with are called addends, and the result is the sum.
- Combining values to find a total quantity
- Initial numbers are called addends
- Result is called the sum
The numbers you add together are called addends.
The result of an addition problem is called the sum.
Source Material
Document: Addition | Math Is Fun
Addition Symbol
The plus sign (+) tells you to add. For example, 4 + 5 means you add 4 and 5. When you see an equals sign (=), it shows the answer comes next: 4 + 5 = 9.
- Plus sign (+) means to add
- Equals sign (=) shows the result follows
Source Material
Document: Addition - Symbol & Meaning
Vertical Addition
In vertical addition, numbers are stacked with digits in columns (ones under ones, tens under tens). You add each column separately, starting from the right. If a column adds up to more than 9, you carry over the extra to the next column.
- Numbers are stacked in columns
- Add from right to left (ones, then tens, etc.)
- Carry over extra value to next column
You carry over the extra to the next column.
Vertical addition involves stacking numbers, adding column by column from right to left, and writes the sum below.
Source Material
Document: How to Do Vertical Addition
Properties of Addition
Addition has special rules:
- Commutative Property: You can swap addends, and the sum stays the same. (3 + 5 = 5 + 3)
- Associative Property: When adding multiple numbers, you can group them differently without changing the sum. (2 + (3 + 4) = (2 + 3) + 4)
- Identity Property: Adding zero to any number keeps it the same. (7 + 0 = 7)
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- Swap numbers, same answer (commutative)
- Change grouping, same answer (associative)
- Add zero, number stays same (identity)
You can swap the numbers and still get the same sum.
Commutative, associative, and identity properties are true for addition.
Source Material
Document: Properties of Addition
Addition with Negative Numbers
When you add a negative number, you're essentially subtracting. For example, 5 + (-3) means you start at 5 and move 3 steps backward, ending at 2.
- Adding a negative moves you backward on the number line
- Example: 5 + (-3) = 2
Source Material
Document: Adding Negative Numbers
Real-Life Examples
- Shopping: If a shirt costs $20 and you buy another for $15, you add 20 + 15 to find the total spent.
- Cooking: If a recipe calls for 2 cups of flour and you add 1 cup of sugar, you add 2 + 1 to find total dry ingredients.
- Travel: If you drive 30 miles in the morning and 20 miles in the evening, you add 30 + 20 to find total miles driven.
- Used in buying, measuring, and calculating totals
- Helps combine quantities from different activities
Source Material
Document: Addition in Everyday Life
Addition is a simple yet powerful tool for combining numbers and understanding the world around us. Its rules and properties make math easier and more logical as you advance.
- Addition means joining numbers to find a total.
- Plus (+) is the symbol for adding; equals (=) shows the answer.
- Properties like commutative and associative help simplify addition.
The result is called the sum.
Addition is used in shopping totals, cooking measurements, and tracking travel distances.
The plus sign means you should add the numbers to find the sum.