Addition

Arithmetic
operation

Also known as: plus, sum, add, total

Grade K-2

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The arithmetic operation of combining two or more numbers into a single total, representing joining or accumulating quantities. Foundation for all arithmetic and algebra — every other operation builds on addition.

Definition

The arithmetic operation of combining two or more numbers into a single total, representing joining or accumulating quantities.

💡 Intuition

Think of putting groups together—3 apples plus 2 apples gives 5 apples.

🎯 Core Idea

Addition is combining quantities into one total; it is commutative and associative.

Example

3 + 2 = 5 — combining a group of 3 and a group of 2 gives a total of 5.

Formula

a + b = c

Notation

The + symbol means 'plus' or 'add'

🌟 Why It Matters

Foundation for all arithmetic and algebra — every other operation builds on addition. Used daily for totaling prices, combining measurements, and tracking scores.

💭 Hint When Stuck

Try using a number line or counters to physically combine the groups before writing the sum.

Formal View

\forall a, b \in \mathbb{R}: a + b = b + a \;(\text{commutativity}), \; (a + b) + c = a + (b + c) \;(\text{associativity}), \; a + 0 = a \;(\text{identity})

See Also

number sense

🚧 Common Stuck Point

Carrying (regrouping) in multi-digit addition: when a column sum reaches 10 or more, carry the tens digit.

⚠️ Common Mistakes

  • Forgetting to carry (regroup) when a column sum exceeds 9 in multi-digit addition
  • Counting on incorrectly from the first addend — starting the count at the number itself instead of the next number
  • Misaligning place values when adding numbers with different digit counts

Frequently Asked Questions

What is Addition in Math?

The arithmetic operation of combining two or more numbers into a single total, representing joining or accumulating quantities.

What is the Addition formula?

a + b = c

When do you use Addition?

Try using a number line or counters to physically combine the groups before writing the sum.

Prerequisites

counting

How Addition Connects to Other Ideas

To understand addition, you should first be comfortable with counting. Once you have a solid grasp of addition, you can move on to subtraction and multiplication.

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