Equality — Definition, Formula & Examples

Equality is a relationship between two values or expressions that have the same amount. You show equality by using the equals sign (=), like in 3 + 4 = 7.

An equality is a mathematical statement asserting that two expressions represent the same quantity, written in the form $a = b$ , where $a$ and $b$ denote the same value. Equality is reflexive ( $a = a$ ), symmetric (if $a = b$ then $b = a$ ), and transitive (if $a = b$ and $b = c$ then $a = c$ ).

Key Formula

a = b

Where:

$a$ = The expression on the left side of the equals sign
$b$ = The expression on the right side, which has the same value as a

How It Works

The equals sign acts like a balance point. Whatever is on the left side must have the same value as whatever is on the right side. If you change one side, you must make the same change to the other side to keep the equality true. This idea is the foundation for solving equations: you perform the same operation on both sides until you find the unknown value.

Worked Example

Problem: Is the statement 5 + 3 = 2 + 6 true or false?

Step 1: Evaluate the left side.

5 + 3 = 8

Step 2: Evaluate the right side.

2 + 6 = 8

Step 3: Compare the two results. Both sides equal 8, so the equality holds.

8 = 8 \quad \checkmark

Answer: True. Both sides equal 8, so 5 + 3 = 2 + 6 is a valid equality.

Why It Matters

Every equation you solve in algebra relies on keeping both sides equal. Understanding equality also matters in computer science, where checking whether two values are equal is one of the most common operations in programming.

Common Mistakes

Mistake: Reading the equals sign as 'the answer is' instead of 'is the same as.'

Correction: The equals sign means both sides have the same value. Writing 3 + 4 = 7 + 1 = 8 is incorrect because 3 + 4 does not equal 7 + 1. Keep each equality statement true on its own.