Difference in Math: Definition & Subtraction Formula

Difference

The result of subtracting two numbers or expressions. For example, the difference between 7 and 12 is 12 – 7, which equals 5.

Key Formula

\text{Difference} = a - b

Where:

$a$ = The number being subtracted from (minuend)
$b$ = The number being subtracted (subtrahend)

Worked Example

Problem: Find the difference of 45 and 18.

Step 1: Set up the subtraction with the larger number first.

45 - 18

Step 2: Subtract to find the result.

45 - 18 = 27

Answer: The difference is 27.

Why It Matters

The word "difference" appears constantly in math problems, so recognizing it as a signal for subtraction helps you translate word problems into equations. It also shows up in formulas across algebra, statistics, and calculus — for instance, the "common difference" in arithmetic sequences or the "difference quotient" used to define derivatives.

Common Mistakes

Mistake: Subtracting in the wrong order, leading to a negative answer when a positive difference is expected.

Correction: When a problem asks for "the difference between" two numbers without specifying order, subtract the smaller from the larger to give a positive result. If order is specified (e.g., "the difference of a and b"), compute a − b, which may be negative.

Related Terms

Expression — Differences can appear inside expressions
Subtraction — The operation used to find a difference
Sum — The result of addition, the inverse operation
Minuend — The number being subtracted from
Subtrahend — The number being subtracted