Difference — Definition, Formula & Examples
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
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