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Negative Integer — Definition, Formula & Examples

A negative integer is any whole number that is less than zero, such as −1-1, −2-2, −3-3, and so on. These numbers sit to the left of zero on the number line and are written with a minus sign.

The set of negative integers is {…,−3,−2,−1}\{\ldots, -3, -2, -1\}, which is the subset of integers Z\mathbb{Z} satisfying n<0n < 0. Negative integers have no fractional or decimal part and do not include zero.

Worked Example

Problem: A submarine is at sea level (elevation 0 meters). It dives 150 meters, then dives another 200 meters. Express the submarine's final depth as a negative integer.
Start: The submarine begins at elevation 0.
First dive: Going down 150 meters means subtracting 150.
0−150=−1500 - 150 = -150
Second dive: Diving another 200 meters from that depth:
−150−200=−350-150 - 200 = -350
Answer: The submarine's final depth is −350-350 meters, a negative integer representing 350 meters below sea level.

Why It Matters

Negative integers show up whenever you need to represent quantities below a reference point — temperatures below zero, floors underground, or money owed. Mastering them in middle school is essential for algebra, where solving equations like x+7=3x + 7 = 3 requires comfort with negative values.

Common Mistakes

Mistake: Thinking that −5-5 is greater than −2-2 because 5 is greater than 2.
Correction: On the number line, numbers further to the left are smaller. Since −5-5 is further left than −2-2, we have −5<−2-5 < -2. The larger the digit after the minus sign, the smaller the negative integer.