Are Negative Numbers Integers? Mathematical Relationship

Yes, Negative Numbers Can Be Integers

The short answer: negative numbers are integers when they are whole numbers without fractions or decimals. This includes -1, -5, -100, and -999. But not every negative number qualifies. -3.5 and -½ don't count. This distinction trips up more people than you'd think. Let's clear it up.

What Exactly Are Integers?

Integers are the set of whole numbers that include:

All positive numbers: 1, 2, 3, 4...
All negative numbers: -1, -2, -3, -4...
Zero: 0

The key characteristic? Integers have no fractional or decimal parts. They're complete numbers sitting on the number line with nothing after the decimal point. The symbol for the set of all integers is ℤ.

What Are Negative Numbers?

Negative numbers are values less than zero. They appear to the left of zero on the number line. Every negative number that is a whole number is an integer. Every negative number with a decimal or fraction is not an integer. That's the entire distinction right there.

Breaking Down the Integer Family

Here's how the different types of negative numbers stack up:

Type	Examples	Is It an Integer?
Negative whole numbers	-1, -42, -1000	Yes
Negative fractions	-½, -¾, -3/7	No
Negative decimals (terminating)	-0.5, -2.75	No
Negative decimals (repeating)	-0.333..., -1.666...	No
Zero	0	Yes

Why Fractions and Decimals Don't Count

Integers must be whole numbers. A fraction like -¾ represents three-quarters of a unit. You can't place it exactly on a whole number position on the number line without splitting units into pieces. That's the rule. No exceptions.

Common Misconceptions

"Negative numbers are all the same"

Wrong. -5 is an integer. -5.3 is not. The decimal part changes everything.

"Zero is neither positive nor negative, so it's not an integer"

Zero is definitely an integer. It's the dividing line between positive and negative integers, but it belongs to the set.

"Negative integers are less useful than positive ones"

Bank accounts, temperatures, elevations below sea level, and football scores all use negative integers. They're essential.

How to Determine If a Negative Number Is an Integer

Follow these steps:

Check for a decimal point. If there's a decimal, it's not an integer.
Check for a fraction bar. If it's written as a fraction, it's not an integer.
Check if it's a whole number. If you can write it without any fractional component, it's an integer.

That's it. Three steps. You're done.

Quick Reference

Integer: -7 ✓
Not an integer: -7.5 ✗
Integer: -1000 ✓
Not an integer: -1000.001 ✗
Integer: -0 (same as 0) ✓

The Bottom Line

Negative numbers fall into two camps: those that are integers and those that aren't. The integer camp holds all negative whole numbers. The non-integer camp holds everything with decimals or fractions attached. When someone asks if negative numbers are integers, the honest answer is: some are, some aren't. It depends entirely on whether the number is a whole number or has a fractional component. The distinction is simple. Don't overcomplicate it.