Mathwords logoReference LibraryMathwords

Negative Number

Negative Number

A real number less than zero. Zero itself is neither negative nor positive.

 

 

See also

Nonnegative number

Key Formula

x<0x < 0
Where:
  • xx = A real number; if this inequality holds, then x is negative

Worked Example

Problem: A hiker starts at an elevation of 120 meters above sea level and descends 185 meters into a valley. What is the hiker's final elevation?
Step 1: Write the starting elevation and the change.
Start=120 m,Descent=185 m\text{Start} = 120 \text{ m}, \quad \text{Descent} = 185 \text{ m}
Step 2: Subtract the descent from the starting elevation.
120−185=−65120 - 185 = -65
Step 3: Interpret the result. A negative elevation means below sea level.
−65 m-65 \text{ m}
Answer: The hiker's final elevation is −65-65 meters, meaning 65 meters below sea level.

Another Example

Problem: Place the numbers 33, −7-7, 00, −2-2, and 55 in order from least to greatest.
Step 1: Identify the negative numbers. Here they are −7-7 and −2-2. Among negatives, the one farther from zero is smaller.
−7<−2-7 < -2
Step 2: Zero comes next, since it is greater than every negative number but less than every positive number.
−2<0-2 < 0
Step 3: Order the positive numbers normally.
0<3<50 < 3 < 5
Step 4: Combine the results.
−7,  −2,  0,  3,  5-7,\; -2,\; 0,\; 3,\; 5
Answer: From least to greatest: −7,−2,0,3,5-7, -2, 0, 3, 5.

Frequently Asked Questions

Is zero a negative number?
No. Zero is neither negative nor positive. It sits exactly at the boundary between positive and negative numbers on the number line. A number must be strictly less than zero to be called negative.
What happens when you multiply two negative numbers?
The product of two negative numbers is always positive. For example, (−3)×(−4)=12(-3) \times (-4) = 12. Intuitively, the two "negations" cancel each other out. This rule follows from the properties of arithmetic and ensures consistency in algebra.

Negative Number vs. Positive Number

A negative number is any real number less than zero (e.g., −5-5), while a positive number is any real number greater than zero (e.g., 55). On a number line, negatives lie to the left of zero and positives to the right. Zero belongs to neither category. Every negative number has a positive opposite (its absolute value), and vice versa.

Why It Matters

Negative numbers let you represent quantities that go below a reference point — temperatures below freezing, debts in a bank account, or elevations below sea level. Without them, subtraction like 3−83 - 8 would have no answer, and entire branches of algebra and science would break down. They also form half of the real number line, making coordinate geometry and graphing possible.

Common Mistakes

Mistake: Thinking that −7-7 is greater than −2-2 because 7 is larger than 2.
Correction: For negative numbers, the one closer to zero is greater. On the number line, −2-2 is to the right of −7-7, so −2>−7-2 > -7.
Mistake: Confusing the negative sign with subtraction and writing expressions like 5+−35 + -3 incorrectly.
Correction: Use parentheses to keep the meaning clear: 5+(−3)=25 + (-3) = 2. The negative sign here is part of the number −3-3, not a subtraction operator by itself.

Related Terms

  • Real Numbers — The set that contains all negative numbers
  • Positive Number — Numbers greater than zero; opposites of negatives
  • Zero — The boundary between negative and positive
  • Nonnegative — Zero or positive; excludes negative numbers
  • Absolute Value — Distance from zero; strips the negative sign
  • Integers — Includes all negative whole numbers
  • Number Line — Visual tool showing position of negatives
  • Opposite — The positive counterpart of a negative number