A negative number is a number less than zero, written with a minus sign, such as −3, −0.5 or −23. On a number line, negative numbers sit to the left of 0. They describe amounts below a starting point: temperatures below zero, depths below sea level, or money owed. Zero itself is neither negative nor positive.
In Spanish
número negativo
Also called
negative integer, number less than zero, minus number
Negative numbers mirror the positive numbers on the left of 0. The farther left a number is, the smaller it is, so −5 < −2.
Formal definition and notation
A real numberx is negative when x < 0. Every positive numbera has an opposite−a, the negative number at the same distance from 0 on the other side of the number line, so a + (−a) = 0. The negative numbers include negative integer values like −7, negative fractions and decimals, and negative irrational numbers like −√2.
Symbol
Read it as
Meaning
−5
negative five
the number 5 units to the left of 0
−(−5)
the opposite of negative five
equals 5; the opposite of an opposite is the number itself
Farther left is smaller.−8 < −3, even though 8 is bigger than 3: −8 is colder, deeper or more in debt.
Every negative number is less than 0 and less than every positive number.
0 is neither positive nor negative. It separates the two sides of the number line.
Adding a negative moves left: 4 + (−6) = −2. Subtracting a negative moves right: 4 − (−6) = 10.
Multiplying or dividing two negatives gives a positive: (−3)(−4) = 12. One negative factor gives a negative: (−3)(4) = −12.
Read −5 as “negative five”. The word “minus” is for the operation of subtracting.
Try it: compare negative numbers
Interactive
Drag the two points, or select one and use the arrow keys. The readout says which number is less and how far each is from 0. Put both points left of 0: is the one closer to 0 greater?
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Negative Number examples, step by step
Example 1: Order from least to greatest
Warm-up
Order from least to greatest: 2, −7, 0, −3.
Negative numbers come first because they are left of 0.
Between −7 and −3, −7 is farther left, so it is smaller.
Then 0, then the positive number 2.
Answer:−7, −3, 0, 2
Example 2: A diver below sea level
Core
A diver is 12 meters below sea level and swims up 5 meters. Write her new position as a number.
Sea level is 0, and below sea level is negative: the diver starts at −12.
Swimming up adds: −12 + 5.
Start at −12 and move 5 units right on the number line: −12 + 5 = −7.
Answer: Her new position is −7 meters, which means 7 meters below sea level.
Example 3: How much warmer?
Test-style
At 6 a.m. the temperature was −8 °F. By noon it was −3 °F. How many degrees did it rise?
A change is new value minus old value: −3 − (−8).
Subtracting a negative is adding its opposite: −3 + 8.
−3 + 8 = 5. On a thermometer, −8 to −3 is 5 marks up.
Answer: The temperature rose 5 degrees.
Common mistakes
✗ Mistake−9 > −4 because 9 is bigger than 4.
✓ Instead−9 < −4: −9 is farther left on the number line.
For negative numbers, a bigger digit means farther from 0 on the left side, which is smaller. Owing 9 dollars is worse than owing 4 dollars.
✗ Mistake−6 − 2 = −4
✓ Instead−6 − 2 = −8
Subtracting 2 moves 2 more units left, away from 0. Starting at −6 and moving left lands on −8.
✗ Mistake0 is a negative number (or a positive number).
✓ Instead0 is neither negative nor positive.
Negative means less than 0 and positive means greater than 0. Zero is not less than or greater than itself.
Not to be confused with
Negative Numbervs.Subtraction sign
The same dash means two things. In 7 − 3 it is the operation subtract; in −3 it is part of the number, negative three. In 7 − (−3) you see both: 7 minus negative three.
Integers are whole numbers and their opposites. −4 is a negative integer, but −4.5 is a negative number that is not an integer.
Quick check: 3 questions
Question 1 of 3
Which number is the least?
Show answer and explanation
Answer: C.−10 is farthest left on the number line, so it is the least. −1 is closest to 0, which makes it the greatest of the negatives.
Question 2 of 3
What is −4 + 9?
Show answer and explanation
Answer: B. Start at −4 and move 9 units right: you pass 0 after 4 units and go 5 more, landing on 5. −13 and 13 add the distances, and −5 has the wrong sign.
Question 3 of 3
A submarine is 150 feet below sea level. Which number describes its position?
Show answer and explanation
Answer: D. Below sea level is negative, so the position is −150 feet. |−150| equals 150, the distance, which loses the direction.
Negative Number: frequently asked questions
Is zero a negative number?
No. Zero is neither negative nor positive. Negative numbers are less than 0 and positive numbers are greater than 0, and zero is not less than or greater than itself. It is the point that separates the two sides of the number line, and it is its own opposite: −0 = 0.
Why is a negative times a negative positive?
Multiplying by −1 flips a number to the other side of 0. Multiplying by a negative flips once; multiplying by a second negative flips back. Patterns show it too: 3 × (−2) = −6, 2 × (−2) = −4, 1 × (−2) = −2, 0 × (−2) = 0. Each step adds 2, so (−1) × (−2) = 2.
What is the biggest negative number?
There is no biggest one. Among negative integers, −1 is the greatest. But −0.1, −0.01 and −0.001 are each greater still, and you can always get closer to 0 without reaching it. So the negative numbers have no greatest value and no least value.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 6.NS.C.5, CCSS 6.NS.C.6.a, CCSS 6.NS.C.7.a
Cite this entry
Effortless Math Team. “Negative Number.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/negative-number/
Flashcard
TermNegative Number−3
DefinitionA number less than zero, left of 0 on the number line. −8 < −3, because −8 is farther left.
Real NumberA real number is any number that can be placed on the number line. The real numbers are all the rational numbers (fractions, integers, terminating and repeating decimals) together with all the irrational numbers (such as √2 and π). Square roots of negative numbers, like √−4, are not real.Number System · Grade 8, Algebra 1NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2OppositeThe opposite of a number is the number the same distance from 0 on the other side of the number line. The opposite of 7 is −7, and the opposite of −7 is 7. Opposites add to 0, and 0 is its own opposite. The opposite of a negative number is positive.Number System · Grade 6, Grade 7, Grade 8SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2Number LineA number line is a straight line with numbers placed at equal distances along it, so every point stands for a number. Zero sits in the middle, positive numbers go to the right and negative numbers to the left. Numbers increase from left to right, so a number line shows order, distance and adding as moving.Number System · Grade 2, Grade 3, Grade 6IntegerAn integer is a whole number, its opposite, or zero: the counting numbers, their negatives, and zero. The integers are …, −3, −2, −1, 0, 1, 2, 3, … and go on forever in both directions. Integers have no fractional or decimal part, so 4.5 and 12 are not integers.Number System · Grade 6, Grade 7, Grade 8Irrational NumberAn irrational number cannot be written as a fraction of two integers. Its decimal form does not end and does not repeat in a pattern. Examples are √2 = 1.41421… and π = 3.14159…. The square root of any whole number that is not a perfect square is irrational.Number System · Grade 8, Algebra 1Absolute ValueThe absolute value of a number is its distance from zero on the number line, so it is never negative. It is written with two vertical bars: |−6| = 6 and |6| = 6. A positive number and 0 keep their value; a negative number loses its minus sign.Number System · Grade 6, Grade 7, Grade 8MeterA meter (m) is a metric unit of length equal to 100 centimeters. It is the base unit of length in the metric system, a little over three feet (about 3.28 feet). A doorway is about 2 meters tall, and 1,000 meters make a kilometer. To change meters to centimeters, multiply by 100.Measurement · Grade 3, Grade 4, Grade 5DegreeA degree is the standard unit for measuring an angle, written with the symbol °. One degree is 1360 of a full turn, so a full turn is 360°, a straight angle is 180° and a right angle is 90°. An angle that turns through 25 one-degree angles measures 25°.Geometry · Grade 4, Grade 5, Grade 7Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5ZeroZero (0) is the number that represents none or no quantity. It is neither positive nor negative and sits in the middle of the number line, between the negative and positive numbers. Adding zero to a number does not change it, as in 9 + 0 = 9, so zero is called the additive identity.Number System · Grade 3, Grade 4, Grade 5Additive InverseThe additive inverse of a number is the value that adds to it to give zero. The additive inverse of 9 is −9, because 9 + (−9) = 0, so it is the same thing as its opposite. To find it, change the sign: the additive inverse of −14 is 14, and 0 is its own.Number System · Grade 6, Grade 7, Grade 8Rational NumberA rational number is any number that can be written as a fraction of two integers, ab, where b is not 0. Fractions, integers, terminating decimals, and repeating decimals are rational numbers: 34, −5 = −51, 1.6 and 0.333… all qualify. Numbers such as √2 and π are irrational.Number System · Grade 7, Grade 8, Algebra 1Coordinate PlaneThe coordinate plane is a flat grid formed by a horizontal x-axis and a vertical y-axis crossing at the origin, (0, 0). Every point is located by an ordered pair, x first then y, such as (3, −2). The two axes divide the plane into four quadrants, numbered I to IV counterclockwise from the upper right.Geometry · Grade 5, Grade 6, Grade 7SubtractionSubtraction is the operation that finds how much is left when you take one amount away from another, or how far apart two numbers are. It is written with a minus sign: 9 − 4 = 5. The answer is called the difference. Subtraction undoes addition, so you can check 9 − 4 = 5 by adding 5 + 4 = 9.Operations · Grade 1, Grade 2, Grade 3Greater ThanGreater than means that one number is bigger than another, and its symbol is >. The statement 7 > 3 reads “seven is greater than three”. The open side of the symbol faces the bigger number and the point aims at the smaller one. On a number line, the greater number is always farther to the right.Symbols and Notation · Grade 1, Grade 2, Grade 3