Introduction to Negative Numbers

Learn what negative numbers are, where they appear in real life, and how to place them on a number line.

Elementary20 minLesson
Printable worksheet

Definition

A negative number is any number less than zero. We write negative numbers with a minus sign in front, like or . On a number line, negative numbers are found to the left of zero, while positive numbers are to the right.
The number zero is special - it is neither positive nor negative. It sits right in the middle of the number line, separating the positive numbers from the negative numbers.
Together, positive numbers, negative numbers, and zero make up the set of integers:

Try it now

Which number is negative?

Worked Examples

A thermometer shows degrees Celsius. What does this mean?

1

Identify the sign

The minus sign () tells us this is a negative number → Negative

2

Understand the meaning

Negative temperature means below zero → is 8 degrees below zero

Common Mistakes

Thinking is greater than because 7 is bigger than 3

Why it's wrong: With negative numbers, the number closer to zero is actually greater. Think of temperature: is warmer (greater) than .

Correct: because is closer to zero and further right on the number line.

Forgetting that zero is neither positive nor negative

Why it's wrong: Zero is the dividing point between positive and negative numbers. It has no sign.

Correct: Zero is neutral - neither positive nor negative. It separates the two types of numbers.

Confusing the minus sign with subtraction

Why it's wrong: The minus sign in front of a number (like ) means negative, not subtract. Context matters!

Correct: In , the minus means negative five. In , the minus means subtract.

Placing negative numbers to the right of zero on a number line

Why it's wrong: Negative numbers are less than zero, so they belong on the left side of the number line.

Correct: Negative numbers go LEFT of zero, positive numbers go RIGHT of zero.

Interactive Visual

Click the buttons to jump left (subtract) or right (add) on the number line.

Balance Scale

x + 3=7
x
3
7
Apply to both sides:

Solution: x = 4

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

18 problems
Problem 1 of 18
Easy

Which number is negative?

Why It Matters

Negative numbers are everywhere in daily life, even if you do not always notice them!
Temperature is one of the most common places we see negative numbers. When the weather report says it is degrees outside, that means the temperature is 5 degrees below zero. In cold places like Canada, Russia, or Scandinavia, winter temperatures often drop well below zero.
Money and banking also use negative numbers. If you spend more money than you have in your bank account, you might have a negative balance. For example, a balance of 20 euros in debt means you owe the bank 20 euros.
Elevation uses negative numbers too. Sea level is considered zero, so places below sea level have negative elevations. The Dead Sea, for instance, is about meters - that is 430 meters below sea level!
Understanding negative numbers is essential for math you will learn later, including algebra, graphing, and working with data.

Real World Applications

Weather and Temperature

Meteorologists use negative numbers every day when reporting temperatures, especially in winter months. Understanding negative temperatures helps us prepare for cold weather and stay safe.

Example:

If today's high is and tonight's low will be , the temperature will drop degrees.

1Try It Yourself

The weather forecast says the morning temperature is and it will rise by 10 degrees by afternoon.

What will the afternoon temperature be?

Step 1: Write the mathematical expression

Start at and add 10 degrees:

Bank Accounts and Debt

Banks use negative numbers to show when you owe money (debt). A negative balance means you have spent more than you had and need to deposit money to get back to zero or positive.

Example:

If your account shows euros, you owe the bank 25 euros. You need to deposit at least 25 euros to have a balance of zero.

2Try It Yourself

Your bank account balance is euros. You deposit 50 euros.

What is your new balance?

Step 1: Write the mathematical expression

Start with your debt and add the deposit:

Elevation and Geography

Geographers measure elevation relative to sea level, which is defined as zero. Mountains have positive elevations, while valleys and underwater locations have negative elevations.

Example:

Mount Everest is about meters above sea level. The Mariana Trench is about meters (below sea level).

3Try It Yourself

A submarine is at meters (200 meters below sea level). It rises 75 meters.

What is the submarine's new depth?

Step 1: Write the mathematical expression

Start at current depth and add the rise:

Key Takeaways

  • 1Negative numbers are less than zero and written with a minus sign (e.g., )
  • 2On a number line, negative numbers are to the LEFT of zero
  • 3Zero is neither positive nor negative - it separates them
  • 4The further left on the number line, the smaller the number
  • 5Comparing negatives: because is closer to zero
  • 6Every number has an opposite: the opposite of is
  • 7Integers include all positive numbers, negative numbers, and zero

Frequently Asked Questions

The minus sign can mean two different things depending on context. When it appears in front of a number by itself (like ), it means the number is negative (5 units below zero). When it appears between two numbers (like ), it means subtraction (take away). Context helps you know which meaning applies.
The minus sign can mean two different things depending on context. When it appears in front of a number by itself (like ), it means the number is negative (5 units below zero). When it appears between two numbers (like ), it means subtraction (take away). Context helps you know which meaning applies.
Think of it like temperature: is warmer than . On a number line, is to the right of , and numbers to the right are always greater. Another way to think about it: is only 3 away from zero, while is 7 away from zero. Being closer to zero makes a negative number greater.
Zero is neither positive nor negative - it is neutral. Zero is the special point on the number line that separates positive numbers (on the right) from negative numbers (on the left). This is why we sometimes say a number is non-negative (zero or positive) or non-positive (zero or negative).
Negative numbers have a long history! Ancient Chinese mathematicians used red and black rods to represent positive and negative numbers over 2,000 years ago. Indian mathematicians like Brahmagupta formally defined rules for negative numbers around 628 CE. European mathematicians were slower to accept them - some called them absurd or fictitious numbers well into the 1700s!
Integers are the set of all whole numbers, including positive numbers (1, 2, 3, ...), negative numbers (..., , , ), and zero. The word integer comes from Latin meaning whole or untouched. Fractions and decimals are not integers.

Glossary

Negative number
A number less than zero, written with a minus sign in front (e.g., , )
Positive number
A number greater than zero (e.g., , )
Integer
Any whole number, including positive numbers, negative numbers, and zero
Number line
A line showing numbers in order, with negative numbers on the left, zero in the middle, and positive numbers on the right
Opposite
Two numbers that are the same distance from zero but on different sides. The opposite of is
Zero
The number that separates positive from negative; neither positive nor negative
Absolute value
The distance a number is from zero, always positive. The absolute value of both and is

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