Negative Numbers

Negative numbers are numbers less than zero, written with a minus sign, used to represent things like debt, temperatures below freezing, and levels below sea level.

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Definition

A negative number is any number that is less than zero. We write it with a minus sign (–) in front, like –5 or –12. On a number line, negative numbers sit to the LEFT of zero. The farther left you go, the smaller the number gets. Negative numbers are the opposites of positive numbers: the opposite of 5 is –5, and together they are called opposites.

Remember the rule

On the number line: RIGHT = bigger, LEFT = smaller. A negative number is ALWAYS less than zero AND less than any positive number. Two negatives: the one closer to zero is the GREATER one (–1 > –100).

Key words

Negative number: A number less than zero, written with a – sign in front, like –3 or –10.
Positive number: A number greater than zero, like 3 or 10. Usually written without any sign.
Zero: The number 0, which is neither positive nor negative. It sits in the middle of the number line.
Opposite: Two numbers the same distance from zero but on different sides, like 7 and –7.
Absolute value: How far a number is from zero, always a positive distance. The absolute value of –6 is 6, written |–6| = 6.
Number line: A straight line with numbers placed in order. Negative numbers go left of zero; positive numbers go right.
Integer: Any whole number, its opposite, or zero. Examples: –3, –2, –1, 0, 1, 2, 3.
Greater than / Less than: On the number line, the number farther RIGHT is always greater. So –2 is greater than –8.

Worked examples

Temperature: It is 4°F outside. Overnight it drops 10 degrees. What is the new temperature?

→ 4 – 10 = –6°F · Starting at 4 and moving 10 steps left on the number line lands you at –6, which is below freezing.

Bank account: You have $15 in your account and you spend $20. What is your balance?

→ 15 – 20 = –$5 (you owe the bank $5) · A negative balance means debt — you have less than nothing in the account.

Ordering: Put these numbers in order from least to greatest: 3, –7, 0, –1, 5

→ –7, –1, 0, 3, 5 · The most negative number is the smallest. Think of the number line from left to right.

Comparing: Which is greater, –3 or –9?

→ –3 is greater than –9 · –3 is closer to zero on the number line, so it is farther to the RIGHT, making it the bigger number.

Absolute value: What is |–8|?

→ |–8| = 8 · Absolute value just asks how far from zero, so the answer is always positive or zero.

Elevation: A submarine is at –250 feet (below sea level). A fish swims at –80 feet. Which is higher up?

→ –80 feet is higher than –250 feet · –80 is closer to zero (the surface), so it is the greater number and the higher position.

Common mistakes

Thinking –10 is bigger than –2 because 10 looks like a larger digit. Remember: on the number line, –10 is far to the LEFT, making it the SMALLER number.
Forgetting that zero is not negative. Zero is neutral — it belongs to neither group.
Confusing the minus sign of a negative number with a subtraction symbol. –5 is just the name of the number; it means '5 below zero,' not 'subtract 5.'
Mixing up absolute value and the number itself. |–4| = 4, not –4. Absolute value is always zero or positive.
When comparing two negative numbers, picking the one with the bigger digit as 'greater.' Always picture the number line — the one closer to zero is always greater.

FAQs

Can you add a negative and a positive number?

Yes! For example, –3 + 7 = 4. Start at –3 on the number line and move 7 steps to the right. You end up at 4.

Is –0 a thing? Is it negative?

No. Zero is just zero. Writing –0 still equals 0, and 0 is neither positive nor negative.

Why does a negative times a negative equal a positive?

That rule comes up in 7th grade, but the short answer is: multiplying by a negative flips direction, and flipping twice brings you back to positive. For now, just remember the rule: neg × neg = positive.

How do I remember which negative number is bigger?

Picture a thermometer or number line. The number higher UP on the thermometer (or farther RIGHT on the line) is always greater. –2 is higher than –9, so –2 is greater.

Do negative numbers exist in real life?

Absolutely! Temperatures below zero, money owed (debt), floors below ground in a building (basement = –1), golf scores under par, and sea-level elevations all use negative numbers every day.

What is the opposite of a negative number?

The opposite of a negative number is positive. The opposite of –5 is 5. They are the same distance from zero, just on different sides of the number line.

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