01 / 20
+ −

Positive & Negative
Numbers

Discover how positive and negative numbers describe opposite directions and real-world quantities: temperature, elevation, money, and more.

6th Grade Math

What Are Positive & Negative Numbers?

Positive numbers are greater than zero and describe quantities like height above sea level, money earned, or temperature above freezing. Negative numbers are less than zero and describe the opposite: depth below sea level, money owed, or temperature below freezing.

The Number Line

\(-4\)
\(-3\)
\(-2\)
\(-1\)
\(0\)
\(+1\)
\(+2\)
\(+3\)
\(+4\)
 Negative Side ← Positive Side → Reference Point

The Meaning of Zero

In every real-world context, zero marks the dividing line between two opposite directions. Its meaning changes depending on the situation:

Temperature
\(0\,^\circ\)F or \(0\,^\circ\)C: the boundary between above and below freezing
Elevation
\(0\) feet: sea level, the boundary between above and below sea level
Money
\(\$0\): neither in debt nor in credit: a balanced account

The Opposite Directions Rule

0 (Sea Level)
\(+100\) ft
 Above
\(-100\) ft
 Below 100 ft 100 ft

Real-World Contexts

\(-\) Below Zero
\(-15\,^\circ\)F in winter means the temperature is 15 degrees below zero
+ Above Sea Level
Denver sits at \(+5{,}280\) ft: 5,280 feet above sea level
\(-\) Debit
\(-\$30\) means you spent or owe \(\$30\)
+ Credit
\(+\$50\) means you received or earned \(\$50\)

Positive vs Negative vs Zero

Property Positive Zero Negative
Sign \(+\) (or no sign) none \(-\)
Compared to 0 \(> 0\) Equal to 0 \(< 0\)
Number line Right of 0 At 0 Left of 0
Example \(+7\), \(+100\) \(0\) \(-3\), \(-50\)

Reading the Sign

Every number has two parts: a sign (positive or negative) and a magnitude (how far from zero). The sign tells the direction; the magnitude tells the distance.

1
Positive sign \((+)\): often left off. Writing \(5\) and \(+5\) mean the same thing.
2
Negative sign \((−)\): always written. \(-5\) means "5 in the negative direction."
3
Zero \((0)\): has no sign. It is the reference point in every context.

How to Represent a Quantity

1
Identify the context: What does zero mean? (e.g., sea level, freezing, no money)
2
Determine the direction: Is the quantity above/more or below/less than zero?
3
Assign the sign: Above/more = positive. Below/less = negative.
4
Write the number: Combine the sign with the magnitude. State what zero means.

Example: Temperature

Problem: A thermometer reads \(12\) degrees below zero Fahrenheit. Represent this as a positive or negative number and explain what \(0\) means.

\(0^\circ\text{F}\)
\(-12^\circ\text{F}\)
 12 below
\(+20^\circ\text{F}\)
\(+10^\circ\text{F}\)
\(-20^\circ\text{F}\)

Example: Elevation

Problem: Death Valley, California, lies \(282\) feet below sea level. A nearby hill is \(150\) feet above sea level. Represent both elevations and explain what \(0\) means.

Sea Level (0 ft)
\(+150\) ft
\(-282\) ft
 Death Valley Nearby Hill

Example: Bank Account

Problem: Marco deposits \(\$200\) into his bank account, then writes a check for \(\$75\). Represent each transaction as a positive or negative number and explain what \(0\) means.

\(\$0\)
\(-\$75\)
 Check
\(+\$200\)
 Deposit

Example: Electric Charge

Problem: A proton has a positive charge and an electron has a negative charge. If a proton's charge is \(+1\) and an electron's charge is \(-1\), what does \(0\) mean?

+ Proton
Charge: \(+1\)
 − Electron
Charge: \(-1\)

Understanding Opposites

Every positive number has a negative opposite that is the same distance from zero on the other side. They are mirror images on the number line.

\(0\)
\(+3\)
\(-3\)
 Same distance from 0 3 units 3 units

Common Mistakes

✕ Calling Zero Positive
Zero is neither positive nor negative. It is the reference point between the two.
✕ Forgetting the Sign
Writing \(15\) when you mean \(-15\). Without the negative sign, it looks positive.
✕ Bigger Means Greater
Thinking \(-100\) is greater than \(-1\). On the number line, \(-1\) is farther right, so it is greater.

Summary Table

Context Positive \((+)\) Negative \((\minus)\) Zero \((0)\)
Temperature Above zero Below zero Freezing point
Elevation Above sea level Below sea level Sea level
Money Credit / earned Debit / owed Balanced account
Electric Charge Proton Electron Neutral
Football Yardage Yards gained Yards lost Line of scrimmage

Question 1 of 5

A submarine dives to a depth of \(450\) feet below sea level. Which number best represents this depth?

Question 2 of 5

A checking account has a balance of \(-\$20\). What does this mean?

Question 3 of 5

In the context of temperature, what does \(0\,^\circ\text{C}\) represent?

Question 4 of 5

Which statement about the number line is true?

Question 5 of 5

A football team gains \(8\) yards on one play, then loses \(5\) yards on the next. How should these plays be represented?