Positive and negative numbers

Numbers below zero

Numbers greater than zero are positive numbers. Numbers less than zero are negative numbers, written with a minus sign: −3, −10, −0.5. Zero is neither positive nor negative.

You’ve seen negatives in:

• Temperatures: −15 °C on a winter morning.
• Bank accounts: a balance of −$20 means you owe $20.
• Elevation: the Dead Sea’s shore is over 400 m below sea level.
• Sports: a golf score of −2 means 2 under par.
• Elevators: floor −1 might be the parking level.

The number line

−5 — −4 — −3 — −2 — −1 — 0 — 1 — 2 — 3 — 4 — 5

• Positives are to the right of zero; negatives are to the left.
• Numbers increase going right and decrease going left.

Opposites

Two numbers the same distance from 0 on opposite sides are opposites: 4 and −4, 7.5 and −7.5. The opposite of the opposite is the original: −(−4) = 4.

Comparing positive and negative numbers

Think of temperature: −2 °C is warmer than −8 °C.

Ordering

Order from least to greatest: 3, −5, 0, −1, 7

Place on a number line: −5, −1, 0, 3, 7.

Describing change with signs

Worked examples

Example 1: Which is the coldest: −5 °C, 0 °C or 3 °C?

The smallest number: −5 °C.

Example 2: What is the opposite of −12?

12.

Example 3: The temperature is −3 °C and rises 8 degrees. What is it now?

Start at −3 and move 8 right on the number line: 5 °C.

Common mistakes

• Thinking −8 is greater than −2 because 8 > 2. On the number line, −8 is further left, so it’s smaller.
• Forgetting the sign when writing an answer.
• Thinking zero is positive.

Try it yourself

1. Which is greater: −6 or −9?
2. Order from greatest to least: −1, 4, −7, 0.
3. Write the opposite of 15.
4. A submarine is 120 m below sea level. Write this as an integer.
5. The temperature is 2 °C and drops 7 degrees. What is it now?

Answers: 1) −6 2) 4, 0, −1, −7 3) −15 4) −120 5) −5 °C

Quick recap

• Positive numbers are above zero; negative numbers are below.
• On a number line, right is greater.
• Opposites are the same distance from zero.