Integers · Meet the integers · 1.1

Below zero.

Integers are the whole numbers together with their negatives and zero. A negative number measures the opposite direction: below zero, in debt, below sea level, a loss.

01 / THE IDEA

See it work.

On the number line

Where does it sit?

-6-5-4-3-2-101-5

Watch the method

Below zero

Every amount has an opposite: +5 and −5 are 5 in opposite directions.

1 / 1
−(−5)-\left(-5\right)
1

Flip the sign

The opposite of a number is the same distance from 0 on the other side.

−(−5)=5-\left(-5\right) = 5
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a whole number — negatives allowed, e.g. -7.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Opposite directions

Positive and negative measure opposite directions from 0: up/down, gain/loss, above/below. The sign tells you the direction.

Why it works

+5 m above sea level vs −5 m below it.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

What is the opposite of -8?

1

Flip the sign

The opposite of a number is the same distance from 0 on the other side. -(-8) = 8

EX 2medium

What is the opposite of 1?

1

Flip the sign

The opposite of a number is the same distance from 0 on the other side. -(1) = -1

EX 3hard

What is the opposite of 1?

1

Flip the sign

The opposite of a number is the same distance from 0 on the other side. -(1) = -1

04 / COMMON TRAPS

Where students slip.

Trap

Reading −5 as “5”.

Fix

The minus sign means the opposite direction, below zero.

Trap

Thinking negatives are “not real”.

Fix

Temperatures, debts, and elevations are negative every day.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

What is the opposite of -8?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
C2

What is the opposite of 1?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
C3

What is the opposite of -5?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
C4

What is the opposite of -7?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
Apply

Apply (4)

A1

What is the opposite of 1?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
A2

What is the opposite of -8?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
A3

What is the opposite of 12?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
A4

What is the opposite of 11?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
Extension

Extension (4)

E1

What is the opposite of 1?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
E2

What is the opposite of -8?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
E3

What is the opposite of 7?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.
E4

What is the opposite of 4?

Need a hint?
  • The opposite is the same distance on the other side of 0.
  • Flip the sign.