Integers · Meet the integers · 1.3

Opposites.

The opposite of a number is the same distance from 0 on the other side. The opposite of 7 is −7; the opposite of −7 is 7. Taking the opposite twice returns the original.

01 / THE IDEA

See it work.

Watch the method

Opposites

The opposite of 7 is −7. The opposite of −7 is 7.

1 / 1
−(7)-\left(7\right)
1

Flip the sign

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

−(7)=−7-\left(7\right) = -7
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.

Same distance, other side

A number and its opposite are mirror images across 0; their sum is 0. −(−n) = n.

Why it works

A reflection in the mirror at 0.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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 2medium

What is the opposite of -12?

1

Flip the sign

The opposite of a number is the same distance from 0 on the other side. -(-12) = 12

EX 3hard

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

04 / COMMON TRAPS

Where students slip.

Trap

Thinking the opposite of −7 is still negative.

Fix

It is +7 — the other side of 0.

Trap

Confusing opposite with reciprocal.

Fix

Opposite flips the sign, not top-and-bottom.

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 1?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
C2

What is the opposite of -8?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
C3

What is the opposite of 10?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
C4

What is the opposite of -7?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
Apply

Apply (4)

A1

What is the opposite of -12?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
A2

What is the opposite of 5?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
A3

What is the opposite of 3?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
A4

What is the opposite of -2?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
Extension

Extension (4)

E1

What is the opposite of -8?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
E2

What is the opposite of -4?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
E3

What is the opposite of 7?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.
E4

What is the opposite of -8?

Need a hint?
  • Flip the sign once.
  • A double flip returns the original.