Integers · Meet the integers · 1.4

Sign and size.

An integer carries two pieces of information: a sign (direction from 0) and a size (how far from 0). −8 and 8 have the same size but opposite signs.

01 / THE IDEA

See it work.

On the number line

Where does it sit?

-9-8-7-6-5-4-3-2-101-8

Watch the method

Sign and size

−8 has sign “negative” and size 8.

1 / 1
∣−8∣\left|-8\right|
1

Distance from zero

Absolute value is how far the number is from 0 — never negative.

∣−8∣=8\left|-8\right| = 8
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.

Two parts of a number

The sign says which side of 0; the size (its absolute value) says how far. They are independent.

Why it works

−8 °C and 8 °C are equally far from 0, opposite directions.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find |3|.

1

Distance from zero

Absolute value is how far the number is from 0 — never negative. |3| = 3

EX 2medium

Find |3|.

1

Distance from zero

Absolute value is how far the number is from 0 — never negative. |3| = 3

EX 3hard

Find |-15|.

1

Distance from zero

Absolute value is how far the number is from 0 — never negative. |-15| = 15

04 / COMMON TRAPS

Where students slip.

Trap

Thinking −8 is “smaller” because it looks like 8 with a minus.

Fix

Its size is 8; its value is less than 0.

Trap

Mixing up sign and size.

Fix

Direction and distance are separate.

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

Find |3|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
C2

Find |6|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
C3

Find |-20|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
C4

Find |-14|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
Apply

Apply (4)

A1

Find |3|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
A2

Find |-11|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
A3

Find |-7|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
A4

Find |1|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
Extension

Extension (4)

E1

Find |-15|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
E2

Find |15|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
E3

Find |6|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.
E4

Find |-14|.

Need a hint?
  • Size is the distance from 0 — drop the sign.
  • Sign is just the direction.