Integers · Absolute value · 3.2

Never negative.

Absolute value itself is never negative, but a minus sign OUTSIDE the bars still applies. |−5| = 5, but −|−5| = −5. Work inside the bars first.

01 / THE IDEA

See it work.

Watch the method

Never negative

−|−5|: |−5| = 5, then the outside minus gives −5.

1 / 1
−∣−5∣-\left|-5\right|
1

Absolute value

|-5| = 5

−5-5
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.

Inside, then outside

Evaluate inside the bars, take the absolute value, then apply any sign outside.

Why it works

The bars clean the sign; a minus outside re-adds one.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate |9| - 9

1

Absolute value

|9| = 9 9 - 9

2

Subtract

9 - 9 = 0 0

EX 2medium

Evaluate -|3|

1

Absolute value

|3| = 3 -3

EX 3hard

Evaluate |5| - 4

1

Absolute value

|5| = 5 5 - 4

2

Subtract

5 - 4 = 1 1

04 / COMMON TRAPS

Where students slip.

Trap

Treating −|−5| as 5.

Fix

The minus outside the bars makes it −5.

Trap

Doing the outside sign first.

Fix

Absolute value (inside) comes before the outside minus.

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

Evaluate |9| - 9

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
C2

Evaluate |9| - 3

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
C3

Evaluate |-9 - 2|

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
C4

Evaluate -|6|

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
Apply

Apply (4)

A1

Evaluate -|3|

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
A2

Evaluate |8| - 2

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
A3

Evaluate -|-3|

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
A4

Evaluate |-6 - 6|

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
Extension

Extension (4)

E1

Evaluate |5| - 4

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
E2

Evaluate |6| - 9

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
E3

Evaluate -|4|

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.
E4

Evaluate |6| - 9

Need a hint?
  • Evaluate inside the bars first.
  • Then apply the sign outside.