Integers · Order of operations · 8.3

Brackets first.

Brackets are done first, then the usual order. Inside-out: clear each bracket, then multiply or divide, then add or subtract — carrying signs throughout.

01 / THE IDEA

See it work.

Watch the method

Brackets first

3 × (−2) + 5: 3 × (−2) = −6, then −6 + 5 = −1.

1 / 2
3×(−2)+53 \times (-2) + 5
1

Multiply

3 × (-2) = -6

−6+5-6 + 5
2

Add

-6 + 5 = -1

−1-1
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 out

A negative in brackets is a single signed value; resolve it, then continue with precedence.

Why it works

Settle each parcel before combining.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate (-3) × (-5) - -3

1

Multiply

-3 × (-5) = 15 15 - -3

2

Subtract

15 - (-3) = 18 18

EX 2medium

Evaluate 2 × (-6) + 6

1

Multiply

2 × (-6) = -12 -12 + 6

2

Add

-12 + 6 = -6 -6

EX 3hard

Evaluate 5 × (-3) + -5

1

Multiply

5 × (-3) = -15 -15 + -5

2

Add

-15 + (-5) = -20 -20

04 / COMMON TRAPS

Where students slip.

Trap

Ignoring the brackets.

Fix

Resolve what’s in brackets first.

Trap

Losing the sign coming out of a bracket.

Fix

Carry the sign into the next operation.

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 (-3) × (-5) - -3

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
C2

Evaluate (-6) × (-2) - 5

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
C3

Evaluate (6) × (4) - 1

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
C4

Evaluate (3) × (-1) - 6

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
Apply

Apply (4)

A1

Evaluate 2 × (-6) + 6

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
A2

Evaluate 3 × (-5) + 1

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
A3

Evaluate (3) × (6) - 2

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
A4

Evaluate 3 × (-5) + 4

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
Extension

Extension (4)

E1

Evaluate 5 × (-3) + -5

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
E2

Evaluate 2 × (-2) + -1

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
E3

Evaluate 2 × (6) + 5

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.
E4

Evaluate (-4) × (6) - -1

Need a hint?
  • Clear the brackets first.
  • Then ×/÷ before +/−.