Integers · Order of operations · 8.1

PEMDAS with signs.

Order of operations is unchanged by negatives: do powers, then × and ÷, then + and −. Carry every sign through. 2 + 3 × (−4) = 2 + (−12) = −10.

01 / THE IDEA

See it work.

Watch the method

PEMDAS with signs

2 + 3 × (−4): multiply first → 2 + (−12) = −10.

1 / 2
2+3×(−4)2 + 3 \times (-4)
1

Multiply

3 × (-4) = -12

2+−122 + -12
2

Add

2 + (-12) = -10

−10-10
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.

Order still rules

Multiplication and division bind tighter than addition and subtraction, negatives or not.

Why it works

Do the strong operations first, signs and all.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate 8 × -4 + 9

1

Multiply

8 × (-4) = -32 -32 + 9

2

Add

-32 + 9 = -23 -23

EX 2medium

Evaluate -4 - 6 × 3

1

Multiply

6 × 3 = 18 -4 - 18

2

Subtract

-4 - 18 = -22 -22

EX 3hard

Evaluate 8 × -4 + 9

1

Multiply

8 × (-4) = -32 -32 + 9

2

Add

-32 + 9 = -23 -23

04 / COMMON TRAPS

Where students slip.

Trap

Adding before multiplying.

Fix

Multiply (×) before you add (+).

Trap

Dropping the negative on the product.

Fix

3 × (−4) is −12, not 12.

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 8 × -4 + 9

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
C2

Evaluate 6 × -4 + 7

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
C3

Evaluate 2 + 2 × -5

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
C4

Evaluate 4 × -2 + 8

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
Apply

Apply (4)

A1

Evaluate -4 - 6 × 3

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
A2

Evaluate -7 - 5 × 3

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
A3

Evaluate 6 × -2 + 2

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
A4

Evaluate 5 × -4 + 9

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
Extension

Extension (4)

E1

Evaluate 8 × -4 + 9

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
E2

Evaluate 3 + 5 × -3

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
E3

Evaluate 3 × -4 + 6

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.
E4

Evaluate 7 + 4 × -6

Need a hint?
  • Do × and ÷ before + and −.
  • Keep each sign as you go.