Integers · Order of operations · 8.4

All four operations.

Longer expressions just apply the order of operations repeatedly: handle the strongest operation, rewrite, and repeat until one number is left.

01 / THE IDEA

See it work.

Watch the method

All four operations

−5 − 6 × 2: 6 × 2 = 12, then −5 − 12 = −17.

1 / 2
−5−6×2-5 - 6 \times 2
1

Multiply

6 × 2 = 12

−5−12-5 - 12
2

Subtract

-5 - 12 = -17

−17-17
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.

One step at a time

Find the highest-priority operation, do it, rewrite, repeat. Subtraction becomes add-the-opposite when you combine.

Why it works

Peel the expression down to a single value.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate -8 - 5 × 4

1

Multiply

5 × 4 = 20 -8 - 20

2

Subtract

-8 - 20 = -28 -28

EX 2medium

Evaluate 8 × -2 + 7

1

Multiply

8 × (-2) = -16 -16 + 7

2

Add

-16 + 7 = -9 -9

EX 3hard

Evaluate 5 + 4 × -5

1

Multiply

4 × (-5) = -20 5 + -20

2

Add

5 + (-20) = -15 -15

04 / COMMON TRAPS

Where students slip.

Trap

Working strictly left to right.

Fix

Precedence beats position: × before −.

Trap

Losing a sign mid-way.

Fix

Rewrite carefully after each step.

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 - 5 × 4

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
C2

Evaluate -5 - 4 × 4

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
C3

Evaluate 3 × -4 + 7

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
C4

Evaluate -6 - 6 × 2

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
Apply

Apply (4)

A1

Evaluate 8 × -2 + 7

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
A2

Evaluate 3 × -2 + 6

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
A3

Evaluate 2 × -4 + 4

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
A4

Evaluate 2 + 4 × -4

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
Extension

Extension (4)

E1

Evaluate 5 + 4 × -5

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
E2

Evaluate 3 + 4 × -3

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
E3

Evaluate 6 × -2 + 8

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.
E4

Evaluate -3 - 5 × 3

Need a hint?
  • Do the strongest operation next.
  • Rewrite and repeat.