Integers · Order of operations · 8.7

Mixed mastery.

Pull it all together: powers, brackets, the sign rules, and order of operations — and sanity-check the sign of your answer at the end.

01 / THE IDEA

See it work.

Watch the method

Mixed mastery

8 − 2 × (−3): 2 × (−3) = −6, then 8 − (−6) = 14.

1 / 2
8−2×(−3)8 - 2 \times (-3)
1

Multiply

2 × (-3) = -6

8−−68 - -6
2

Subtract

8 - (-6) = 14

1414
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.

Check your sign

After evaluating, ask whether the sign makes sense — a quick guard against a dropped minus.

Why it works

Estimate the sign before trusting the value.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate 6 + 5 × -6

1

Multiply

5 × (-6) = -30 6 + -30

2

Add

6 + (-30) = -24 -24

EX 2medium

Evaluate -7 - 5 × 3

1

Multiply

5 × 3 = 15 -7 - 15

2

Subtract

-7 - 15 = -22 -22

EX 3hard

Evaluate 3 + 3 × -6

1

Multiply

3 × (-6) = -18 3 + -18

2

Add

3 + (-18) = -15 -15

04 / COMMON TRAPS

Where students slip.

Trap

Rushing and dropping a minus.

Fix

Slow down on each signed step.

Trap

Skipping the final check.

Fix

Verify the sign is reasonable.

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 6 + 5 × -6

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
C2

Evaluate 8 × -4 + 5

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
C3

Evaluate 7 + 5 × -2

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
C4

Evaluate 3 × -2 + 2

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
Apply

Apply (4)

A1

Evaluate -7 - 5 × 3

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
A2

Evaluate -6 - 5 × 4

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
A3

Evaluate -9 - 4 × 3

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
A4

Evaluate 9 + 5 × -6

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
Extension

Extension (4)

E1

Evaluate 3 + 3 × -6

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
E2

Evaluate 3 + 2 × -3

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
E3

Evaluate 2 × -3 + 5

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.
E4

Evaluate 4 + 2 × -6

Need a hint?
  • Apply precedence and the sign rules.
  • Check the final sign.