Integers · Capstone · C1

Pick the right move.

The final skill is choosing: compare on the line, add by zero pairs, subtract by adding the opposite, and multiply or divide by the sign rules — then check the sign.

01 / THE IDEA

See it work.

Watch the method

Pick the right move

Read the operation, then apply the right rule — and check the sign.

1 / 2
−5×(−6)-5 \times (-6)
1

Multiply the sizes

Ignore the signs first: 5 × 6 = 30.

5×6=305 × 6 = 30
2

Decide the sign

Same signs → the answer is positive.

(−5)×(−6)=30(-5) × (-6) = 30
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.

The decision

Add: compare/cancel signs. Subtract: add the opposite. Multiply/divide: like signs +, unlike −. Powers: mind the parentheses.

Why it works

Pick the right tool for the operation.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate -6 - 6 × 3

1

Multiply

6 × 3 = 18 -6 - 18

2

Subtract

-6 - 18 = -24 -24

EX 2medium

Evaluate -6^2

1

What is squared?

−6^2 means −(6^2); the minus is applied last — only the 6 is raised. -(6^2)

2

Raise, then negate

6^2 = 36, then apply the minus. -(36) = -36

EX 3hard

Evaluate 3 × -1

1

Multiply the sizes

Ignore the signs first: 3 × 1 = 3. 3 × 1 = 3

2

Decide the sign

Different signs → the answer is negative. 3 × (-1) = -3

04 / COMMON TRAPS

Where students slip.

Trap

Using the addition rule for multiplication.

Fix

Adding compares sizes; multiplying counts signs.

Trap

Dropping a minus under time pressure.

Fix

Check the sign of your answer.

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 - 6 × 3

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
C2

Evaluate -2^2

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
C3

Evaluate -9 × 2

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
C4

Evaluate 9 × -7

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
Apply

Apply (4)

A1

Evaluate -6^2

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
A2

Evaluate -6 + 12

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
A3

Evaluate -12 ÷ -4

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
A4

Evaluate -3^2

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
Extension

Extension (4)

E1

Evaluate 3 × -1

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
E2

Evaluate -6^2

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
E3

Evaluate -7 + 12

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.
E4

Evaluate (-3)^3

Need a hint?
  • Identify the operation first.
  • Apply its rule, then check the sign.