Integers · Multiply · 6.3

Negative × negative.

A negative times a negative is positive. Watch the pattern: −5 × 2 = −10, −5 × 1 = −5, −5 × 0 = 0, −5 × (−1) = +5 — each step up by 5. So −5 × −6 = 30.

01 / THE IDEA

See it work.

Watch the method

Negative × negative

−5 × (−6): same signs → positive → 30.

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.

Why it’s positive

Following the pattern as the multiplier drops past 0, the products keep rising by 5 — they must turn positive. Same signs → positive.

Why it works

Removing debts repeatedly leaves you richer.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Multiply -3 × -4

1

Multiply the sizes

Ignore the signs first: 3 × 4 = 12. 3 × 4 = 12

2

Decide the sign

Same signs → the answer is positive. (-3) × (-4) = 12

EX 2medium

Multiply -12 × -9

1

Multiply the sizes

Ignore the signs first: 12 × 9 = 108. 12 × 9 = 108

2

Decide the sign

Same signs → the answer is positive. (-12) × (-9) = 108

EX 3hard

Multiply -3 × -5

1

Multiply the sizes

Ignore the signs first: 3 × 5 = 15. 3 × 5 = 15

2

Decide the sign

Same signs → the answer is positive. (-3) × (-5) = 15

04 / COMMON TRAPS

Where students slip.

Trap

Leaving neg × neg negative.

Fix

Two negatives multiply to a positive.

Trap

Treating it like addition.

Fix

Two negatives ADD to a bigger negative, but MULTIPLY to a positive.

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

Multiply -3 × -4

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
C2

Multiply -4 × -4

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
C3

Multiply -6 × -3

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
C4

Multiply -12 × -5

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
Apply

Apply (4)

A1

Multiply -12 × -9

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
A2

Multiply -9 × -6

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
A3

Multiply -7 × -9

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
A4

Multiply -11 × -6

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
Extension

Extension (4)

E1

Multiply -3 × -5

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
E2

Multiply -9 × -7

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
E3

Multiply -10 × -9

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.
E4

Multiply -11 × -4

Need a hint?
  • Same signs → positive.
  • Multiply the sizes, sign is +.