Integers · Multiply · 6.4

Count the negatives.

When multiplying several numbers, multiply all the sizes, then count the negative factors: an even number of negatives gives a positive, an odd number gives a negative.

01 / THE IDEA

See it work.

Watch the method

Count the negatives

(−1)(−2)(−3): three negatives (odd) → negative → −6.

1 / 2
−1×(−2)×(−3)-1 \times (-2) \times (-3)
1

Multiply

-1 × (-2) = 2

2×(−3)2 \times (-3)
2

Multiply

2 × (-3) = -6

−6-6
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.

Pair them up

Each pair of negatives makes a positive. One left over makes the whole product negative.

Why it works

Negatives cancel in twos.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Multiply -2 × -2 × -4

1

Multiply

-2 × (-2) = 4 4 × (-4)

2

Multiply

4 × (-4) = -16 -16

EX 2medium

Multiply -1 × -3 × -4

1

Multiply

-1 × (-3) = 3 3 × (-4)

2

Multiply

3 × (-4) = -12 -12

EX 3hard

Multiply -1 × -3 × -3

1

Multiply

-1 × (-3) = 3 3 × (-3)

2

Multiply

3 × (-3) = -9 -9

04 / COMMON TRAPS

Where students slip.

Trap

Ignoring how many negatives there are.

Fix

Count them — parity sets the sign.

Trap

Adding the factors instead.

Fix

Multiply the sizes, then apply the sign.

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 -2 × -2 × -4

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
C2

Multiply -1 × -2 × -3

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
C3

Multiply -2 × -2 × -3

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
C4

Multiply -2 × -3 × -2

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
Apply

Apply (4)

A1

Multiply -1 × -3 × -4

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
A2

Multiply -4 × -3 × -2

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
A3

Multiply -2 × -3 × -3

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
A4

Multiply -3 × -4 × -4

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
Extension

Extension (4)

E1

Multiply -1 × -3 × -3

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
E2

Multiply -2 × -3 × -2

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
E3

Multiply -1 × -2 × -2

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.
E4

Multiply -2 × -3 × -2

Need a hint?
  • Multiply all the sizes.
  • Count negatives: odd → negative.