Integers · Multiply · 6.1

Repeated addition.

Multiplying by a positive is repeated addition. 3 × (−4) means −4 added three times: −4 + (−4) + (−4) = −12. A positive times a negative is negative.

01 / THE IDEA

See it work.

On the number line

Start at 3, hop left 4.

3 + 4 = -1

-2-101234-1

Watch the method

Repeated addition

3 × (−4) = −4 + (−4) + (−4) = −12.

1 / 2
3×(−4)3 \times (-4)
1

Repeated addition

3 × (-4) means (-4) added 3 times.

(−4)+(−4)+(−4)=−12(-4) + (-4) + (-4) = -12
2

Sign rule

A positive times a negative is negative.

3×(−4)=−123 \times (-4) = -12
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.

Groups of a negative

k × n is k groups of n. Three groups of −4 is −12 — three equal hops left.

Why it works

Three withdrawals of $4 each.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Multiply 3 × -8

1

Repeated addition

3 × (-8) means (-8) added 3 times. (-8) + (-8) + (-8) = -24

2

Sign rule

A positive times a negative is negative. 3 × (-8) = -24

EX 2medium

Multiply 2 × -9

1

Repeated addition

2 × (-9) means (-9) added 2 times. (-9) + (-9) = -18

2

Sign rule

A positive times a negative is negative. 2 × (-9) = -18

EX 3hard

Multiply 5 × -8

1

Repeated addition

5 × (-8) means (-8) added 5 times. (-8) + (-8) + (-8) + (-8) + (-8) = -40

2

Sign rule

A positive times a negative is negative. 5 × (-8) = -40

04 / COMMON TRAPS

Where students slip.

Trap

Making the answer positive.

Fix

Groups of a negative stay negative.

Trap

Multiplying the sizes but guessing the sign.

Fix

Pos × neg is always negative.

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 × -8

Need a hint?
  • Add the negative that many times.
  • The result is negative.
C2

Multiply 6 × -3

Need a hint?
  • Add the negative that many times.
  • The result is negative.
C3

Multiply 5 × -4

Need a hint?
  • Add the negative that many times.
  • The result is negative.
C4

Multiply 5 × -3

Need a hint?
  • Add the negative that many times.
  • The result is negative.
Apply

Apply (4)

A1

Multiply 2 × -9

Need a hint?
  • Add the negative that many times.
  • The result is negative.
A2

Multiply 4 × -4

Need a hint?
  • Add the negative that many times.
  • The result is negative.
A3

Multiply 2 × -7

Need a hint?
  • Add the negative that many times.
  • The result is negative.
A4

Multiply 5 × -4

Need a hint?
  • Add the negative that many times.
  • The result is negative.
Extension

Extension (4)

E1

Multiply 5 × -8

Need a hint?
  • Add the negative that many times.
  • The result is negative.
E2

Multiply 2 × -4

Need a hint?
  • Add the negative that many times.
  • The result is negative.
E3

Multiply 2 × -3

Need a hint?
  • Add the negative that many times.
  • The result is negative.
E4

Multiply 5 × -3

Need a hint?
  • Add the negative that many times.
  • The result is negative.