Integers · Divide · 7.1

Divide & sign.

Division undoes multiplication, so it follows the same sign rules: divide the sizes, then different signs give a negative, same signs a positive. −12 ÷ 3 = −4.

01 / THE IDEA

See it work.

Watch the method

Divide & sign

−12 ÷ 3: 12 ÷ 3 = 4, different signs → −4.

1 / 2
−12÷3-12 \div 3
1

Divide the sizes

Ignore the signs first: 12 ÷ 3 = 4.

12÷3=412 ÷ 3 = 4
2

Decide the sign

Different signs → the answer is negative.

(−12)÷3=−4(-12) ÷ 3 = -4
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
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— / WHY IT WORKS

The idea underneath.

Undo the product

Since (−4) × 3 = −12, we have −12 ÷ 3 = −4. Sizes divide; signs follow the multiply rule.

Why it works

Share a debt of 12 among 3 → each owes 4.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Divide 12 ÷ 6

1

Divide the sizes

Ignore the signs first: 12 ÷ 6 = 2. 12 ÷ 6 = 2

2

Decide the sign

Same signs → the answer is positive. 12 ÷ 6 = 2

EX 2medium

Divide 5 ÷ 5

1

Divide the sizes

Ignore the signs first: 5 ÷ 5 = 1. 5 ÷ 5 = 1

2

Decide the sign

Same signs → the answer is positive. 5 ÷ 5 = 1

EX 3hard

Divide 28 ÷ 7

1

Divide the sizes

Ignore the signs first: 28 ÷ 7 = 4. 28 ÷ 7 = 4

2

Decide the sign

Same signs → the answer is positive. 28 ÷ 7 = 4

04 / COMMON TRAPS

Where students slip.

Trap

Using different sign rules for division.

Fix

They are identical to multiplication.

Trap

Forgetting the sign on the quotient.

Fix

Apply the sign rule after dividing sizes.

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

Divide 12 ÷ 6

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
C2

Divide -30 ÷ 5

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
C3

Divide -56 ÷ 8

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
C4

Divide 10 ÷ 2

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
Apply

Apply (4)

A1

Divide 5 ÷ 5

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
A2

Divide 16 ÷ 8

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
A3

Divide -16 ÷ 8

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
A4

Divide 36 ÷ 4

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
Extension

Extension (4)

E1

Divide 28 ÷ 7

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
E2

Divide 18 ÷ 9

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
E3

Divide 16 ÷ 2

Need a hint?
  • Divide the sizes.
  • Different signs → negative.
E4

Divide 42 ÷ 7

Need a hint?
  • Divide the sizes.
  • Different signs → negative.