Mental Math · Division · D3

Factor the divisor.

Dividing by a tricky number? Break the divisor into two smaller factors and divide by each in turn. ÷6 becomes ÷2 then ÷3; ÷12 becomes ÷3 then ÷4. Two easy divisions beat one hard one.

01 / THE METHOD

How to think about it.

Watch the method

Factor the divisor

96 ÷ 6: since 6 = 2 × 3, divide by 2 (96 → 48), then by 3 (48 → 16). Two small steps you already know.

1 / 2
96÷696 \div 6 = ?
1
96÷2=4896 \div 2 = 48

6 is 2 × 3, so divide by 2 first.

2
48÷3=1648 \div 3 = 16

Then divide by 3.

02 / YOUR TURN

Practice until it feels easy.

Your turn

Solve it in your head.

Use the method, then check. Stuck? Reveal the steps.

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— / WHY IT WORKS

The idea underneath.

Split the divisor, divide twice

Dividing by a product is the same as dividing by each factor one after another. ÷6 = ÷2 ÷3, ÷12 = ÷3 ÷4, ÷15 = ÷3 ÷5. Choose factors from your times tables.

Why it works

Sharing among 6 people = first split into 2 big groups, then each into 3.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

84 ÷ 6

1

÷2

84 → 42.

2

÷3

42 → 14.

EX 2medium

96 ÷ 6

1

÷2

96 → 48.

2

÷3

48 → 16.

EX 3hard

180 ÷ 15

1

÷3

180 → 60.

2

÷5

60 → 12.

04 / COMMON TRAPS

Where students slip.

Trap

Adding the factors instead of using both as divisors.

Fix

÷6 is ÷2 THEN ÷3 — two divisions, not ÷5 (2+3).

Trap

Choosing factors that don't multiply to the divisor.

Fix

The two factors must multiply back to the divisor: 2 × 3 = 6, 3 × 4 = 12.

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

96 ÷ 6 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
C2

84 ÷ 6 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
C3

72 ÷ 6 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
C4

90 ÷ 6 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
Apply

Apply (4)

A1

96 ÷ 12 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
A2

144 ÷ 12 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
A3

90 ÷ 15 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
A4

120 ÷ 15 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
Extension

Extension (4)

E1

168 ÷ 12 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
E2

216 ÷ 12 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
E3

252 ÷ 6 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).
E4

180 ÷ 15 = ?

Need a hint?
  • Break the divisor into two smaller factors.
  • Divide by one factor, then by the other (÷6 = ÷2 ÷3).