Mental Math · Multiplication · M3
Nine and eleven sit right next to ten, so lean on ten. ×9 is ×10 minus one copy. ×11 is ×10 plus one copy — which for a two-digit number becomes the famous 'add the digits in the middle' pattern.
Watch the method
9 is one less than 10. So 7 × 9 = 7 × 10 − 7 = 70 − 7 = 63. Multiply by ten, then subtract one copy.
Multiply by 10 — the easy one.
9 is one less than 10, so subtract one 7.
Your turn
Use the method, then check. Stuck? Reveal the steps.
×9 = ×10 − itself. ×11 = ×10 + itself. For a two-digit number times 11, that 'add itself' lines up as: keep the outside digits, and put their sum in the middle (carry if it's 10 or more).
Why it works
35 × 11 = 350 + 35 = 385 — and 3, then 3+5, then 5 spells 385.
8 × 9
×10
8 × 10 = 80.
Subtract one copy
80 − 8 = 72.
23 × 11
Outside digits
Keep the 2 and the 3.
Middle
2 + 3 = 5 goes between them.
Read it
2, 5, 3 → 253.
57 × 11
Middle sum
5 + 7 = 12 — carry the 1.
Carry
5 + 1 = 6, middle is 2, last is 7.
Read it
627.
For ×9, multiplying by 10 and subtracting 10.
Subtract one COPY of the number, not 10. 7 × 9 = 70 − 7, not 70 − 10.
Forgetting to carry in the ×11 middle digit.
If the two digits add to 10 or more, carry into the next place. 57 × 11: 5 (12) 7 → 627.
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.
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).7 × 9 = ?
8 × 9 = ?
12 × 9 = ?
6 × 9 = ?
23 × 11 = ?
35 × 11 = ?
14 × 11 = ?
26 × 11 = ?
23 × 9 = ?
45 × 9 = ?
52 × 11 = ?
57 × 11 = ?