The ×11 Sandwich Rule: Multiply Any Two-Digit Number Instantly

Why Multiplying by 11 Is Special

Any two-digit number multiplied by 11 can be split using place value: 11 × n = 10n + n. When you line up n and 10n, the digits of n slide one place to the left and overlap with themselves — which is exactly why a simple "sandwich" pattern shows up in the answer.

The Rule in Three Steps

Write the two digits of the original number as the outer digits of your answer (the "bread").
Add the two digits together — that sum is the middle digit (the "filling").
If the sum is 10 or more, write only the last digit in the middle and carry the 1 to the left digit.

Worked Example: No Carrying

45 × 11

Outer digits: 4 and 5
Middle digit: 4 + 5 = 9
Slide them together: 4, 9, 5 → 495

Worked Example: With Carrying

68 × 11

Outer digits: 6 and 8
Middle sum: 6 + 8 = 14 — write the 4, carry the 1
Add the carry to the left digit: 6 + 1 = 7
Answer: 7, 4, 8 → 748

Two More to Lock It In

72 × 11 → 7 + 2 = 9, no carry → 792
57 × 11 → 5 + 7 = 12 → write 2, carry 1 → left digit becomes 5 + 1 = 6 → 627

Common Mistakes to Avoid

Forgetting the carry when the digit sum is 10 or higher is the single biggest error students make.
Double-check with an estimate: 68 × 11 should be a little more than 68 × 10 = 680, and 748 fits that estimate.
This trick applies directly to two-digit numbers; for three-digit numbers, the same overlapping-addition idea extends, but you add pairs of neighbouring digits instead of just two.

Where This Helps

Multiplication by 11 shows up constantly in speed tests — quick totals, squaring near-11 quantities, and multi-step arithmetic problems where every second counts. Once the sandwich pattern feels automatic, you can multiply two-digit numbers by 11 as fast as you can write the answer.

Try timing yourself: pick ten random two-digit numbers and multiply each by 11 using this rule. Most students who practice this for a few minutes a day get comfortably under three seconds per question within a week.