How to Multiply Any 2-Digit Number by 11 in 3 Seconds

In our classroom, one of the first mental math tricks I teach students is multiplying by 11. When students first see a problem like 45 × 11, they immediately reach for scratch paper or start setting up vertical columns. But once they learn this simple trick, they can solve it faster than someone typing it into a calculator.

The Split and Add Rule

The rule is wonderfully simple: take the two digits of the number you are multiplying, split them apart, add them together, and place the sum in the middle.

Example 1: No Carrying Needed

Let's solve 35 × 11 together:

• Step 1: Split the digits 3 and 5 apart: 3 _ 5
• Step 2: Add the digits: 3 + 5 = 8
• Step 3: Place 8 in the middle: 385

Check with a calculator: 35 × 11 = 385. It works every single time!

Example 2: What Happens When the Sum is 10 or Greater?

A common question students ask is: "Teacher, what do I do if the two numbers add up to more than 9?"

Let's try 78 × 11:

• Step 1: Split 7 and 8 apart: 7 _ 8
• Step 2: Add the digits: 7 + 8 = 15
• Step 3: You cannot put two digits in the middle. Put the 5 in the middle and carry the 1 to the first digit (7 + 1 = 8).
• Result: 858

Why Does This Math Trick Actually Work?

Math tricks are not magic; they are algebra in disguise. When you multiply any number by 11, you are really multiplying by (10 + 1). For 35:

35 × 11 = 35 × (10 + 1)
        = (35 × 10) + (35 × 1)
        = 350 + 35
        = 385

Notice how the middle digit is always the sum of the tens and units digit! When students understand the reasoning, they remember the trick for life.

Teacher Practice Challenge

Try these three problems in your head right now before looking at the answers:

1. 26 × 11 = ?
2. 53 × 11 = ?
3. 67 × 11 = ?

Answers: 1) 286, 2) 583, 3) 737 (remember to carry the 1 from 6+7=13).