How to Divide by 11

Instructor: Joy Blake

Joy has been a teacher for over ten years. She has primarily taught Middle School Math and has a Master's degree in Educational Leadership.

How can you know if you can divide your Halloween candy up with eleven friends without using a calculator? In this lesson you will learn how to apply the divisibility rule of eleven to determine if a number is divisible by eleven.

Divisibility Rule of Eleven

Maurice is going on a field trip for eleven days and his parents give him $539. How much can he spend each day?

Division means to break something up into equal parts or groups.

The Divisibility Rule of Eleven is that you must subtract and then add the digits in an alternating pattern from left to right. If your answer is 0 or 11 then it is divisible by 11.

Example of Dividing by 11

So let's go back to Maurice and his field trip money. Is $539 divisible by 11? Let's apply the divisibility rule.

Subtract the first digit by the second digit then add the second digit to the third digit. So we would do (5-3+9) = ? If our answer is 11 or 0 we know that 539 is divisible by 11.

5-3=2

2+9 = 11

The answer is 11, so 539 is divisible by 11. Maurice can split the $539 evenly over the 11 days of his trip. Maurice wonders to himself if there's a way to solve his problem using mental math.

Two-Digit Division

When you divide by 11 you are splitting something up into 11 equal groups. You can use the dividend within the equation to help you figure out what you are splitting up. The dividend is the number being split up into groups. In the equation,

caption

88 is the dividend because 88 is getting split into 11 groups.

If we have the equation,

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The number 66 is a two-digit number where both digits are the same. The answer to a division problem like this is always the number that is being repeated. For instance,

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Three-Digit Division

Dividing by 11 using three-digit numbers can seem challenging but you actually can do it in your head.

To solve

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Lastly, let's go back to Maurice and figure out how much money he can spend each day. His parents gave him $539. So our equation is

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