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How to Divide by 11

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  • 0:04 Divisibility Rule of 11
  • 0:30 Sample Problem
  • 1:10 2-Digit Division
  • 1:59 3-Digit Division
  • 2:57 Lesson Summary
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Lesson Transcript
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 do you know if you can divide up your Halloween candy among 11 friends without using a calculator? In this lesson, you'll learn how to apply the divisibility rule of 11 to determine if a number is divisible by 11.

Divisibility Rule of 11

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

To solve this problem, we'll need to use division. Division means to break something up into equal parts or groups.

According to the divisibility rule of 11, we must subtract and then add the digits in an alternating pattern from left to right. If the answer is 0 or 11, then the result is divisible by 11.

Sample Problem

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

Subtract the second digit from the first digit in 539. Then, add the second digit to the third digit: 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.

2-Digit Division

Recall that dividing by 11 means splitting a number into 11 equal groups. We can use the dividend, or the number being organized into groups, to help us figure out what we're splitting up.

In the equation:

88 / 11 = 8

88 is the dividend because 88 is being split into 11 equal groups.

In the equation:

66 / 11 = 6

66 is the dividend.

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's being repeated. For instance, in the equation:

66 / 11 = 6

6 is the number being repeated, so that's the answer.

Similarly,

22 / 11 = 2

because 2 is the number being repeated in 22.

3-Digit Division

Dividing by 11 using three-digit numbers can seem challenging, but we actually can do it in our heads.

To solve:

286 / 11

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