**High School Number Sense Lesson 9: Finding the Remainder when Dividing by 9**

This concept relates to the one I posted last Monday (Div9). But instead of calculating the

**quotient**when dividing by 9, we will discover how to determine the

**remainder**when dividing by 9. Once again, we will accomplish this by adding. On tests this year, RemainDiv9 appeared 7 times between questions 7 and 13 (inclusive).

**Number Dojo Level: 90**

**How it Works:**

- Add all the digits in the number.
- If the sum of the digits is 9, your remainder is 0. If the sum is greater than 9, add the digits of the sum.
- Repeat step 2 until you have a remainder less than 9. This is your answer.

**Notes:**

- You don't have to get the sum down below 9 to determine your remainder. For example, if one of your sums in step 1 or 2 is 19, you can probably recognize quickly that the remainder will be 1 because 19 ÷ 9 = 2
**remainder 1**. - If any of the digits of the original number (or the sum of any group of digits in the original number) is 9, simply ignore these digits when you are adding them. This concept is "
**canceling out nines**" or "canceling nines" and saves a bit of time if the original number has more than a few digits. - This concept also applies to finding the remainder when
**dividing by 3**--which also shows up on number sense tests, but not as often.

**Example 1: 911 ÷ 9 has a remainder of ___**

- 9 + 1 + 1 = 11.
- 1 + 1 =
**2**. This is your remainder. You could have ignored the 9 in the original number and added 1 + 1 to get**2**.

**Example 2: 1974 ÷ 9 has a remainder of ___**

- 1 + (ignore the 9) + 7 + 4 = 12.
- 1 + 2 =
**3**(your remainder).

**Example 3: The remainder of 79366 ÷ 9 is ___**

- 7 + (ignore the 9) + (ignore the 3 and 6 because they add up to 9) + 6 = 13.
- 1 + 3 =
**4**(your remainder).

**Example 4: 658785 ÷ 9 has a remainder of ___**

- 6 + 5 + 8 + 7 + 8 + 5 = 39.
- 3 + (ignore the 9) =
**3**(your remainder).

**Here's a free worksheet to help you practice RemainDiv9:**

remaindiv9.pdf |

**Up Next for High School: EstAddWhole**