**High School Number Sense Lesson 5: Dividing by 9**

Dividing by 9 is a concept that showed up 8 times this year. Many students don't realize there is a simple way to solve these problems (without long division). I will show you both methods:

**Number Dojo Level: 45**

**The Old Way: Long Division**

Let's say you are given the problem

**2015**

**÷ 9 = ___ (mixed number)**. Here's how you would solve it without learning Div9:

- 9 goes into 2 zero times. Use 20 instead. 9 goes into 20,
**2**times with a remainder of 2. - 9 goes into 21,
**2**times with a remainder of 3. - 9 goes into 35,
**3**times with a reminder of 8. - The answer is
**223 8/9**.

**The New Way: Divide by Adding**

- Add all the digits of the dividend. This will determine the fractional part of the answer, with 9 as the denominator. 2 + 0 + 1 + 5 = 8, so write
**8/9**. - Excluding the units digit, add the remaining digits. 2 + 0 + 1 =
**3**. Write this down in front. - Work your way to the left. Excluding the units and tens digits, add the remaining digits. 2 + 0 =
**2**; write this down. - You are left with only one digit on the left:
**2**. Write this down. - The answer is
**223 8/9**.

**Notes:**

- When adding all the digits in step 1 above, if you get a number > 8, you must convert the fraction to either a whole number (if the sum is a multiple of 9) or a mixed number (if not). I will illustrate this in the examples below. Regroup the whole number with your next addition.
- When adding any remaining digits, if the sum is > 9, simply regroup with the next step like you would in any addition problem.

**Example 1 (easy): 3210 ÷ 9 = ___ (mixed number)**

- Add all the digits of the dividend. 3 + 2 + 1 + 0 = 6. Place this over 9 for your fractional portion of the answer. 6/9, reduced, is
**2/3**. - Excluding the units digit, add the remaining digits. 3 + 2 + 1 =
**6**. Write this in front. - Work your way to the left. 3 + 2 =
**5**. Write this down. - You are left with the
**3**. Write this in the front. - The answer is
**356 2/3**.

**Example 2 (with regrouping): 1974 ÷ 9 = ___ (mixed number)**

- Add all the digits of the dividend. 1 + 9 + 7 + 4 = 21. Place this over 9 for your fractional portion. 21/9 = 2 3/9 = 2 1/3. Write
**1/3**and regroup the 2. - Excluding the units digit, add the remaining digits. 1 + 9 + 7 (+ regrouped 2) = 19. Write the
**9**in front and regroup the 1. - Work your way to the left. 1 + 9 (+ regrouped 1) = 11. Write the
**1**and regroup the 1. - You are left with a 1 (+ regrouped 1) =
**2**. Write this in front. - The answer is
**219 1/3**.

**Example 3: 314159 ÷ 9 = ___ (mixed number)**

- Add all the digits of the dividend. 3 + 1 + 4 + 1 + 5 + 9 = 23. Place this over 9 for your fractional portion. 23/9 = 2 5/9. Write the
**5/9**and regroup the 2. - Exclude the units digit. 3 + 1 + 4 + 1 + 5 (+ regrouped 2) = 16. Write the
**6**in front and regroup the 1. - Exclude the units and tens. 3 + 1 + 4 + 1 (+ regrouped 1) = 10. Write the
**0**and regroup the 1. - Keep working to the left. 3 + 1 + 4 (+ regrouped 1) =
**9**. Write this down. - 3 + 1 =
**4**; write this down. - You are left with the
**3**; write this down. - The answer is
**34906 5/9**.

**Here's a free worksheet to help you practice Div9:**

div9.pdf |

**Up Next for High School: ConvFracDeci**