**High School Number Sense Lesson 36: Dividing Mixed Numbers**

We've already looked at adding (

**AddMixDiff**), subtracting (

**SubMixDiff**), and multiplying (

**MultMixDiff**&

**MultMixF+1**) mixed numbers. Now let's look at dividing them. This concept appeared

**13 times**this year at the median placement of

**question # 34**.

**Number Dojo Level: 115**

Not every number sense concept has a great time-saving method. Unfortunately, DivMix falls into this category. To solve these problems, I crank through them the "old-fashioned" way.

**(If you know of a quicker way, please leave a comment below!)**

**How to Solve:**

- Convert each mixed number to an improper fraction.
- Flip the divisor (the fraction you're dividing by) so you're working with its reciprocal, and change the operation to a multiplication.
- Cancel any common factors if possible.
- Multiply the resulting fractions & reduce if possible. (Make sure to give your answer in the appropriate form).

**Example 1: 4 5/8 ÷ 4 3/8 = ___ (mixed number)**

- Convert each mixed number to an improper fraction. 4 5/8 =
**37/8**, and 4 3/8 =**35/8**. - 37/8 ÷ 35/8 becomes
**37/8 x 8/35**. - Cancel the 8's. You're left with
**37/1 x 1/35**. - 37/1 x 1/35 =
**37/35**. You were asked for a mixed number answer, so it's**1 2/35**.

**Example 2: 3 1/3 ÷ 1 2/3 = ___**

- Convert to improper fractions. 3 1/3 =
**10/3**, and 1 2/3 =**5/3**. - 10/3 ÷ 5/3 becomes
**10/3 x 3/5**. - Cancel the 3's, and you're left with
**10/1 x 1/5**. Cancel the 5's, and you have**2/1 x 1/1**. - 2/1 x 1/1 = 2 x 1 =
**2**. (*Hopefully you figured out this answer directly from the beginning of Step 2*).

**Example 3: 7 1/5 ÷ 2 1/4 = ___ (mixed number)**

- Convert to improper fractions. 7 1/5 =
**36/5**, and 2 1/4 =**9/4**. - 36/5 ÷ 9/4 becomes
**36/5 x 4/9**. - Cancel the 9's, and you have
**4/5 x 4/1**. - 4/5 x 4/1 =
**16/5**. You were asked for a mixed number, so it's**3 1/5**.

**Example 4: 3 3/4 ÷ 1 3/7 = ___ (mixed number)**

- Convert to improper fractions. 3 3/4 =
**15/4**, and 1 3/7 =**10/7**. - 15/4 ÷ 10/7 becomes
**15/4 x 7/10**. - Cancel the 5's, and you have
**3/4 x 7/2**. - 3/4 x 7/2 =
**21/8**. You were asked for a mixed number, so it's**2 5/8**.

**Example 5: 2 1/4 ÷ 3 3/5 = ___**

- Convert to improper fractions. 2 1/4 =
**9/4**, and 3 3/5 =**18/5**. - 9/4 ÷ 18/5 becomes
**9/4 x 5/18**. - Cancel the 9's, and you have
**1/4 x 5/2**. - 1/4 x 5/2 =
**5/8**. This doesn't reduce.

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

divmix.pdf |

**Up Next for High School: RemainExp**