**Middle School Number Sense Lesson 29: Order of Operations (Special Case using Fractions)**

This concept disguises itself as an Order of Operations (OrderOfOper) question, but it ends up being a bit easier once you recognize the pattern. It appeared

**10 times**this year--most often at

**question # 26**.

**Number Dojo Level: 103**

To identify this concept, look for a question that contains 2 or more division signs (÷, actually called an

**obelus**) and at least one addition or subtraction (or both). That narrows it down, right? It will look something like this:

**14 + 7 ÷ 5 + 3 ÷ 5 = ___**.

**How to Solve:**

- Change the division signs (
**obeluses**or**obeli**) :) to fractions--with the number before as the numerator and the number after as the denominator. So**7 ÷ 5**becomes**7/5**and**3 ÷ 5**becomes**3/5**. - Combine the fractions and add (or subtract, depending on the sign).
**7/5 + 3/5 = 10/5**. - The sum (or difference) of the fractions will normally reduce to a whole number.
**10/5 = 2**. Simply add to (or subtract from) the whole number in the original problem to get your answer.**14 + 2 = 16**.

**Example 1: 8 + 5 ÷ 6 + 1 ÷ 6 = ___**

- Change the obeli to fractions. 5 ÷ 6 becomes
**5/6**, and 1 ÷ 6 becomes**1/6**. - You now have
**8 + 5/6 + 1/6**. Combine the fractions & add. 5/6 + 1/6 =**6/6**. You are left with**8 + 6/6**. - 6/6 reduces to
**1**. You are left with**8 + 1**. Your answer is**9**.

**Example 2: 5 + 13 ÷ 3 + 17 ÷ 3 = ___**

- Change to fractions. 13 ÷ 3 becomes
**13/3**, and 17 ÷ 3 becomes**17/3**. - You now have
**5 + 13/3 + 17/3**. Combine the fractions & add. 13/3 + 17/3 =**30/3**. You are left with**5 + 30/3**. - 30/3 reduces to
**10**. You are left with**5 + 10**=**15**.

**Example 3: 4 + 13 ÷ 5 - 8 ÷ 5 = ___**

- Change to fractions. 13 ÷ 5 becomes
**13/5**, and 8 ÷ 5 becomes**8/5**. - You now have
**4 + 13/5 - 8/5**. Combine the fractions & subtract. 13/5 - 8/5 =**5/5**. You are left with**4 + 5/5**. - 5/5 reduces to
**1**.**4 + 1 = 5**.

**Example 4: 8 - 9 ÷ 4 - 3 ÷ 4 = ___**

- Change to fractions. 9 ÷ 4 becomes
**9/4**, and 3 ÷ 4 becomes**3/4**. - You now have
**8 - 9/4 - 3/4**. Combine the fractions & subtract. - 9/4 - 3/4 =**-12/4**. You are left with**8 - 12/4**. - 12/4 reduces to
**3**. 8 - 3 =**5**.

**Example 5: 25 ÷ 11 + 3 - 14 ÷ 11 = ___**

- Change to fractions. 25 ÷ 11 =
**25/11**and 14 ÷ 11 =**14/11**. - You now have
**25/11 + 3 - 14/11**. Combine the fractions & subtract. 25/11 - 14/11 =**11/11**. You are left with**11/11 + 3**. - 11/11 reduces to
**1**. 1 + 3 =**4**.

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

orderofoperf.pdf |

**Up Next for Middle School: Prime**