**High School Number Sense Lesson 84: Estimating with Order of Operations**

Today's lesson is a bit of a "catch-all" concept. The reason is because there are endless variations of operations that can be tested in an estimation problem. We have covered the most common combinations, and these are the non-specialized leftovers. These problems have shown up

**9 times**so far this year, with a median placement at

**question # 40**.

**Like our Facebook Page (**

**https://www.facebook.com/numberdojo/**

**) if you want to see new number sense posts on your wall. I will reward you with a free concept index or flashcard file of your choice. Thank you!**

**Number Dojo Level: 74**

(It may be a good idea for you to review

**OrderOfOper**and/or

**OrderOfOper2**before proceeding.)

The best way to approach these problems is with caution. Pay attention to what is being asked, and be careful to round appropriately. Let's look at some examples.

**Example 1: Estimate: * 12 x 121 + 2011 = ___**

- This one's a bit of a "softball pitch." I would not round the 12, but round the 121 to a 120. 12 x 120 =
**1440**. - Round the 2011 to 2000 and add. The answer is
**3440**. - The exact answer is
**3463**, and the acceptable (+/- 5%) range is**from 3290 to 3636**.

**Example 2: Estimate: * (9999 + 666) ÷ 33 = ___**

- You may be tempted to add within the parentheses first, but I would rather use the distributive property. 9999 ÷ 33 =
**303**, and 666 ÷ 33 is about**22**. - Now add: 303 + 22 =
**325**. - The actual answer is
**323.181818...**, and the acceptable (+/- 5%) range is**from 308 to 339**.

**Example 3: Estimate: * 135 x 246 + 789 = ___**

- I would round 246 to
**250**and 135 to**136**to make the multiplication easier. - 136 x 250 = 136 x 1000 ÷ 4 136 ÷ 4 x 1000 = 34 x 1000 =
**34000**. - Your answer is
**34789**. The actual answer is**33999**, and the acceptable (+/- 5%) range is**from 32300 to 35698**.

**Example 4: Estimate: * 55 x 45 x 35 ÷ 25 = ___**

- Since we are dividing by 25, I'm going to break it up and divide both 55 and 45 by 5.
- We are left with
**11 x 9 x 35**. Since 11 x 9 is 99, we can round that to 100 and then multiply by 35. - Our answer is
**3500**. The exact answer is**3465**, and the acceptable range is**from 3292 to 3638**.

**Example 5: Estimate: * 17 x 23 + 1723 = ___**

- We can use
**DiffSquares1**to multiply 17 x 23, which is**391**. - Round 391 to 400, and round 1723 down to 1700. 400 + 1700 =
**2100**. - The exact answer is
**2114**, and the acceptable range is**from 2009 to 2219**.

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

estorderofop.pdf |

**Up Next for High School: AddRecipPID**