**High School Number Sense Lesson 101: Estimating with Multiplication of 4 Close Whole Numbers**

This problem is very similar to (and an extension of)

**EstMult3Close**. It appeared just

**4 times**this year, with a median placement at

**question # 50**.

**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: 307**

In many cases, the 4 numbers will be consecutive integers. It will probably not be sufficient to square one of the middle two numbers, and then square the result. Instead, try to pick a pair of numbers that is easy to multiply, and then square the result.

Be careful with these problems, because sometimes the numbers are too far apart to use a “square twice” strategy.

**Example 1: * 8 x 9 x 10 x 11 = ___**

- Personally, I would multiply 9 x 11 first to get
**99**. - Round 99 to 100, and then multiply by 8 to get
**800**. - Multiply by 10 to get
**8000**. - The exact answer is
**7920**, and the acceptable (+/- 5%) range is**from 7524 to 8316.**

**Example 2: * 9 x 10 x 11 x 12 = ___**

- Use a similar strategy here. 9 x 11 =
**99**; round to 100 - 100 x 12 x 10 =
**12000**. - The exact answer is
**11880**, and the acceptable (+/- 5%) range is**from 11286 to 12474**.

**Example 3: * 11 x 12 x 13 x 14 = ___**

- 12 x 13 =
**156**. Round to 160 - 14 x 160 = (14 x 16) x 10. Use
**Mult10s,U+10**to get**224 x 10**, which is**2240** - 11 x 2240 (using
**Mult11**) = 24640. - The exact answer is
**24024**, and the acceptable (+/- 5%) range is**from 22823 to 25225**.

**Example 4: * 13 x 14 x 15 x 16 = ___**

- 14 x 15 = 7 x 30 =
**210** - Now square this result. 210 x 210 =
**44100**. - The exact answer is
**43680**, and the acceptable (+/- 5%) range is**from 41496 to 45864**.

**Example 5: * 16 x 17 x 18 x 19 = ___**

- 17 x 18 = (17 x 17 + 17) = 289 + 17 =
**306** - Round this to 310, and square. Your answer is
**96100**. - The exact answer is
**93024**, and the acceptable (+/- 5%) range is**from 88373 to 97675**.

**Example 6: * 12 x 24 x 36 x 48 = ___**

- Factor this to be
**(12 x 12 x 12) x (2 x 3) x 48** - 123 = 1728. Round this down to
**1700**. - 1700 x 6 =
**10200**. Round this to**10000**. - 48 x 10000 =
**480000**. - The exact answer is
**497664**, and the acceptable (+/- 5%) range is**from 472781 to 522547**.

**Up Next for High School: CirclesEqua**