**Middle School Number Sense Lesson 20: Estimating with Multiplication of Whole Numbers**

It has been over a month since we have covered an estimation concept. You will probably want to pay close attention, because EstMultWhole appears more often than any other concept on the test. In addition to various special cases, we saw these

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

**question # 20**. It may be helpful for you to review EstAddSub before we continue, so you can refresh your memory on how estimation problems work.

**Number Dojo Level: 57**

**Reminders:**

- As with all estimation problems, the answers must be given as
**integers**, and are considered correct as long as they are within 5% (above or below) the exact answer. Remember that the smaller your factors, the smaller the product, and therefore the smaller the margin of error. Be more careful with small numbers. - Try to
**round**to an easier number before multiplying. In multiplication problems, if you round one of the factors up a little, try to round the other down a little to minimize the risk of landing outside your margin of error.

**How to Solve:**

- For each factor being multiplied, round it to a number that is easier to multiply. This is usually a multiple of 10, 100, or 1000, OR the equivalent of the decimal equivalent of a common fraction (such as 333 for 1/3 of 1000, 167 for 1/6 of 1000, 125 for 1/8 of 1000, 111 for 1/9 of 1000, etc.). The test-writers seem to enjoy testing these decimal equivalents within the estimation problems.
- Perform the multiplications with these (easier-to-use) round numbers. Combine terms (even out of order) if they make the operations easier. For example, if we have 40 x 37 x 25, multiply 40 by 25 to get 1000 first, and then multiply by 37 to get 37000.

**Example 1: * 95 x 199 = ___**

- You may be tempted to round both numbers to the nearest hundred, but 100 is more than 5% higher than 95 (trust me). Instead, round the 199 to
**200**, but leave the**95**alone. - 95 x 200 =
**19000**. Write this as your answer. - The exact answer is
**18905**, so the acceptable (+/- 5%) range would be between**17960 & 19850**. Notice that the high end of the range is still below 20000, which would be your answer if you had rounded 95 to 100.

**Example 2: * 332 x 605 = ___**

- Change 332 to
**333**, which is about 1/3 of 1000. Round 605 down to**600**, which is easy to divide by 3. - 333 x 600 is about
**1/3 x 1000 x 600**. Multiply**1/3 by 600**first to get**200**, then multiply this by 1000 to get**200000**. - The exact answer is
**200860**, so the acceptable (+/- 5%) range would be between**190817 & 210903**. We are well within range.

**Example 3: * 18 x 11 x 799 = ___**

- You may be tempted to round 18 to 20 and 11 to 10, which could be dangerous because both numbers would change more than 5%. We can easily multiply 18 by 11 to get
**198**, which we'll round to**200**. In this case, your rounding would give you the same result! :) Round 799 to**800**. - 200 x 800 =
**160000**. - The exact answer is
**158202**, so the acceptable (+/- 5%) range would be between**150292 & 166112**. We are well within range.

**Example 4: * 833 x 720 = ___**

- 833 is very close to the decimal equivalent of 5/6 of 1000. So change this problem to
**5/6 x 720 x 1000**. - 5/6 x 720 =
**600**. 600 x 1000 =**600000**. - The exact answer is
**599760**, so the acceptable (+/- 5%) range would be between**569772 & 629748**. We are well within range.

**Example 5: * 888 x 342 = ___**

- 888 is very close to the decimal equivalent of 8/9 of 1000. Since 342 is divisible by 9, change this problem to
**8/9 x 342 x 1000**. - 342 ÷ 9 = 38. 38 x 8 =
**304**. 304 x 1000 =**304000**. - The exact answer is
**303696**, so the acceptable (+/- 5%) range would be between**288512 & 318880**. We are well within range.

**Example 6: * 425 x 475 = ___**

- Round 425 to
**430**and 475 down to**470**. - We are left with
**430 x 470**. Think of this as**43 x 47 x 100**. Using the concept of**Mult10s,U+10**, we can quickly determine that 43 x 47 =**2021**. 2021 x 100 =**202100**. - The exact answer is
**201875**, so the acceptable (+/- 5%) range would be between**191782 & 211968**. We are well within range.

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

estmultwhole.pdf |

**Up Next for Middle School: Double/Half**