**High School Number Sense Lesson 20: Estimating with Division of Whole Numbers**

On average, this concept appeared more than once per test. It showed up

**25 times**this year--11 times at

**question # 20**, 4 times at # 30, 4 times at # 40, 4 times at # 60, and twice at # 70.

**Number Dojo Level: 138**

**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 closer your divisor is to your dividend, the smaller your quotient will be, and therefore the smaller the margin of error. Be very careful with these problems!
- Try to
**round**to an easier number before multiplying. In division problems, if you round one of the factors up a little, try to round the other up as well, to minimize the risk of landing outside your margin of error.

**How to Solve:**

- Try to round both the dividend and divisor to a number that will make it easier to divide. This will often be a multiple of 10 or 100, etc., but it may also be the decimal equivalent of a common fraction (such as 125 for 1/8 of 1000, 111 for 1/9 of 1000, etc.).
- Divide using these (easier-to-use) round numbers, being as exact with your quotient as possible.

**Example 1: * 92015 ÷ 498 = ___**

- Round 92015 to
**92000**and 498 to**500**. **92000 ÷ 500**is the same as**920 ÷ 5**. Personally, I then use the DivDouble1st concept to change this to**1840 ÷ 10**. The answer is**184**.- The actual answer is about
**184.77**, so the acceptable (+/- 5%) range would be between**176 & 194**. We are well within range.

**Example 2: * 796854 ÷ 395 = ___**

- Since we will round 395 up to
**400**, I also would round 796854 up to**800000**. **800000 ÷ 400**is the same as**8000 ÷ 4**. The answer is**2000**.- The actual answer is about
**2017.35**, so the acceptable (+/- 5%) range would be between**1917 & 2118**. We are well within range.

**Example 3: * 321123 ÷ 111 = ___**

- Since 111 is almost exactly 1/9 of 1000, we can think of this problem as 321123 ÷ (1000/9), or 321123 x (9/1000), which is the same as 321123 ÷ 1000 x 9. Personally, I would just knock of the last 3 digits of the dividend and calculate
**321 x 9**. - 321 x 9 =
**2889**. - The actual answer is
**2893**, so the acceptable (+/- 5%) range would be between**2749 & 3037**. We are well within range.

**Example 4: * 26331 ÷ 124 = ___**

- Round 124 to
**125**, which is 1/8 of 1000. We can then think of this problem as 26331 ÷ (1000/8), or 26331 x (8/1000), which is the same as 26331 ÷ 1000 x 8. Again, I just knock off the last 3 digits of the dividend and calculate**26 x 8**. - 26 x 8 =
**208**. - The actual answer is about
**212.35**, so the acceptable (+/- 5%) range would be between**202 & 222**. We are safely within range.

**Example 5: * 3192016 ÷ 765 = ___**

- I would round 765 down to
**750**, which is 3/4 of 1000. This would make the problem the same as 3192016 ÷ 1000 ÷ 3/4, or**3192 x 4/3**. - Divide first. 3192 ÷ 3 =
**1064**. 1064 x 4 =**4256**. - The actual answer is about
**4172.57**, so the acceptable (+/- 5%) range would be between**3964 & 4381**. We are within range.

**Example 6: * 6102325 ÷ 525 = ___**

- Notice that 525 is exactly 5% above
**500**. If we round 525 down to 500, we need to round 6102325 down by 5% as well, which would be fairly close to 6000000. - 6000000 ÷ 500 is the same as 60000 ÷ 5. The answer is
**12000**. - The actual answer is about
**11623.48**, so the acceptable (+/- 5%) range would be between**11043 & 12204**. We are within range, but barely.*(This question was # 60 on the state test, so it was meant to be difficult!)*

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

estdivwhole.pdf |

**Up Next for High School: FindMeanAvg**