**Middle School Number Sense Lesson 40: Estimating the Multiplication of Percents**

Back in July we introduced the topic of percents with

**Mult%**. You may want to review that lesson now if you haven't done so lately. Today we will estimate with percents. This concept appeared

**14 times**this year in middle school, with a median placement at

**question # 40**.

**Number Dojo Level: 127**

Multiplying percents is the same as dividing by 100. So on these types of problems, we get really good at ignoring the last 2 digits of the number. Here's how to solve these:

- Remove 2 digits from the whole number (rounding in the process).
- Remove the % sign, and round the remaining numbers if necessary..
- Multiply.
*Remember to write your answer as an integer!*

**Example 1: * 45% of 1107**

- Remove the last 2 digits from 1107 to get
**11**. - Remove the
**%**sign from the**45**. - Multiply 11 x 45 to get
**495**. Write down this answer. - The exact answer is
**498.15**, so the acceptable (+/- 5%) range would be from**474 to 523**. We are well within range.

**Example 2: * 23% of 4821**

- Remove the last 2 digits from 4821 to get
**48**. - Remove the % sign from the
**23**. - Multiply 48 x 23. Use your
**Double/Half**skills twice to change this to**12 x 92**. Now use your**MultUs,10+10**skills to get**1104**. - The exact answer is
**1108.83**, so the acceptable (+/- 5%) range would be from**1054 to 1164**. We are well within range.

**Example 3: * 62.49% of 803**

- Hopefully you'll notice (remember) that
**62.5%**is the same as**5/8**. So essentially, this is**5/8 of 800**. - Multiply 5/8 x 800. The answer is
**500**. - The exact answer is
**501.7947**, so the acceptable (+/- 5%) range would be from**477 to 526**. We are well within range.

**Example 4: * 32% of 75% of 499 is ___**

- Think of this as 32% x 3/4 x 499. I personally multiply 32% x 3/4 first to get
**24% x 499**. - Round 499 to
**500**and then remove 2 digits to get**5**. - Remove the % sign from the
**24**. - Multiply 5 x 24 to get
**120**. - The exact answer is
**119.76**, so the acceptable (+/- 5%) range is from**114 to 125**. We are within range.

Example 5: * 66 2/3% x 11995

Example 5: * 66 2/3% x 11995

- Hopefully you'll notice (remember) that 66 2/3% is the same as
**2/3**. So this is the same as**2/3 x 11995**. - Round the 11995 to
**12000**. - Multiply 2/3 x 12000 to get
**8000**. - The actual answer is about
**7996.67**, so the acceptable (+/- 5%) range would be from**7597 to 8396**. We are well within range.

**Example 6: * 14 2/7% of 34899**

- Hopefully you'll notice (remember) that 14 2/7% is the same as
**1/7**. So this is the same as**1/7 x 34899**. - Round the 34899 to
**35000**. - Multiply 1/7 x 35000 to get
**5000**. - The actual answer is about
**4985.57**, so the acceptable (+/- 5%) range would be from**4737 to 5234**. We are well within range.

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

estmult_.pdf |

**Up Next for Middle School: Mult%2**