**High School Number Sense Lesson 13: Multiplying Percents**

This is another concept with lots of practical application--especially when shopping. One of my pet peeves is to see how some sales are advertised. For example, a common marketing tactic is to see things as "

**Buy one, get one 50% off!**" If you understand percents, you will realize that:

- The discount is really only
**25% off**. **They are forcing you to buy 2**to take advantage of the sale. For this reason, this type of sale is less appealing to me than a straight 25% off sale.

**70% off**sales at a jewelry store when the item "on sale" was selling above retail value to begin with. I saw an even more obvious example over a decade ago with a

**BOGOF**(buy one, get one free) sale on a 2-quart generic bottle of apple juice...

**priced at $4.59**. This was back when the brand name bottle was

**only $1.99**.

On high school tests, this concept appeared

**29 times**, making it a very important skill to master. 13 of these appearances showed up around question 14, 7 showed up in the 20s, and 9 showed up in the 30s. We will cover several different variations.

**Number Dojo Level: 105**

As a reminder, the word

*percent*means

**per 100**. So multiplying by a percent includes dividing by 100. Follow these steps (in either order):

- Ignore the % sign and multiply the numbers.
- Divide by 100, either by removing 2 zeros or by moving the decimal 2 places to the left.

**Example 1: 15% of 400 = ___**

- Ignore the % sign. 15 x 400 =
**6000**. - Divide by 100. 6000 ÷ 100 =
**60**.

**60.**

**Example 2: 50% of 13 = ___**

- Ignore the % sign. 50 x 13 =
**650**. - Divide by 100. 650 ÷ 100 =
**6.5**

**Example 3: 1.25% of 400 is ___**

- Remove 2 zeros to get 1.25 x 4.
- Multiply these to get
**5**.

**Example 4: 80% of 80 = ___**

- Remove 2 zeros (one from each number) to get 8 x 8.
- Multiply these to get
**64**.

**Order of Operations with Percents**

Sometimes you are asked to perform multiple operations with one or more percent calculations. You will need to consider the proper order of operations (covered in a previous post as OrderOfOper) for these. Here are some examples:

**Example 5: 80% of 70 minus 60 is ___**

- Think: (80% x 70) - 60 = ___
- Ignore the % sign and remove 2 zeros to get:
**(8 x 7) - 60**. - 8 x 7 =
**56**. 56 - 60 =**-4**.

**Example 6: 45 less 30% of 40 is ___**

- Think: 45 - (30% x 40) = ___
- Ignore the % sign and remove 2 zeros to get:
**45 - (3 x 4)**. - 3 x 4 =
**12**. 45 - 12 =**33**.

**Example 7: 40% of 50 plus 60% of 70 = ___**

- Think: (40% x 50) + (60% x 70) = ___
- Ignore the % signs and remove 2 zeros from each pair to get:
**(4 x 5) + (6 x 7)**. - 4 x 5 =
**20**. 6 x 7 =**42**. 20 + 42 =**62**.

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

mult_.pdf |

**Up Next for High School: PercentAis_%**