**Middle School Number Sense Lesson 41: Multiplying Percents (Twice)**

Now we finally get into the "back 40" of the test--the 2nd half. I get asked about today's concept pretty often--probably because it looks harder than it is.

*Well played, number sense test writers (Larry, Andy, and Jack)!*It appears in the form of

**A% of B is C% of D**, where one of those numbers is missing (usually D). This concept appeared

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

**question # 41**.

**Number Dojo Level: 177**

At this point, I would typically refer you back to a similar concept like

**Mult%**. While that one is a very common concept tested, and a very useful skill to learn, it is actually unnecessary today. The process for this concept is actually a little closer to

**SolveX**.

**How to Solve:**

- Ignore the % signs completely, and then translate the math sentence into operations.
- Cancel out any common factors, and then multiply the constants on one side of the equation (if necessary).
- Divide both sides by the remaining coefficient (if necessary).

**Example 1: 20% of 90 is 40% of ___**

- Ignore the % signs completely; change this to
**20 x 90 = 40 x D**. - Cancel out the common factors (in this case, let's try 20). You're left with
**90 = 2 x D**. - Divide by the remaining coefficient.
**90 ÷ 2 = 2 ÷ 2 x D**. You're left with**45 = D**.

**Example 2: 12% of 48 is 36% of ___**

- Ignore the % signs completely; change this to
**12 x 48 = 36 x D**. - Cancel out the common factors (in this case, let's try 12). You're left with
**48 = 3 x D**. - Divide by the remaining coefficient.
**48 ÷ 3 = 3 ÷ 3 x D**. You're left with**16 = D**.

**Example 3: 14% of 78 is 39% of ___**

- Ignore the % signs; change this to
**14 x 78 = 39 x D**. - Cancel out the common factors (in this case, 39). You're left with
**14 x 2 = D**. - 14 x 2 =
**28**. This is your answer.

Example 4: 24% of 16 is the same as 8% of ___

Example 4: 24% of 16 is the same as 8% of ___

- Ignore the % signs; change this to
**24 x 16 = 8 x D**. - Cancel out the common factors (in this case, 8). You're left with
**24 x 2 = D**. - 24 x 2 =
**48**. This is your answer.

**Example 5: 18% of 16 is the same as 4 1/2 % of ___**

- Ignore the % signs; change this to
**18 x 16 = 4 1/2 x D**. - Cancel out the common factors (in this case, 4 1/2). You're left with
**4 x 16 = D**. - 4 x 16 =
**64**. This is your answer.

**Example 6: 36% of ___ is 12% of 210**

- Ignore the % signs; change this to
**36 x B = 12 x 210**. - Cancel out the common factors (in this case, 12). You're left with
**3 x B = 210**. - Divide by the remaining coefficient.
**3 ÷ 3 x B = 210 ÷ 3**. You're left with**B = 70**.

**Example 7: 43% of 6 is ___% of 2**

- Ignore the % signs; change this to
**43 x 6 = C x 2**. - Cancel out the common factors (in this case, 2). You're left with
**43 x 3 = C**. - 43 x 3 =
**129**. This is your answer.

**Here's a free worksheet to help you practice Mult%2:**

mult_2.pdf |

**Up Next for Middle School: Rectangle**