Mult%2

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:

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

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

1. Ignore the % signs completely; change this to 20 x 90 = 40 x D.
2. Cancel out the common factors (in this case, let's try 20).  You're left with 90 = 2 x D.
3. 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 ___

1. Ignore the % signs completely; change this to 12 x 48 = 36 x D.
2. Cancel out the common factors (in this case, let's try 12).  You're left with 48 = 3 x D.
3. 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 ___

1. Ignore the % signs; change this to 14 x 78 = 39 x D.
2. Cancel out the common factors (in this case, 39).  You're left with 14 x 2 = D.
3. 14 x 2 = 28.  This is your answer.

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

1. Ignore the % signs; change this to 24 x 16 = 8 x D.
2. Cancel out the common factors (in this case, 8).  You're left with 24 x 2 = D.
3. 24 x 2 = 48.  This is your answer.

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

1. Ignore the % signs; change this to 18 x 16 = 4 1/2 x D.
2. Cancel out the common factors (in this case, 4 1/2).  You're left with 4 x 16 = D.
3. 4 x 16 = 64.  This is your answer.

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

1. Ignore the % signs; change this to 36 x B = 12 x 210.
2. Cancel out the common factors (in this case, 12).  You're left with 3 x B = 210.
3. 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

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

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

mult_2.pdf
File Size:	229 kb
File Type:	pdf

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Up Next for Middle School: Rectangle