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Question
Hi,

For the following equation, I simplified it:

15/4 b+10/9 b

- Simplified expression -> 95/36 b

Does it matter where I put the "b" in the simplified equation?

- Meaning, can I put it after the "95" or the "36" or after the "line" dividing the two numbers apart, and it won't matter? And will it still be that same equation?

- Thanks

Answer
Julieanna, For this and the next question you asked, the term "associative law" should be "distributive law". Sorry.

For clarity, first off I'd write the original expression as

(15/4)b + (10/9)b

where b multiplies the 2 ratios in the parentheses. Using the associative property, we can write

[(15/4 + 10/9)]b.

Next, you want to write the ratios so that they have a common denominator and so can be added. You end up doing what is called "cross-mutiplying" to get the common denominator of 36

[  (9/9)(15/4) + (4/4)(10/9) ]b = [ (9・15)/(9・4) + (4・10)/(4・9) ]b = [ 135/36 + 40/36 ]b = (175/36)b.

This is different than your answer, so check our work!

As far as the placement of b is concerned, you could write it the way you have since the convention in a string of operations is to do the division before the multiplication. It is more clear the way I have written it. You could also write 175b/36  = (175b)/36, but 175/(36b) is wrong.

Randy

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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