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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

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.


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randy patton


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


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