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Binomial division

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by SFtraveler » Wed Nov 24, 2010 11:30 pm
What is the rule on why 5a + 9 = 3b becomes 5a/3 + 9/3 = b and not (5a + 9)/3 = b when solving for b? I'm very rusty at algebra and trying to learn the rule to avoid making the mistake of not splitting up the numerator into two separate fractions, which leads to the wrong answer. [In this case, the right answer ends up being 5a/3+3=b.]
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by shovan85 » Wed Nov 24, 2010 11:44 pm
SFtraveler wrote:What is the rule on why 5a + 9 = 3b becomes 5a/3 + 9/3 = b and not (5a + 9)/3 = b when solving for b?
5a + 9 = 3b

This is the original equation.

Left Hand Side (LHS) is 5a + 9 and Right Hand Side (RHS) is 3b

Step 1: Multiple both sides by 1/3 (this also means "Divide both sides by 3")

Thus, (5a + 9) * (1/3) = 3b * (1/3)

Step 2: Open the brackets and make each term individual

Thus, (5a/3) + (9/3) = 3b/3

=> 5a/3 + 3 = b (Desired Answer)
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by SFtraveler » Thu Nov 25, 2010 12:02 am
Thanks shovan85, but I am looking for the rule on why your Step 2: "Open the brackets and make individual" is used so I know what to do in future on similar problems. Under what conditions is this the proper step to take?
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by shovan85 » Thu Nov 25, 2010 1:03 am
SFtraveler wrote:Thanks shovan85, but I am looking for the rule on why your Step 2: "Open the brackets and make individual" is used so I know what to do in future on similar problems. Under what conditions is this the proper step to take?
Hi

It is not a rule but to clarify your doubt I have pointed out. See the below again and the the line marked RED has been removed from your actual question that caused Doubt within you.

5a + 9 = 3b

=> (5a + 9) * (1/3) = 3b * (1/3)

=> (5a/3) + (9/3) = 3b/3

=> 5a/3 + 3 = b (Desired Answer)

Basically, In elementary algebra parentheses, ( ), are used to specify the order of operations, terms inside the bracket are evaluated first, hence 2×(3 + 4) is 14 and (2×3) + 4 is 10.
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