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Algebra/A factoring question

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Question
Hello,

There is a tiny part of my math lesson that I am not quite getting. Here is the example problem:

Factor: 1/2x + 3/2y - 1/2

Their answer: 1/2(x+3y-1)

I am getting a grasp on how to factor in general, but the fractions in this case are throwing me off. I have no idea how they got whole numbers in the parentheses. Shouldn't the answer have fractions in there? How do I factor out when what I must factor by is a fraction?

Thanks for any help you can give,
Tressa

Answer
Hello Tressa,

Consider this problem:  2x+6y-2=2(x+3y-1), yes?

Now look at: (1/2)x+(3/2)y-1/2=(1/2)x+(1/2)*3y-(1/2)*1,
now factor the common factor of 1/2 (just like in the above problem we factored out the 2)...
This gives: (1/2)(x+3y-1)

Makes sense now?

TTYL, Abe

Algebra

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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