My Math Forum Fractions in Order of Operations

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 August 23rd, 2018, 01:39 PM #1 Newbie   Joined: Aug 2018 From: Utah Posts: 6 Thanks: 0 Fractions in Order of Operations When using order of operations, do you simply put the top part of the fraction next to the bottom part of the fraction with a division sign in between them, or do the upper and lower parts of the fraction act as equations in parentheses? I have been simply rewriting the fraction as a division problem before trying to simplify anything. Is this acceptable? Would the parts of the equation that were written as a fraction need to be put in parentheses? Is (-10) - 6 (-2)^2 followed by - 5 functionally the same as (I wasn't sure how to make it clear that the "- 5" wasn't part of the fraction) -10 - 6 / (-2)^2 - 5 ? Or does it need to be [(-10) - 6] / [(-2)^2] - 5 ? Last edited by inomztietuseoe; August 23rd, 2018 at 01:45 PM.
August 23rd, 2018, 01:41 PM   #2
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Quote:
 Originally Posted by inomztietuseoe When using order of operations, do you simply put the top part of the fraction next to the bottom part of the fraction with a division sign in between them, or so the upper and lower parts of the fraction act as equations in parentheses? I have been simply rewriting the fraction as a division problem before trying to simplify anything. Is this acceptable? Would the parts of the equation that were written as a fraction need to be put in parentheses? Is (-10) - 6 (-2)^2 followed by - 5 functionally the same as (I wasn't sure how to make it clear that the "- 5" wasn't part of the fraction) -10 - 6 / (-2)^2 - 5 ?
You are missing parens on the last line. Do you see why? Could you please fix it and then go on?

Last edited by Maschke; August 23rd, 2018 at 01:48 PM.

August 23rd, 2018, 03:57 PM   #3
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Quote:
 Originally Posted by inomztietuseoe When using order of operations, do you simply put the top part of the fraction next to the bottom part of the fraction with a division sign in between them, or do the upper and lower parts of the fraction act as equations in parentheses? I have been simply rewriting the fraction as a division problem before trying to simplify anything. Is this acceptable? Would the parts of the equation that were written as a fraction need to be put in parentheses? Is (-10) - 6 (-2)^2 followed by - 5 functionally the same as (I wasn't sure how to make it clear that the "- 5" wasn't part of the fraction) -10 - 6 / (-2)^2 - 5 ? Or does it need to be [(-10) - 6] / [(-2)^2] - 5 ?
I think what you are asking is this

Does $\dfrac{(-\ 10) - 6}{(-\ 2)^2} - 5 = (-\ 10) + \{(-\ 6) \div (-\ 2)^2\} - 5$

or does $\dfrac{(-\ 10) - 6}{(-\ 2)^2} - 5 = \{(-\ 10) - 6\} \div \{(-\ 2)^2\} - 5$

The correct interpretation is the second. The horizontal bar separaring the numerator and denominator of a fraction acts like a grouping symbol (parenthesis) for both numerator and denominator simultaneously.

Once you understand that, PEMDAS will steer you correctly.

 August 23rd, 2018, 05:08 PM #4 Math Team     Joined: May 2013 From: The Astral plane Posts: 1,888 Thanks: 765 Math Focus: Wibbly wobbly timey-wimey stuff. Unfortunately I have caught a couple of both HS and College teachers interpret x + 3y / 2y - x as (x + 3y)/(2y - x). I tell you it's a blot on the profession! -Dan
August 24th, 2018, 10:57 AM   #5
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Quote:
 Originally Posted by Maschke You are missing parens on the last line. Do you see why? Could you please fix it and then go on?
I don't see it. Where? I'll admit I'm kinda flying blind here.

 August 24th, 2018, 11:52 AM #6 Global Moderator   Joined: Dec 2006 Posts: 19,541 Thanks: 1750 Don't worry - they were omitted so that your question made sense.

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