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August 23rd, 2018, 02:39 PM   #1
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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 02:45 PM.
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August 23rd, 2018, 02:41 PM   #2
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Quote:
Originally Posted by inomztietuseoe View Post
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?
Thanks from topsquark

Last edited by Maschke; August 23rd, 2018 at 02:48 PM.
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August 23rd, 2018, 04:57 PM   #3
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Quote:
Originally Posted by inomztietuseoe View Post
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.
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August 23rd, 2018, 06:08 PM   #4
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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
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August 24th, 2018, 11:57 AM   #5
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Quote:
Originally Posted by Maschke View Post
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.
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August 24th, 2018, 12:52 PM   #6
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Don't worry - they were omitted so that your question made sense.
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