Joseph B.

asked • 10/29/14

How do you write this expression: The quotient of fifteen and three minus four?

Is a parentheses necessary, or not? 15/3-4 or (15/3)-4
 
 
This is a link to the worksheet, with the answer key, but I think it's wrong. Aren't the parentheses redundant here?
http://mrmaffesoli.com/Printables/5OA2/5OA2-TPT1.pdf

2 Answers By Expert Tutors

By:

Christopher R. answered • 10/29/14

Tutor
4.8 (84)

Mobile Math Tutoring

See tutors like this
See tutors like this
The parenthesis is not necessary; however, the the parenthesis can be used as a guide in determining that division comes before subtraction, and its not correct to say the expression is 15/(3-4).
Upvote • 0 Downvote
More
Report

Michael W.

Christopher,
 
If there aren't any quotes or parentheses in the original statement, then doesn't the english follow order of operations, too?
 
The quotient of 15 and '3 minus 4': would be 15/(3-4)
The quotient of 15 and the quantity 3 minus 4: would be 15/(3-4), too.
The quotient of 15 and 3 minus 4:  that's just 15/3 - 4 or (15/3) - 4, in the order it was stated
 
Why would we assume that the original wording implied "3 minus 4" in quotes?  I'm going with Joseph's answer key on this one.
Report

10/29/14

Michael W.

Oops!  I mis-read Christopher's original response.  All on the same page.  :)
Report

10/29/14

Christopher R.

The parentheses is necessary due to 15/3-4 is not equal to 15/(3-4). Moreover, 15/3-4=5-4=1, and 15/(3-4)=15/-1=-15. This is the order of operations. Note: The quotient implies division of two numbers. In this case, it would be 15 and (3-4)=-1.
Report

10/10/19

Michael W. answered • 10/29/14

Tutor
5.0 (1,458)

Patient and Passionate Tutor for Math & Test Prep

See tutors like this
See tutors like this
Joseph,
 
Necessary?  No.  Order of Operations says that division comes before subtraction anyway.
 
But it makes it 100% clear that it's not 15/(3-4).  Technically, it's not wrong.  Some would probably say that using the parentheses is better, just so it removes any doubt as to which order you intended.  Maybe it's something you should ask your teacher about in terms of their preference? 
 
Great question!
 
-- Michael
 
 
 
Upvote • 0 Downvote
More
Report

Joseph B.

This was my daughter's fifth grade homework. She did not put parentheses and got marked wrong because it didn't match the key. I thought her answer was correct without the parentheses. It seems redundant the way the key has it.
 
Joe
Report

10/29/14

Michael W.

Joe,
 
So, how about asking the teacher for some clarification so your daughter can improve her skills?  "My daughter wrote this, the key said that, and she was a little confused as to what the difference is or how she should write it going forward."
 
Seems innocent enough, and then everyone benefits from additional clarity.
Report

10/29/14

Christopher R.

Actually, the parentheses is necessary due to 15/3-4 is not the same as 15/(3-4). Moreover, 15/3-4=5-4=1, and 15/(3-4)=15/-1=-15. Note: The quotient implies division between two sets of numbers. In this case, it is 15 and 3-4=-1.
Report

10/10/19

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.