Amr A.

asked • 05/11/22

I am confused regarding order of operation

Hi

in this example

10+5/2+1

first I know the answer is of course 5

but order of operation stated that we must divide first then add or subtract

so how we here add first then divide?

another question regarding this too is why can't I just cancel out common factors

like the 2 and 10 here?

please note am a beginner also self taught so be easy on me thanx in advance


Peter R.

tutor
Not clear from your written question if it's 10 + 5/2 + 1 (3 terms being added) or (10 + 5)/(2 + 1) (division of 2 terms). 5 is the answer to the latter (= 15/3), but not the former.
Report

05/12/22

Brenda D.

tutor
Agreed. Amr A. Is your example written just like you have it above in your question? Or are you being asked to group the terms PEMDAS that yield the answer? Division of 2 terms appears to be the format that yields the correct answer.
Report

05/14/22

2 Answers By Expert Tutors

By:

Peter R. answered • 05/12/22

Tutor
5 (7)

Experienced Instructor in Prealgebra, Algebra I and II, SAT/ACT Math.
About this tutor ›
About this tutor ›

10 + 5/2 + 1 = 10 + 2 1/2 + 1 = 13 1/2.

vs. (10 + 5)/(2 + 1) = 15/3 = 5 PEMDAS (order of opns) says do operations in parentheses 1st.

[10/2 + 5/1 doesn't give correct answer] Not sure what you mean by "common factors".



Upvote • 1 Downvote
More
Report

Amr A.

please note am a beginner so pardon for "common factors" what I meant is in this example (10x5/2x1) I can directly divide 10 by 2 then multiply the quotient with 2 and get the result but if change the Multiplication sign in this example to + or - I can't divide the 10 by 2 my question is why?
Report

05/12/22

Amr A.

hope that clears it for you and thanks for replying
Report

05/12/22

Peter R.

tutor
If it's a multiplication problem (10x5/2x1) you can divide the 10 by the 2 and mult the quotient by the 5 (not 2) to get answer of 25. That's the same answer as if you just multiplied the tops and divided by the bottoms (10x5x1, all divided by 2 is also 25). PEMDAS rules say that you can do mult and division at the same level (left to right). The basic answer as to why it doesn't work the same way if you do + or - instead of x is that it doesn't give the correct answer! What about 5/2 + 10? That's 2 1/2 + 10 = 12 1/2. But, if you were to divide the 2 into the 10, you'd get 5 + 5 = 10 (wrong!)
Report

05/12/22

Amr A.

thanks a lot
Report

05/14/22

Maria J. answered • 05/17/22

Tutor
New to Wyzant

Making Sense of Math! Elementary and Special Ed Tutor, M.Ed.
About this tutor ›
About this tutor ›

Hi Amr A,

I hope I can help you make sense of order of operations! I use the GEMS acronym for the correct order. G - groupings, parentheses, E - exponents, M - multiplication and division, as they appear in problem left to right, S - subtraction and addition, as they appear in the problem left to right. So let’s start, 10+5/2+1. Any groupings, parentheses? No. Any exponents? No. Any multiplication or division? Yes, only one. 5/2=2 1/2. I encourage students to rewrite the problem as they solve. So now our problem reads 10+2 1/2 +1. Now we go to subtraction and addition in the order left to right. 10+2 1/2=12 1/2. Rewriting our problem 12 1/2+1=13 1/2 and that is our final answer, 13 1/2 or 13.5 if you prefer decimals.

Upvote • 0 Downvote
More
Report

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.