[CHALLENGE] Order of Operations

BigBeachBanana

BigBeachBanana

Senior Member
Joined
Nov 19, 2021
Messages
2,181
Instruction: Write the following mathematical expressions as to how you would enter them into a calculator using the following operations only:
Addition[+], Subtraction[-], Multiplication[*],Division[/], and Parenthesis[( )]. No latex code are allowed.
(Note: This challenge is meant for @eddy2017 to practice parenthesis)

Q1)[math]\frac{1}{1-x}[/math]Q2)[math]\frac{x(m-1)}{x-3}[/math]Q3)[math]\frac{m(x-1)+n(y-1)}{x-y}[/math]Q4)[math]\frac{x(m-1)}{x-y}-\frac{2x}{y}[/math]Q5)[math]\frac{x(m-1)}{x-y}-\frac{y}{2x}[/math]Q6)[math]\frac{x(m-1)}{x-y}+\frac{k(m-1)}{p-q}[/math]Q7)[math]\frac{x(m-1)}{x-y}+\frac{k(m-1)+10}{p-q}[/math]
 
Last edited:
I do not understand the instructions. Put it in perspective for me, please. I get you want me to assign grouping symbols where they belong in case they are needed. Is it what you want?.
 
Because I usually get equations with grouping symbols and I need to simplify those equations. That is what how we usually get tested on this. Simplifying algebraic expressions is the skill tested.
 
mmm posted one for me and got confused at the time because I did not lnow that 3 parentheses meant braces and thst two meant brackets. That confused me, but nothing else after that. I practice and practice, and I can say, I may make a mistake out of carelessnees but not because I don't know what to do.
 
eddy2017 said:
mmm posted one for me and got confused at the time because I did not lnow that 3 parentheses meant braces and thst two meant brackets. That confused me, but nothing else after that. I practice and practice, and I can say, I may make a mistake out of carelessnees but not because I don't know what to do.
Click to expand...
I'll do Q1) as an example.
[imath]\frac{1}{1-x}=[/imath]1/(1-x)
You only need to use () only, don't worry about using [ ] or { }
 
Last edited:
2-------(m-1)/(x-3)

3-------m(x-1)+n(y-1)/x-y

4-------x(m-1)/ (x-y)-(2x/y)

5-------x(m-1)/(x-y)- (y/2x)

6-----x(m-1)/(x-y) + k(m-1)/(p-q)

7-----x(m-1)/(x-y)+ k(m-1)+10/(p-q)
 
Last edited:
2-------(m-1)/(x-3) What happened to x?

3-------m(x-1)+n(y-1)/x-y Incorrect. Lack of parenthesis.

4-------x(m-1)/ (x-y)-(2x/y) Correct

5-------x(m-1)/(x-y)- (y/2x) Correct

6-----x(m-1)/(x-y) + k(m-1)/(p-q) Correct

7-----x(m-1)/(x-y)+ k(m-1)+10/(p-q) Incorrect. Lack of parenthesis.
 
Not that bad, eh.
and let lme tell you. a math teacher told me that the expression in the denominator does not necessary have to be in parentheses. it depends. in the case you marked as wrong he marked it ok. not saying you are wrong. just telling you
 
eddy2017 said:
Not that bad, eh.
Click to expand...
Also, not perfect. It means you need more practice.
eddy2017 said:
a math teacher told me that the expression in the denominator does not necessary have to be in parentheses. it depends.
Click to expand...
I agree, but you failed to recognize when necessary and when it's not.
eddy2017 said:
in the case you marked as wrong he marked it ok. not saying you are wrong. just telling you
Click to expand...
Who is this teacher you're referring to? If he told you this is correct, we're going to have a long conversation.
Test it for yourself with a calculator why the parenthesis makes a difference. In Q3, let m = 1, n=1, x = 4,y=2, plug those values into
Your answer: m(x-1)+n(y-1)/x-y
Correct answer: (m(x-1)+n(y-1))/(x-y)
You will get two different results, meaning what you have is incorrect.
 
Last edited:
eddy2017 said:
and let lme tell you. a math teacher told me that the expression in the denominator does not necessary have to be in parentheses. it depends. in the case you marked as wrong he marked it ok.
Click to expand...

Let me interject here, eddy2017. You did not tell us the context of the feedback from the math teacher. If he/she was referring to the vertical style as seen in the first post, then the math teacher is correct. Else, if he/she is referring to the
horizontal style as in post # 8, then the math teacher is incorrect.

Please write in sentences for our easier reading.
For example, capitalize the first words of your
sentences so we can readily see the breaks
between intended sentences.
 
BigBeachBananas said:
Also, not perfect. It means you need more practice.

I agree, but you failed to recognize when necessary and when it's not.

Who is this teacher you're referring to? If he told you this is correct, we're going to have a long conversation.
Test it for yourself with a calculator why the parenthesis makes a difference. In Q3, let m = 1, n=1, x = 4,y=2, plug those values into
Your answer: m(x-1)+n(y-1)/x-y
Correct answer: (m(x-1)+n(y-1))/(x-y)
You will get two different results, meaning what you have is incorrect.
Click to expand...
wowwww, you are right!!.
withput paretheses=1.25
with paretheses=3.5

one question now,
WILL I HAVE TO ALWAYS USE PARETHESES WHEN HAVING SOMETHING LIKE THIS

X(X-1) + 10 DIVIDING ENTIRE EQUATION/ X-Y
This x-y , does it always have to be in parentheses?. if not when parentheses can be disregarded?
 
eddy2017 said:
wowwww, you are right!!.
withput paretheses=1.25
with paretheses=3.5

one question now,
WILL I HAVE TO ALWAYS USE PARETHESES WHEN HAVING SOMETHING LIKE THIS

X(X-1) + 10 DIVIDING ENTIRE EQUATION/ X-Y
This x-y , does it always have to be in parentheses?. if not when parentheses can be disregarded?
Click to expand...
It depends on what you're trying to express:

[imath](x(x-1)+ 10)/(x-y) =\frac{x(x-1)+10}{x-y}[/imath]

[imath]x(x-1)+ 10/(x-y)=x(x-1) + \frac{10}{x-y}[/imath]

[imath]x(x-1)+ 10/x-y=x(x-1) + \frac{10}{x}-y[/imath]

Please study the differences.
 
BigBeachBananas said:
It depends on what you're trying to express:

[imath](x(x-1)+ 10)/(x-y) =\frac{x(x-1)+10}{x-y}[/imath]

[imath]x(x-1)+ 10/(x-y)=x(x-1) + \frac{10}{x-y}[/imath]

[imath]x(x-1)+ 10/x-y=x(x-1) + \frac{10}{x}-y[/imath]

Please study the differences.
Click to expand...
I have search for the correct way in which to use grouping symbols and I have found nothing but the same old stuff about PEMDAS GEMDAS and you work in side the brackets first and blah blah, nothing about these differences you're talking about. If you have videos or links where this is explained, please let me know. as far as working with equations and simplifying them i feel pretty confident. this is one skill I will be tested on.
 
Lay it on me, buddy!
Happy New Year's eve for you and lookagain!
lookagain, woow, there is a lot of math too in that head, my man!
 
eddy2017 said:
Lay it on me, buddy!
Happy New Year's eve for you and lookagain!
lookagain, woow, there is a lot of math too in that head, my man!
Click to expand...
Eddy

Let’s turn it around.

If you want to divide y by the sum of x and ten, you write it this way

[math]\dfrac{y}{x + 10} \text { or } y/(x + 10).[/math]
If you want to divide x by y and add the quotient to ten, you write it this way

[math]\dfrac{y}{x} + 10 \text { or } y/x + 10.[/math]
Math notation is a LANGUAGE. What is meant in any language is determined by that language‘s grammar. Grammar is arbitrary. But you must choose your grammar to fit your meaning. What is grammatical for one meaning is not grammatical for another meaning.

“Lucy loves Anthony“ has an entirely different meaning in English from “Anthony loves Lucy.”

The two sentences above contain identical words but have different meanings in English because the rules of English grammar are highly dependent on the order of words. In Latin, “Lucia amat Antonium,” “Lucia Antonium amat,” “Antonium Lucia amat,” and “Antonium amat Lucia“ all mean the same thing because Latin grammar is not highly dependent on the order of words.

You cannot do mathematics without learning the grammar of math notation.

PEMDAS is an abbreviation, an overly simple mnemonic, for part of the grammar of mathematical notation.
 
JeffM said:
Eddy

Let’s turn it around.

If you want to divide y by the sum of x and ten, you write it this way

[math]\dfrac{y}{x + 10} \text { or } y/(x + 10).[/math]
If you want to divide x by y and add the quotient to ten, you write it this way

[math]\dfrac{y}{x} + 10 \text { or } y/x + 10.[/math]
Math notation is a LANGUAGE. What is meant in any language is determined by that language‘s grammar. Grammar is arbitrary. But you must choose your grammar to fit your meaning. What is grammatical for one meaning is not grammatical for another meaning.

“Lucy loves Anthony“ has an entirely different meaning in English from “Anthony loves Lucy.”

The two sentences above contain identical words but have different meanings in English because the rules of English grammar are highly dependent on the order of words. In Latin, “Lucia amat Antonium,” “Lucia Antonium amat,” “Antonium Lucia amat,” and “Antonium amat Lucia“ all mean the same thing because Latin grammar is not highly dependent on the order of words.

You cannot do mathematics without learning the grammar of math notation.

PEMDAS is an abbreviation, an overly simple mnemonic, for part of the grammar of mathematical notation.
Click to expand...
that is something to be developed and learned as I go, with time and practice of can anyone find tutorials, videos or books dealing specfically with you are talking about hereabout this so called ''mathematical grammar''?. Thanks
 
eddy2017 said:
that is something to be developed and learned as I go, with time and practice of can anyone find tutorials, videos or books dealing specfically with you are talking about hereabout this so called ''mathematical grammar''?. Thanks
Click to expand...
It's something you can master within a day or even hours. This is all you need. Understand the differences below.

[imath](x(x-1)+ 10)/(x-y) =\frac{x(x-1)+10}{x-y}[/imath]

[imath]x(x-1)+ 10/(x-y)=x(x-1) + \frac{10}{x-y}[/imath]

[imath]x(x-1)+ 10/x-y=x(x-1) + \frac{10}{x}-y[/imath]
 
You must log in or register to reply here.
Top