Order of Operations: Simplify 60/5(7-5) and 2+5(8-5)

This video reviews how to simplify two basic expressions using the order of operations.

With so many questions about these 2 expressions, here is verification of the values using Wolframalpha:

[jiminverness]

0:49 Multipy and divide left to right? But there is no explicit multiplication symbol. What do your "order of operations" say about implicit multiplication by juxtaposition? Just ignore it and magically insert a * symbol? That's what you seem to be doing, and there is nothing about that written in your list of "order of operations".

[wokeupinapanic]

The two is still a parenthesis. You can't just ignore that. You haven't simplified the parenthesis down, and are thus ignoring a step.

[charlevaanderson]

I want to know in the first equation you didn't do 5(2) but did 5(3) in the second?

[summerscott]

But it says multiple and divid from left to right ?

[bryanortega]

You don't ignore the parentheses just because you feel like it. There's no rule that states it's to be ignored because a single integer is remaining

[charkman]

this math sentence mean 60 divide by 5 of the difference of 7 and 5.
think about x= 7-5 then 60 divide 5X
what you think?

[rogersummers]

You can also think of the division sign as the line in a fraction that separates the numerator and denominator. For example 1/2 means 1 divided by 2 or .5 . If we look at the problem the same way (and we are not changing the problem if we do we can so 60 divided by 5(7-5) or 60 over 5(7-5) as in a fraction. Therefore 60 divided by 10 = 6

[Barakamengi]

In the UK we call BIDMAS, and did the same and got 17 too. Thanks

[dgkcpa]

Answer is unambiguously 6.
5(7-5) is a product. Division by a product = division by its factors .
Too many people mistakenly assume that because 5(7-5) is a product, that they can divide by 5 and then multiply the result by 2, instead of continuing to divide by the remaining factor (2).
This easy and careless mistake is overlooked by most people performing "order of operations"
60÷5(7-5) = (60÷5) ÷ (7-5) not (60÷5) * (7-5) or more simply, 60/5/2, not 60/5*2.

What about calculators like Wolframalpha? It gives two different results, depending on the symbol used:
60/5(7-5) evaluates as 24, but
60:5(7-5) evaluates as 6 - go figure.
BTW, WA is not wrong or at fault, it tells you the assumptions it makes.
It's up to you to determine whether those assumptions are correct and appropriate to the expression being evaluated.

Which is the right answer? We can prove this easily

60÷5(7-5) = n
Multiply both sides by 5(7-5) and you get
60 = n * 5(7-5)
Simplify
60= n* 5(2)
60 = 10n
divide both sides by 10
6 = n

Proof:
6*5(7-2) = 60
divide both sides by 5(7-5) and voila:
6= 60÷5(7-5)

We can prove this another way:
5(7-5) is an example of the distributive property in action: 5(7-5) = (35-25)
If we substitute (35-25) for 5(7-5) we get:

60÷5(7-5) = 60÷(35-25) = 60÷(10) = 6

Six is the correct answer, 24 is an error and the result of an easily made mistake when evaluating the expression.

[GrimReaper]

Ok, I'm lost. 2+5(3) PEMDAS says to do what's IN parentheses. 2 and 5 is not in there. So how is 5 automatically in the parentheses. Because the VERY FIRST STEP you did. Was (8-5). Nowhere in there does a 5 magically fall into 3×5 when 5 isn't in there.

[summersunrise]

This is a great lesson in the multiply and divide from left to right. Otherwise, students may say the answer to problem one is 6.

[jojobaltan]

5(2) is still an unresolved parenthetical expression, and this notation is denoted by juxtaposition, therefore it has higher precedence than explicit multiplication or division lol. Algebra and all of math laws agree with me though. Lol

[duckmanjoel]

But in the first example you still have parenthesis. You must get rid of the parenthesis first. So 5(2) =10. 60 divided by 10 equals 6. Or you can look at it 60/5(2). 60/5=12. Move left to right 12/2=6. Or you can 60/5(7-5)= 60/(35-25)= 60/10=6..Anyway you do it, the answer is 6. You used PEMDAS incorrectly. Parenthesis FIRST. This is simple math. But don't feel bad because Google has it wrong too. The equation tricks the computer The computer interprets the parenthesis as a multiplication only. Harvard professor says 6. The juxtaposition of the 5(7-5) cannot be ignored and is understood by real mathematicians. The problem is a trick for math teachers and standardized thinkers who get 24. But the real answer is 6.

[TaeterTot]

Isn’t 60÷5(7-5) the same as saying:
60
———— ?
5(7-2)

[delwinjohnson]

This 5x(7-5) does NOT come before 60÷5. And in no situation do you multiply 5x7 and 5x5. I can not even comprehend how someone could come up with that. Parenthesis always come first.

[madisonwalton]

GEMS is a much better acronym than PEMDAS

[teotheterrible]

Another proof - the division is before the parenthesis, so if you divide by multiplier, then you divide by the result in the parenthesis. Otherwise you cannot do the expression in reverse and get the same divisible. Example 60 / 5 / (7 - 5) = 6.

[teotheterrible]

Another proof - with example. Lets say you have 60 sheets of paper. On the other hand you have 5 groups of students. The groups of students used to be 7 people each, now 5 students of each group are sick. So you have to divide the 60 sheets of paper equally to each student of the 5 groups. So you have 60 sheets / 5 groups (7 - 5 students) = how many sheets per student?
Simple 60 sheets / (5 groups * 7 students total - 5 groups * 5 students missing) = 60 sheets / (35 students total - 25 students missing) = 60 sheets / 10 students present = 6 sheets per student. You don't divide by a multiplier! Each number in the parenthesis gets multiplied by the initial multiplier infront! SIMPLE!

[Nixha]

I’m here to win a Twitter argument against a guy named Brian thank you

[tjsn-vision]

This is why I hated this. The steps are never the same and very confusing because how the set up is the same but it changes.