# data[].attributes.body
Prediction: Diana is correct
What Diana did  :
(40 ÷ 2) × 4

=80

What Cindy did:

40 ÷ (2× 4)

=5

ANS:Diana is correct.Since the divide came first,Cindy should work out the divide first and follow the order of operation instead of doing the times first but then tho if the bracket is added in like this :

40 ÷ (20 × 11)

we do the times first because everything in bracket need to be done first.

# data[].attributes.body
Diana is correct

Diana’s method
(40/2)x4
=20x4
=80

Cindy’s method
40/(2x4)
=40/8
=5

Conclusion:
This time both answers are different.
We should follow the order of operation so we should do it from left to right
In this case we have to do / then x so therefore Diana is correct as she followed the order of operation

# data[].attributes.body
Prediction:Diana is correct.

Cindy's working
40/2*4
=40/8
=5
Diana's working
40/2*4
=20*4
=80
examples :
72/6*2
Cindy:6*2=12
72/12=6
Diana:72/6=12
12*2=24

conclusion: They should use order of operation to solve questions like this.If the division comes first we should fiest do it. If multiplicatin comes first we  can do that or division.Division means we know the total so if it comes first we should do that first.
So Diana is correct in this situation.

# data[].attributes.body
A

# data[].attributes.body
Prediction: Diana is correct

(40/2) x 4
=20 x 4
=80
Ans: 80
Ans: Diana is correct

Conclusion:

The similarity between Thursday's example and today's is that both questions have a fluke in it but the example in Thursday's fluke was the same as the correct answer. Because when you carry out a operation for example; 3 x 4/2, we carry it out by making 3 x 4 which is = to 12, then divide it into 2 which is 12 divided by 2 which will give you a final answer of 6

# data[].attributes.body
Prediction:Diana

Answer:Diana:40/2x4
=(40/2)x4
=20x4=80
Cindy:40/2x4
=40/(2x4)
=40/8
=5
Diana is correct

Conclusion:According to the Order Of Operation for multipication an division we should solve the equation based on which one comes first.But to simplify things up it is just this: if the division symbol comes before the multipication symbol you must do the division first and vice versa.

Examples:
Example1:Diana's method,42/7x9
=54
Example2:Cindy's method,42/7x9
=2646

# data[].attributes.body
Prediction:Diana

Answer:
Diana: (40/2) x 4
=20 x 4
=80
Cindy: 40/(2 x 4)
=40/8
=5

Answer: Diana is correct

Conclusion : We cannot add a bracket behind a division or subtraction.

# data[].attributes.body
Prediction:Diana is correct
Cindy:2 x 4 = 8
40÷8= 5
Ans:5
Diana:40÷2=20
20 x 4 = 80
Ans:80
Answer: Diana is correct.According to Order of Operations, we do ÷ before x as ÷ came before x.

Conclusion:If the ÷ comes first,we cannot do x first, but if x comes first,we can do ÷ or x first

# data[].attributes.body
Prediction :
Diana is correct.

Working :

Cindy :
40 / 2 x 4
= 40 / 8
= 5

Diana :
40 / 2 x 4
= 20 x 4
= 80

Answer :
Diana is correct.

Conclusion :
According to the order of operations, we must do the one which comes first.
In this case, '/' comes first so we got to divide first, followed by 'x' which we will times next.

# data[].attributes.body
Prediction: Diana is correct
Cindy:
40 ÷ 2 x 4
=40 ÷ 8
=5
Diana:
40 ÷ 2 x 4
=20 x 4
80
Conclusion:Diana is correct. According to the order of operation for multiplication and division, we are supposed to work from left to right. In this case, division comes before multiplication, so we are supposed to do division first and that is why Diana is correct.
In the question that we did on Thursday, " x " comes before "÷"
but in this question, "÷" comes before " x ".
Example :
30 ÷ 5 x 2
Method 1(Do " x " first):
30 ÷ 5 x 2
= 30 ÷ 10
= 3
Method 2 (Do " ÷ " first):
30 ÷ 5 x 2
=6 x 2
= 12
When we use a calculator to work out the answer for the example, the answer is 12. From there we can conclude that we are supposed to work from left to right.

# data[].attributes.body
Prediction:I think that Diana is correct.
Working:
Cindy's method:
40÷2×4
＝40÷8
＝5
Diana's method:
40÷2×4
＝20×4
＝80
Answer:Diana is correct
Conclusion:
According to the order of operation,we will do the one that comes first so in this case the division comes first so we should do division first but not multiplication.

# data[].attributes.body
Prediction: Diana is correct
Diana: 40 divide by 2 times 4
=80
Cindy: 40 divide by 2 times 4
=5
Correct method: Diana's
According to Oder of Operations: we must work from left to right. If there is a bracket in the mathematical statement, we do the bracket first, then from left to right. If + or - comes first but times or divide comes second, we will have to do times or divide, then + or minus second.

# data[].attributes.body
Prediction : Both Diana and Cindy are correct.
Conclusion : Only Diana is corect.
Working:
Cindy : 40/2*4 = 40/8
= 5
Diana : 40/2*4 = 20*4
= 80
The definitely correct method is Diana's. However, Cindy's method can still be used if the question is:

40/(2*4)=40/8
=

# data[].attributes.body
Prediction: Diana is correct.
Cindy: 2x4=8
40÷8=5
Diana: 402=20
20x4=80
Conclusion: Diana is correct.
Explanation: Based on the order of operation, x and ÷'s order is from the left to the right which is whoever who comes first, hence Diana is correct as she solved the question based on the order of operation.

# data[].attributes.body
Prediction:
Diana is correct.
Working:
Cindy : 2x4=8
40 ÷ 8=5
Diana: 40÷2=20
20x4=80
Answer: Diana is correct.
Conclusion:
According to the order of operations, for multiplication and division, we should work from left to right, so in this case, Diana is correct.
The difference between this and Thursday's question is the position of the multiplication sign and the division sign.
We can also conclude that we can divide first if there are only multiplication and division sign even if it is after the multiplication sign.

# data[].attributes.body
Diana is correct
Cindy:2x4= 8
40/8=5
Ans:5
Diana:40/2=20
20x4=80
Ans:80
Diana is correct according to the order of operations,we will do the one that comes first and in this case, / came before x so Diana is correct

# data[].attributes.body
Jun Yang
Prediction: Diana is correct
Cindy method: 40 ÷ 2 × 4 = 40 ÷ 8 = 5
Diana method: 40 ÷ 2 × 4 = 20 × 4 = 80
Answer: Diana is correct.
Conclusion: According to the order of operations (for multiplication and division) , we should work it out based on which one come first
Example 1 : 30 ÷ 2 × 4 = 15 × 4 = 60
Example 2 : 30 ÷ 2 × 4 = 30 ÷ 8 = 3/1/4

# data[].attributes.body
Prediction : Diana is correct.
Working :
Cindy : 2 x 4=8
40÷8=5
Ans :5
Diana : 40÷2=20
20 x 4= 80
Ans :80
Answer : Diana is correct. Since the ÷ came before the x, we do the ÷ first (according to the order of operations).

Comparison : in this case, the ÷ came before the x, but for the other one, the x came before the ÷. another difference is that in this case, if we do either the ÷ or X first, we will get different answers. For the other one, regardless of whether we did ÷ or X first, we would still get the same answer.

# data[].attributes.body
(prediction): Diana is correct.
explanation:
Cindy:  2 x 4=8
40/8=5
Ans:5
Diana: 40/2=20
20 x 4=80
Ans : 80
So Diana is correct. As in this case the / came first not the x , so / should be done first .

# data[].attributes.body
My prediction:Diana is correct.
Working:
Diana:40÷2=20
20×4=80
Ans:80
Cindy:2×4=8
40÷8=5
Ans:5
Ans:Diana is correct.
According to order of operations we should do ÷ for that question but for the Thursday question we can do ÷ or ×
first.
Examples:
80÷4×5
Ans:100
4×6÷2

# data[].attributes.body
Prediction: Diana is correct.
Diana:
40/2x4
=(40/2)x4
=20x4
=80
Cindy:
40/2x4
= 40/(2x4)
=40/8
=5

Ans: Diana is correct.

Conclusion: We must follow the order of operations for this question ,starting with either x or / . But the question we did on Thursday will still allow us to get the same answer despite starting with different equations thus making the both of them correct.

# data[].attributes.body
Prediction: Diana is correct.
Diana:40/2×4
=40/2=20
20×4=80
Cindy:40/2×4
=2×4=8
40/8=5
Ans:Diana
We can do either × or ÷ first when × come first but we cannot do either ×or ÷ first when ÷ come first.
Examples 1 :
20÷2×4
=20÷2
=10
10×4
=40
20÷2×4
=2×4
=8
20÷8
=2/1/2
Example2:
20×4÷2
=20×4
=80
80÷2
=40
20×4÷2
=4÷2
=2
20×2
=40

# data[].attributes.body
prediction- Diana is correct
reason Diana's method
(40/2) x 4
=20 x 4
=80
cindy's method
40/(2 x 4)
=40/8
=5

why do we get different answers? now, lets take look, even if we did the subtraction sign or the plus sign first, both got the same answer

example
4+6-1
=10-1
=9
4+6-1
=4+5
=9

this proves that whenever it is addition or subtraction, order of operation does not matter. now lets try it on for multiplication and divison

4 x 6/12
=24//12
=2
4 x 6/12
=4 x 1/2
=2

we got the same answer

conclusion
whenever addition or subtraction come as a pair, or multiplication and division as a pair, order of operation do not matter(but if there is a bracket then we have to do the bracket first) . however ,if the come like this: 60- 5 x 5 , then the rule of order of operation must be applied . but  if it is like this:4 x 6/12 or 4+6-1,then it is not a must to follow the order of operation.

# data[].attributes.body
Prediction: Diana is correct.

Cindy's working:
40÷2x4
=40÷8
=5

Diana's working:
40÷2x4
=20x4
=80

Conclusion:

Diana is correct.

Reason: 40÷2x4
=40/2x4
=40x2
=80
40÷2x4
≠40÷8
But...
40÷2x4
=40÷(2÷4)
=40÷1/2
=40x2
=80
Just like addition and subtraction, if the addition is placed in front, order of operation would not matter, but if the subtraction is placed in front, in the bracket, the addition sign need to change to subtraction.

Example:
2+4-1
=2+3
=5
2+4-1
=6-1
=5

4-1+2
=3+2
=5
4-1+2
≠4+(-1)
4-1+2
=4-(1-2)
=4-(-1)
=4+1
=5

9÷3x6
=3x6
=18
9÷3x6
=9÷(3÷6)
=9÷1/2
=9x2
=18
9÷3x6
≠9÷18

# data[].attributes.body
40 ÷ 2 x 4
Cindy : we must do x then ÷
Diana : We do ÷ then x
Prediction:  Diana is correct.
Working:
Cindy- 40/8=5
Diana-20*4=80
Explanation:
Direct:
Diana is correct. According to the order of operations, we must work from left to right for multiplication and division.

2)

Who is correct? Cindy or Diana?
40 ÷ 2 x 4
Cindy: we must do x then ÷
Diana: We do ÷ then x

Actually, it depends on how you see it.

Cindy and Diana are regrouping the statement-in other words, using the Associative Property.

As how most people see it, the following statement is incorrect:

40/ (2*4) = (40/2) *4

However, by using the Associative Property, the following statement is correct:

40/ (2*4) = (40/2)/4

If you typed 40 ÷ 2 x 4 into the computer, the answer you would get would be 40/(2*4)=5 not (40/2)*4=80.

Division is associative. It is just that most people directly see it as 40/ (2*4) instead of (40/2)/4 which is the proper method.
https://www.jstor.org/stable/2972726?seq=1#page_scan_tab_contents
(The link also explains question one.)

In the past,  this was how they did it:
40 ÷ 2 x 4
=(40)/(2*4)
=40/8
=5
They would take the entire statement behind the divide sign and divide it by the entire statement in front of the divide sign.
But now, this method is discouraged.

# data[].attributes.body
Prediction:Diana is correct
Working for Diana=40/2=20
20*4=80
Working for Cindy=2*4=8
40/8=5
Conclusion:Diana is correct because as we can see that both Diana's and Cindy's  answer is different but  Diana is correct as she followed the order of operations and the comparison  between the thursdays's question and this is that  the thursday's question would give us the same answer if we divide or multiply first but this question would give us different answer even tough the signs in the question are the same.Hence, I think that Ben in the previous question was a fluke.
Example:
30/2*3
=30/2
=15
15*3
=45 (correct)

30/2*3
2*3
=6
30/6
=5(wong-did not follow order of operations)

Example 2:
60/3*2
60/3=20
20*2
=40(correct)

60/3*2
=3*2
=6
60/6
=10(wrong-did not follow order of operations)

# data[].attributes.body
Prediction: Diana is correct

Workings for Cindy:
2 x 4 = 8
40/8= 5
Workings for Diana:
40/2 = 20
20 x 4 = 80

Conclusion:
Diana is correct because in orders of operations stated that we need to use brackets first, then multiply or divide and lastly addition and minus. And in this question, we need to do divide first and then multiply so we can get the answer if we solve the answer from left to right. Thus, Diana is correct and Cindy is wrong.

# data[].attributes.body
Prediction:Diana is correct.

Working:
Cindy:
2 x 4=8
40/8 =5
Diana:
40/2 =20
20 x 4=80

Conclusion: Diana is correct because according to the order of operations, if multiplication comes first, then you must multiply first. But, if division comes first, then you must divide first.
So, in this case, division came first and Diana did division first so she is correct.

The question we did on Thursday was solvable as we were able to use two different methods
(Left to right and right to left)
and both of them were still able to get the same answer. But the right method is from left to right in order for us to get the correct answer.

# data[].attributes.body
Prediction: Diana is correct.

Cindy:
2 x 4 =8
40 / 8 = 5
Diana:
40 / 2 = 20
20 x 40 = 80
Conclusion: Diana is correct but Cindy is wrong. This is because Diana followed the order of operations by going in which comes first.
Here is the order:
Parenthesis
Exponents
Multiply OR Divide
Add OR Subtract
and also
which comes first.

# data[].attributes.body
Prediction:Diana is correct.
Working: 2 x 4 =8
40 /.8 =5(Cindy)
40/2=20
20 x 4 =80(Diana)
Conclusion: Diana is correct because according to the rules of order of operation, we should do the division first, than we do the multiplication.

The question that we did on Thursday was able to do from both directions of the questions but for this question, we must stick to the rules of operation  in order to solve it;.

# data[].attributes.body
Prediction: Diana is correct
workings:
Cindy: 2 x 4 =8
40/8=5
Diana:40/2=20
20 x 4 =80

Conclusion:Diana is correct,Cindy is wrong. According to the order of operation, we should start from  left to right, therefore in this case  we should divide first then multiply,so  Diana is correct and Cindy is wrong.
in the previous example, the question is solvable using 2 different methods from left to right and also right to left, however for this question , it is only solvable by using the order of operation, starting from left to right.
Example:
16 X 4 /2
following the order of operation, :
16 X 4=64
64/2=32
without following the order of operation: 4 /2=2
16 X 2 =32

# data[].attributes.body
Prediction :Diana is correct

Working for Cindy:
2 x 4= 8
40 / 8 = 5

Working for Diana:
40 / 2 = 20
20 x 4 = 80

Conclusion: Diana's method  is correct and Cindy's is wrong.
According to the order of operations, we must do which ever sign comes first, in this case, the divide comes first. So we are supposed to do the division first and not the multiplication.

The question we did on Thursday:

Both people are correct.

We can do the equations, and still get the same answer, even if we do it from left to right or right to left.

But for this question:

Only Diana is correct

We must follow the order of operations (working it out from left to right) in order to get the right answer.

# data[].attributes.body
Prediction: Diana is correct
Question 40/2X4
Cindy:40/2X4
=40/8
=5
Diana:40/2X4
=20X4
=80
Conclusion:Diana is correct. The rules of the order of operation stated that we have to solve the equation in the brackets then exponents then subtraction or addition. Also, we need to solve the question starting with the left and ending at the right.  Since the division sign came first, correct Order of this question should be division then multiplication.Cindy solved the question from the left to the right(multiplication then division) which is the wrong method but Diana followed the rules of the order of operation which is solving it from the left to right( multiplication then division) so her answer is correct.

The question we did on Thursday was solvable as Ben and Alan used different methods(right to left and left to right) but were still able to get the same answer.

# data[].attributes.body
Prediction: Diana is correct
*Diana's working*
(40 ÷ 2) * 4
= 20 * 4
= 80
(Because multiplication and division are supposed to be done together but from LEFT to RIGHT)

*Cindy's working*
40 ÷ (2 * 4)
= 40 ÷ 8
= 5
Conclusion: Diana is correct

But that was the boring part...
Let's take a look at why this is so:

When we ÷ or - (divide or subtract), we are performing what is known as a negative/non-associative operation

When we * or + (multiply or add), we are performing what is known as a positive/associative operation

In mathematics, we are always adding terms together, regardless of whether they are unknown variables or known integers.

This is why 3.5 means 3+0.5 and not 3-0.5

But how can this be? We also subtract at times, don't we?

Let's take a look at what we are actually doing when we subtract:
40-28

Like we do when we simplify algebraic expressions, let's break this equation down into each specific term:

(+40)|(-28)
We have a positive 40 and a negative 28.  What should we do find the answer to our equation? Add of course!

(+40)+(-28)
When we add things, we are basically taking a step on the number line. When we add negative numbers, we are also taking a step, but BACKWARDS. So, let's take 28 steps behind 40, what do we get? The answer is 12

Now, check if this correct by punching the equation onto your calculator. You should get 12! See? It's that simple

With that in mind, let's move on to the next part of the explanation. So, let's take a look at 2 things we say quite often:
Yes and No

When we say yes, we agree to something, in other words, we are positive about the decision and everything is okay.

When we say no, however, we disagree with it, in other words, we are negative about the decision, and feel something is wrong.

Now, you would realise that when we say yes, we can fully expand our answer to "Yes, I will go." (if the question is "Will you go?")

When we say no, we can fully expand our answer to "No, I will not go." (if the question is "Will you go?")

In other words, when we say yes, we keep the original meaning of the question in the answer but when we say no, we "flip" or reverse the meaning of the question.

Since we have already established that yes=positive and no=negative and that in mathematics, we are always adding things, we can safely say that when we do a negative operation, we flip the content inside.

So, when we do:
90 ÷ 6

We are basically doing:
90 * (1/6)
(As 6= (6/1) , when we "flip" it over, we get (1/6))

Go punch the first equation and the new equation in your calculator; you should get the same answer  – 15!

What does this mean? If we had multiplied first instead (like Cindy), our equation would be something like this:

40 ÷ (2*4)

Using what we have learnt so far, we can remove the brackets by "flipping" whatever is inside them

40  ÷  2  ÷  4
(Since the "flipped" version of * is  ÷ )

You would now realise that our new equation is DIFFERENT from our original question. Since we have already established that Diana is correct, since Cindy's equation has a TOTALLY DIFFERENT meaning, we can safely say her answer is wrong

But how come in the last problem, it works regardless of order?

4*10/2

We would realise that here, the multiply sign comes before the divide sign. So, over here, there is nothing for the divide sign  to "flip" except for the 2. But that would just complicate things.

So, since there is a multiply sign, we just keep everything like it is. So,
4*(10/2)
=4*5
=20

AND

(4*10)/2
=40/2
=20

In other words, we must always work from left to right to achieve the correct answer, regardless of which sign comes first.

OR

We can also just divide first ALL the time. It really works!

6*9 ÷ 2*5
=(6*9) ÷ 2*5
= 54 ÷ 2*5
=27*5
=135

OR

Divide first (even though it doesn't come first):

6*9  ÷ 2*5
=6*(9 ÷ 2)*5
=6*4.5*5
=135

So, it all boils down to your own taste. Whether you find the left to right rule easier or just dividing first...

If you want to know more about when we should divide first and when we should multiply first, you can look up facts about associative property on the internet.

Note:
The same applies for adding and subtracting as multiplication is basically repeated addition and division is basically repeated subtraction.

# data[].attributes.body
Prediction:
I think that Diana is correct.

Cindy:
2x4=8
40/8=5

Diana:
40/2=20
20x4=80

Conclusion:
Diana is correct. In the Order of Operations, we must solve the numbers in this sequence:
Brackets
Exponents
Multiplication/Division
Addition/Subtraction

For Multiplication/Division and Addition/Subtraction, we must solve it from left to right, whichever who comes first. For this case, we are suppose to solve the division first then the multiplication as the division sign came first so Diana is correct as she followed the rules of Order of Operations.

We were able to solve the question we did on Thursday using both methods as they happened to be the same answers and able to be solved using the two methods so it depends on the question but the right method would definitely be solving it from left to right.

# data[].attributes.body
I predict that Diana is correct.

Cindy's method:
2x4=8
40/8=5 (wrong)
Diana's method:
40/2=20
20x4=80 (correct)

Conclusion:
Diana's method is correct as she followed the rules of Order of Operations, doing the question from left to right. Cindy's method was to start doing the question from right to left, which is wrong.

The question we did on Thursday was able to be solved using both methods as the numbers coincidentally fitted both methods, even using the wrong method. Although we still get the correct answer using the wrong method, it is considered as a fluke But today's question is able to be solved by the correct method. If we use the wrong method to do this question, we will get the wrong answer.

# data[].attributes.body
Prediction : Diana is correct.

Working for Cindy : 40/2x4
=40/8
=5
Working for Diana : 40/2x4
=20x4
=80
Conclusion: Diana has the correct working . As stated in the rules of Order of Operations, we must go from left to right , so for this question we should be doing 40/2 first instead of 2x4.
Comparison: The question on Thursday was solvable by using both type of methods - solving from left to right and from right to left. However , this question is only workable if we solve from left to right , as stated in the rules

# data[].attributes.body
Prediction:
Diana is correct.

Working:
Cindy
40÷2×4

=40÷8

=5
Diana
40÷2×4
=20×4
=80

Conclusion
As you can see, Diana's answer and Cindy's answer are different. So Diana is definitely correct while Cindy is wrong. Like the rules of the Order of Operations we had learnt, we must do everything in the brackets first, then the exponents, following by multiplication or division and lastly addition or subtraction. As for the multiplication or division and addition or subtraction, we must always do it from the left to right.
Example:6÷2×7
=3×7 =21(√)
6÷2×7
=6÷14
=6/14(χ)

# data[].attributes.body
Diana is correct.(Prediction)
Cindy:40÷2×4=40÷8=5
Diana:40÷2×4=20×4=80
Diana is correct. (Conclusion)

# data[].attributes.body
Diana is correct .

working:
diana:

40/2*4
=20*4=80

cindy:

40/2*4
=40/8
=5

conclusion and comparison

Diana is still correct as we must follow the  order of operations. Do the 'bigger' signs first : '×' and '÷, then the 'smaller' signs: '+' and'-'. Also, we must go from left to right.If we compare this with Thursday's, both Alan and Ben were correct. Though they arrived at the same answer, I personally consider Ben's as a fluke as when we do the same thing this time, both arrive at different answers. So, it is always safest to stick to Alan's and Diana's working.