### 20120229: What's Wrong with this Solution?

Refer to the set of solution written in the board.
Identify as many error that you can spot and pen them in the comments.

After discussion:

1. (1 1/3)^3 and 1 4/5 should be converted to improper fractions before calculating.

1. elaborate more... why should (in fact, it's a must) we convert both fractions into improper fractions before calculating? (When what kind of calculations involved?)

2. Line 1:1 1/27 should be 2 10/27.
Line 2:should do the multiplication first.
Others in correct order.

1. Explain why 1 1/27 is not 1 1/27? and tell us how you obtain 2 10/27.

3. Line 1: 1 4/5 should be changed to 9/5 before the canceling method can be used{errata}.

Line 2: Even though 1 9/27 could be changed to 1 1/3 without changing to improper fraction, it is much safer to do so.

Line 3:Due to the person being crossed eye, he mistook the "-" sign as the "+" sign, making a foolish error

Line 4: He was correct to express the answer in improper question

1. Yes, you are right that "1 4/5" should be converted to improper fraction first as we are multiplying fractions (a rule to follow). By the way, we are used to saying 'cancelling' the numerator and denominator (for convenience and visual cue); however, in actual fact, there isn't such a method known as "cancelling method".

We can say, reducing the fractions by dividing the numerator and denominator with the common factors.

When penning down comments for error analysis, "being crossed eye" cannot be cite as a reason to justify the error made; hence, there is no such error that's known as "foolish error".

While the working values are already incorrect, conceptually, we know that from the 2nd last line, it's a smaller number subtracting a bigger number. Hence, it should result a negative value.

2. BTW, L.Z.Z is .....?

4. And one important thing, change mixed fractions to improper ones

1. Be specific to which line you are referring to.
Tell us why 'bother' to convert?

5. The answer is Negative(-) 103/12 or Negative(-) 8 7/12
Line 1:1 1/3 cube is 2 10/27. 1 4/5 x 25/4 = 45/4 or 11 1/4(Bodmas rule)
Line 2:2 2/3 - 11 1/4
Line 3:2 2/3 - 11 1/4(Un-simplify-able)

1. You have computed the 'actual' answer.
However, are you able to explain (conceptually) why, based on line 3, the final answer presented should be negative?

Similarly, for the rest of the steps, describe the conceptual error.

6. And one last thing I almost forgot, minus is NOT ADDITION!!!!!!(Line 3)

1. Still, need to be specific in your description, why "minus is not addition"?

7. (1 1/3)^3=2 10/27
because (1 1/3) x (1 1/3) x (1 1/3) = 2 10/27 and not 1 1/27 and also (1 1/3) must be converted to improper fractions

1 4/5 must be converted to improper fraction

1. Good explanation for the first part. It would be better if you move the part about 'converting to improper fractions' to the beginning of the sentence, then followed by describing how it should be done.

Next, why 1 4/5 must be converted first? Elaborate further.

8. Line 1:1 1/3^3 is not 1 1/27.
Line 2&3:1 4/5 x 25/4 is not 5
Line 4:3 2/3 is supposed to be -8 7/12

1. You have pointed out the errors. However, you have not explained why these are errors. What's wrong with them? Elaborate.

9. Error 1:(1 1/3)^3 is not (1 1/27). It should be converted into an improper fraction before calculating (1 1/3)^3 = (4/3)^3

Error 2:(1 4/5) should be converted into an improper fraction before calculating (1 4/5) ÷ (4/25) = (9/5) ÷ (4/25) = (9/5) * (25/4) = (9/1) * (5/4) = 9 * (5/4) = 45/4 = 11 1/4

Error 3:(1 9/27) --> The 9 and 27 should not be cancelled. It is the wrong concept. It should be 9 ÷ 9 and 27 ÷ 9 to show that it is simplified.

Error 4: (1 1/3) - 5 is not (3 2/3). 1 - 5 is -4. The fraction should be left untouched as it is being subtracted by a whole number. So the answer should be -(4 1/3)

1. Explanations for the first two errors are clear.

For error 3, in the midst of showing working within the expression, it is acceptable to write the ÷ in the form of "/". You are right that the proper way to describe, especially when we describe the working verbally, it should be like to simplify the fractions by finding common factors between the numerator and denominator, and divide them by this factor.

For error 4, a more direct manner to explain (without making reference to calculated value) would be the size of the number: i.e. subtracting a bigger number from a smaller number will result in a negative value.

10. line 1=we have to convert the 25/4 to improper fraction before calculating.

11. Line 1 : 1 1/27 should be 2 10/27 because (1 1/3)^3 is (1 1/3)^3x (1 1/3)^3x (1 1/3)^3 which is 2 10/27
Line 2 : it should not be 1x5 but instead 1 9/27 - 9/5 x 4/25 because you have to solve from left to right and 1 4/5 have to change to improper fraction which is 9/5.
Line 3 : it should be -7/15x4/25 instead of 1 1/3-5
( very confusing........)

1. Explanation for line 1 is correct.

For line 2, it is a good practice that we should following - work from left to right.
However, if it is obvious that the group of fractions does not involve any other operations like x or ÷ , then we can go ahead to work on the addition and subtraction first.

12. All mixed numbers should be converted to improper fractions before doing the calculations, the first two mix fractions should have their whole numbers multiplied by the power of 3(my english fail)

1. Explain why all mixed numbers should be converted to improper fractions first?
Need to elaborate/ describe further who you mean by "the first two mix fractions should have their whole numbers multiplied by the power of 3"?

13. Line 1:
1 1/27 should be 4/3^3=64/27
1 4/5=1 1/1 should be 9/5=9/1
25/4=5/1 should be 25/4=5/4

1. Tell us "why" these mixed numbers should be something else (as you've suggested).
The reasons to justify "what's wrong".

14. Error 1~<-Line 1->(1 1/3)^3 should convert into improper fractions and when solving the power, both the denominator and numerator must be to the power of 3. It should be (1 1/3)^3 = (4/3)^3 =(64/9)

Error 2~<-Line 1-> 1 4/5 should convert to improper fractions before dividing by 4/25.It should be 1 4/5 / 4/25 =9/5 / 4/25 =9/5 mu

1. The explanations are clear.
Note: It seems like you have not finished explaining "error 2"? (unfinished sentence?)

15. The two improper fractions should be converted to improper fractions at the start, before calculating.
he forgot the negative sign at the last line

1. Tell us why the impropoer fractions should be converted to improper fractions? Is this critical?

When explaining conceptual errors, "forgot" would not be a justification to the error.
What makes you think that it should be a negative value at the last line?

16. The fractions (1 1/27) and (1 4/5) should be converted into improper fractions.
The answer for (1 1/3)-5 is not (3 2/3),the answer should be a negative fraction as 5 is a whole number.

1. Tell us why we should convert them to improper fractions.

You are right that the final answer, based on whatever working presented (before that line) should be negative. However, you would need to 'generalise' your explanation, like it's because we are subtracting a bigger number from a smaller number, it will therefore result a negative value.

17. Line 1•(1 1/3)^3 should be 2 10/27 and not 1 1/27.
1 4/5 should have been converted into improper fraction which
would be 9/5.As this was not done, there was a mistake in
multiplying it by 25/4
Line 2•1 9/27 should not have been simplified
Line 3•no error
Line 4•the answer should be in negative. The answer is definitely wrong.

1. Tell us why (1 1/3)^3 should be 2 10/27? You are telling us the 'correct answer' for this part. By describing how you obtain 2 10/27, you would be able to point out how the error came about.

To explain "1 4/5 should have been converted into improper fraction", you would need to bring in the point that what must we do when we multiply 2 fractions?

Why 1 9/27 should not have been simplified?

Tell us what makes you think that the answer should be negative.

18. In the first line the mixed number 1 1/27 is wrongly evaluated from the number (1 1/3)^3. It should be 2 10/27. Not only that it should be changed to improper fraction and the last and final answer there should be a negative sign before the answer.

1. Tell us why it should be 2 10/27. By describing how you obtain this value, you should be able to point out how this error was made.

Tell us what makes you think that the final value should be negative (instead of positive value)?

19. In line 1, (1 2/27) is not equal to (1 1/3)^3. It is (1 1/3)*(1 1/3)*(1 1/3).
In line 2, the first fraction should not be (1 9/27) and should be (2 2/3).
In line 2, it is not (-1*5).
Overall, he should have taken note of the mixed fractions. Failing to notice them will result in confusion and ultimately his answer will be wrong.

Poon Wai Kit (19)

1. You have described what should be done. Would you be able to figure out how the error (1 1/27) came about?

You've attempted to do a generalisation "he should have taken note of the mixed fractions". Elaborate more on this.