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:

40 comments:

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

    ReplyDelete
    Replies
    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?)

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

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

      Delete
  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

    ReplyDelete
    Replies
    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.

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

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

      Delete
  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)
    Line 4:Answer:-8 7/12

    ReplyDelete
    Replies
    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.

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

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

      BTW, instead of adding posts, next time, please add further explanations via the "Reply" link to your original comment. It would be neater.

      Delete
  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

    ReplyDelete
    Replies
    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.

      Delete
  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

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

      Delete
  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)

    ReplyDelete
    Replies
    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.

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

    ReplyDelete
  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........)

    ReplyDelete
    Replies
    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.

      Delete
  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)

    ReplyDelete
    Replies
    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"?

      Delete
  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

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

      Delete
  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

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

      Delete
  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

    ReplyDelete
    Replies
    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?

      Delete
  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.

    ReplyDelete
    Replies
    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.

      Delete
  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.

    ReplyDelete
    Replies
    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.

      Delete
  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.

    ReplyDelete
    Replies
    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)?

      Delete
  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)

    ReplyDelete
    Replies
    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.

      ReplyDelete

      Delete
    2. Since he did not changed the mixed fraction to improper fraction, he took (1/3) and cubed it. After that, he added the answer with 1, thus he arrived at the answer of (1 1/27).
      Not taking note of the mixed fractions will result in major errors, as the whole number in every mixed number is part of the fraction and whenever we want to do something with it (e.g multiplication or addition) we must convert it to improper. The whole number then will not be left out. In this case of the working shown above, the person left out the whole number and only cubed the fraction [(1 1/3)^3].

      Delete