Thursday, April 28, 2011

Chapter 4: Algebra... Help! What's Wrong?

Jane did the following:
  • 3a + b = 3ab
  • 2s + 4t = 6st
Do you think Jane applied the correct algebraic manipulations process?
If yes, please write down examples to show that her answer is correct.

If not, explain to Jane her mistakes and help her to correct.

Enter your response in Comments.

12 comments:

  1. 3a + b ≠ 3ab

    3ab would mean -> 3 x a x b
    It would mean that a and b are multiplied together with 3. 3ab = 3a + 3b. There is 2 extra "b"s in 3ab.

    3a + b would mean that there are 3 of the variables "a" and 1 of the variable "b".

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    2s + 4t ≠ 6st

    6st would be 6 x s x t. Meaning there are 6 variables "s" and 6 variables "t". The answer would have vary a lot from the correct answer.

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    Jane is trying to simplify 2 algebraic expressions when they have already been simplified. There is no equation to this unless the numerical value of the variables are told.

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  2. Spot on this is about the wrong application of commutative laws for addition and multiplication.

    ReplyDelete
  3. 3ab= 3 x a x b which is not 3a+b

    6st= 6 x s x t which is not 2s+4t

    ReplyDelete
  4. Wrong.
    3a+b≠3ab
    '3a' is one variable and 'b' is another variable.
    3ab = 3xaxb
    example a=1 b=2
    so 3x1x2= 6
    but ,3x1+2= 5
    so it Jane is wrong

    For the second algebra expression, Jane did the same mistake again.
    2s+4t≠6st
    s+t does not mean s x t!
    So, Jane is wrong.
    She had add two different together and give a answer even though the original expression is the answer already

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  5. 3a+b=a+a+a+b therefore it is not equal to 3ab as 3ab means:3 x a x b
    2s+4t=s+s+t+t+t+t so it is not equal to 6st as 6st=6 x s x t

    ReplyDelete
  6. 3ab means 3 x a x b. The question asked for 3 x a + b. So she is wrong. 3a+b is not equal to 3ab.
    6st means 6 x s x t. The question asked for 6 x s + t. So she is wrong.
    6s+t is not equal to 6st.

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  7. the only way to get 3ab is via multiplication, so 3a+b will still be 3a+b
    the concept also applies for the second question.

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  8. 3a+b= 3a+b
    while jane ans is 3ab.
    3xaxb=3ab
    2s + 4t = 2s + 4t
    6st=6xsxt
    so , all the ans jane came out by multiply
    while the qn wants plus

    ReplyDelete
  9. a-> Orange
    b-> Apple
    3a+b-> 3 Oranges + 1 Apple
    Apple is not the same as Oranges
    3a+b is not 3ab as a and b are different
    'things'.
    3a+b = 3a+b and NOT 3ab
    --------------------------------------------------
    s->Books
    t->Handphones
    4s+2t-> 4Books + 2Handphones
    Books and Handphones are not the same 'things'
    4s+2t = 4s+2t and NOT 6st

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  10. 3a+b=(3*a)+b
    ≠3ab

    3ab=3*a*b


    2s+4t=(2*s)+(4*t)
    ≠6st

    6st=6*s*t

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  11. 3ab= 3 x a x b is the product of the two variables unlike 3a+b which is the sum of the two products
    so,

    3ab= 3 x a xb
    3a+b=3a+b

    AND

    2s+4t=2s+4t

    jane repeated the same mistake in the second question

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  12. She is wrong in both of the equations

    3a + b is not 3ab because it is addition and not multiplication

    2s + 4t is not 6st because it is addition and not multiplication

    ReplyDelete