## 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.

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".

--------------------------------------------------
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.

--------------------------------------------------

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.

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

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

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

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.

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

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.

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.

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

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

10. 3a+b=(3*a)+b
≠3ab

3ab=3*a*b

2s+4t=(2*s)+(4*t)
≠6st

6st=6*s*t

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

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