### Chap 4 Algebra... Help! What's Wrong?

Jane did the following:
• 3a + b = 3ab
• 2s + 4t = 6st
Do you think Jane is correct in her algebraic manipulations?
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. No,
3a + b= 3a+b
2s+4t = 2s+4t
They cannot be put together as the multiplied times of all the digits differ.

2. No.

Each alphabet represents a different number and the equation differ. Her answer shows that it is multiplied and not addition.

It should be:
3a + b = 3a + b
2s + 4t = 2s + 4t

3. no, she is not correct.

she is solving the problem through multiplication. so it is incorrect.

its suppose to be:
3a + b= 3a+b
2s + 4t= 2s+4t

4. No, she is not correct.

She is solving the problems by adding all the numbers and variables together.

It should be:
3a + b = 3a+b
2s + 4t = 2s+4t

5. Jane is not solving the problem with the correct method.

3a + b = 3ab

2s + 4t = 6st

It should be...

3a + b = 3a + b

2s + 4t = 2s + 4t

Reason : The value of a/b/s/t might not be the same, thus we cannot place the number which may have different values together.

6. No.

It should be:

3a + b = 3a + b

2s + 4t = 2s + 4t

The value of a,b,s and t may be different and we cannot put numbers that are different with different values together.She is also solving the problem using multiplication,which is incorrect.

7. No.

3a +b = 3a + b

and

2s + 4b = 2s +4b

8. This comment has been removed by the author.

9. Answer: No, Jane is incorrect in her algebraic manipulations.

Explanation: We all know that 3a is 3xa, and Jane's first answer was 3ab, which was definitely incorrect. If her answer was this, it should be 3xaxb and it does not have a quotient of 3a+b. They are totally different answers. The numbers of the algebraic expressions are different too.

Correct answers of the following questions:

1. 3a+b=3a+b
2. 2s+4t=2s+4t

No difference in mathematics

10. To:
Zhengjie
Yi Lin
Jurvis
Carisa
Jasper
Shamemi
Su En
Benz

You have rightly pointed out the mistakes and presented the right answer (i.e. the expressions are already in their simplest form).

What would you do (and how) to convince Jane that she's incorrect?

11. The rest of you... Would like to hear your responses to Jane soon?

- Pei Shan
- Abilash
- Hao En
- Lincoln
- Shakti
- Jia Sheng
- Christopher
- Darryl
- Yuzhe
- Priyanka
- Jaime
- Idris
- Lionel
- Karan
- Teo Yun

12. I would give her examples and tell her that that is not the simplest term in algebra as they are already simplified.

Here's the examples:

Example 1:
Let a&b be 2&3 respectively.
So 3a+b=3x2+3 that sums up to 9.
If Jane assumes that the answer is 3ab which is 3x2x3, it equals to 18 which is wrong.

Example 2:
Let s&t be 3&2 respectively.
So 2s+4t=2x3+4x2=14.
If Jane assumes the answer is 6st which is 6x3x2=36, it is wrong.

I think that this is enough to convince Jane that she is incorrect.

Benz Kew

13. Ans: No. Jane is wrong.

a,b,s,t are different numbers, by putting them together, she is multiplying them instead of adding them together.

Example 1:

Take (a) as 10 and (b) as 20

3a + b = 3ab

3a= 13
b = 20

13+ 20 = 33

That is how she should add them up instead of putting everything up.
So if she put 3ab, it is:;

20 x 10 + 3 = 203

There is a vast difference in the answers.

14. Miss loh, my name is TeoH Yun not Teo Yun, I have a H in my surname

15. No,
This is because when we add a alphabet with another,we will get for example ƒ+a= ƒ+a
So, the correct answer should be 3a + b = 3a + b
and 2s + 4t = (2s + 4t)

16. No, Jane is not correct.
First,lets simplify the first working.
3 x a + b =3a+b (This is the correct answer)
To get Jane's answer,substitute the plus for a 'x' to get the correct working: 3 x a x b
For the second working,to get the correct answer:
2s + 4t = 2s + 4t
To get Jane's answer: (2+4) x s x t : 6st

17. @Teoh Yun

Ah! My apologies :D

18. Benz and Teoh Yun

Yes.. you have provided good examples to convince Jane that the statements are not correct :D

Jia Sheng would be clearer if we try to use numbers?

Lionel: Ah! You were trying to describe where Jane might have made her mistake?

Hm... A Challenge to all...
What happens if a = b &
What happens if s = t
Will Jane be correct?
{hahah... it is growing to become more complicated...}

19. No. Jane has not expressed the terms correctly . To help her understand better and convince her , I have put some more examples.

3a + b = 3ab
2s + 4t = 6st

This expression is wrong. It should be ,

3a + b = 3a + b
2s + 4t = 2s + 4t

She should misunderstood the concept and confused herself with multiplication.Her answers would be correct if the pluses were replaced by times.

Here are other examples.

5y + z = 5y + z
8u + 6t = 8u + 6t

So , we can deduce that she has misunderstood these equations and each alphabet does not have the same value.

20. Hm... yes... it could be because Jane was careless and there's transfer error, apart from another likely reason - she 'mixed up' additon and subtraction :D

For the 2nd expression, 2s + 4t = 6st.
Jane insists she is correct.
Make a guess, how she would show us that she is correct?

21. No. 3a + b = 3ab cannot be right.
Because 3 x a x b = 3ab
So, 3a + b = 3a + b

2s + 4t = 6st is wrong too.
2s + 4t = 2s+4t.

22. Putting two algebraic expressions such as ab or xy is showing a multiplication of both expressions. For example u can use the exaple of backets. Puting 2 sets of brackets together means that you want to multiply them.
(2+3)(2+3)= 25 It is the same as...
ab= a*b= (a)(b)
Thus 3a + b = 3a +b as it cannot be simplified further. The same applies to the other one.
2s+4t= 2s+4t
I hope this is enough for poor... Jane. :)

23. No, because 3a + b = 3 * a + b
but 3ab = 3 * ab and is not 3 * a + b so it
is wrong.

2s + 4t = 2 * s + 4 * t

24. This comment has been removed by the author.

25. No,both of her algebraic manipulations are incorrect...
because...
a)3a + b =(3xa)+b
3ab=3xaxb

so if a=2,and b=4
then...
3a + b =(3xa)+b
=(3x2)+4
=6+4
=10
3ab=3xaxb
=3x2x4
=6x4
=24
Since 3a+b=10 ,and 3ab=24,it is not possible for 3a + b to be 3ab.

b)2s + 4t =(2xs)+(4xt)
6st=6xsxt

so if s=3,and t=5
2s + 4t =(2xs)+(4xt)
=(2x3)+(4x5)
=6+20
=26
6st=6xsxt
=6x3x5
=18x5
=90
Since 2s + 4t=26 ,and 6st=90,it is not possible for 2s + 4t to be 6st.

26. I think that Jane is wrong. She made a mistake that we all can make when we realise that when we say s times t = st. This is what we will be learning in Algebra later on.

Let me point out her first algebraic mistake.
3a + b = 3ab

She only made one mistake which is to get 3ab she needs to have 3a x b. At first glance this does not seem to be true, but this is how 3a x b will look in unsimplified manner. 3 x a x b. So if she did not mistake the plus sign for the multiplication sign, this is how it would have looked like.

3a x b = 3ab

This is true because in algebra the times sign is removed when numbers are multiplied with letters that represent missing numbers.

Let me point out to you her second algebraic mistake.

2s + 4t = 6st

Again she made the same mistake of mistaking plus for multiply. If she did not do that she would have gotten the correct answer.

If everything was correct it would like this.

2s x 4t = 8st

27. This comment has been removed by the author.

28. If Jane insisted that it was correct she would say that 2 + 4 = 6 and s & t is st. To a person who has not learn algebra yet he/she would think that what she says is logical, but it isn't. For s & t to become st there has to be a multiply sign.

29. No, I do not think that she has done a correct algebraic manipulation.

3a + b = 3ab
2s + 4t = 6st