### Chapter 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. Jane is not correct. 3a+b is already in its simplest form, as 3a is added to b, which is a different variable,not multiplied. It can only be 3ab if they are multiplied together.
2s+4t is not 6st, as s and t are also two different variables, thus 4 and 2 cannot be added together, neither can s and t.
Different variables in conclusion cannot be added together, but only multiplied together. So the answers are 3a+b and 2s+4t.

2. No, Jane is not correct. For the first statement, 3a+b=3ab,a and b are two different things. Thus, they cannot just be added like that. 3ab means, 3a*b/a*3b. The answer to 3a+b is (3a+b) as it cannot be simplified further. For the second statement, 2s+4t=6st, s and t are two different things. They cannot be added as they do not have the same value. The answer for 2s+4t is (2s+4t).

3. Both of Jane's statement are not correct.For the first equation, 3a+b is in the simplest form already hence it cannot be simplified anymore.3a+b is not equal to 3ab.3ab is actually 3a x b which is multiplication and not addition hence, this adds on to support my statement.
For the second equation, 2s+4t is not equal to 6st as they are two different variables which cannot be added together unless converted to the same form.6st is also a product of two variables multiplied together, which in this case, there definitely cannot be an addition sign.

4. Jane is incorrect, for 3a+b, she makes the mistake of changing the mathematical expression to 3axb, which would make it 3ab, but 3a+b=3a+b.
Her second answer is also wrong as she adds the numbers together and then multiplies the answer with the 2 letters, the correct answer should be 2s+4t=2s+4t

5. Jane is incorrect because 3a+b cannot be simplified further. What she did was put the 2 letters together. This is only valid if the 2 letters in the expression were the same, which in this case is not

For her 2nd answer, it is also incorrect. She made the same mistake as the first expression.

6. Jane is incorrect in both her statements. For her first statement, 3a+b is already in its simplest form. If the '+' was a 'x' instead, the statement would then be correct.
For her second statement, she cannot simplify it that way because s and t are of different values. Thus they cannot be added together.

7. Jane is incorrect, cause 3a+b is already simplified, which cannot be simplified further.

Jane is incorrect she made the same mistake as she did for the first question.

8. Jane is incorrect as a and b are two different values and are at their simplest form so it is wrong.

Jane is incorrect as she made the same mistake for the first question.

9. Jane is incorrect. ab= a X b which means that 3a + b is not = 3ab as 3ab is (a X b) x 3 and a and b are two different numbers the two number added are not equal to the two number multiplied.

Jane is incorrect. She made the same mistake as she did for the first equation. ( st= s X t which means that 2s + 4t is not = 6st as 6st is (s X t) x 6 and s and t are two different numbers the two number added are not equal to the two number multiplied.)

10. No, Jane is not correct.3a+b is already in its simplest form as a and b are two different things. 3ab in an normal equation is 3a*b/a*3b.
Jane repeats the same mistake on the second statement.

11. Jane is wrong. 3a+b and 2s+4t is already the simplest form. The variable must be the same for them to add. If the equation was 3a*b her answer would be correct. She repeated the mistake for the 2nd question.

12. No, Jane is not correct because she cannot simply put the letters together by adding. It is for multiplication. If the sign of operation was multiplication, then she would be correct.

13. No, Jane is not correct. 3a + b is not 3ab
3a + b = 3 x a + b.
3ab = 3 x a x b.
Lets assume a is 5 and b is 7.
3 x 5 + 7 = 22. (3a + b)
3 x 5 x 7 = 105 (3ab)

Likewise for 2s + 4t = 6st, 2s + 4t is not 6st.

We cannot put letters together if we want to add. It is considered as multiplication.

14. To all who have posted your responses.
Yes, you are correct!
Jane has mixed up the 2 operations "+" with "X".

Would someone be able to tell us a SPECIAL CASE when 2s + 4t equals 6st?
That is, what are possible values of s and t if 2s + 4t is equal to 6st?