## Monday, 17 February 2014

### 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. 3ab is actually 3 x a x b. 3a+b actually equals to 3a+b. 2s+4t equals to 2s+4t. 6st is 6 x s x t

2. No. 3a+b is not 3ab but actually 3a+b or 3b+a Since when broken down it is 3xa+b.
No. 2s+4t is not 6st but actually 2s+4t since when broken down it is (2xs)+(4xt).

3. No. They are both wrong. 3a+b is actually equal to 3a+b, while 3ab is actually equals to 3a x b.
2s+4t is actually equals to 2s+4t, while 6st is actually equal to 2s x 3t.

4. No. 3a + b cannot be simplified. 3ab is actually 3xaxb whereas 3a + b is 3xa + b
2s+4t = 6st is also wrong because 2s+4t is actually 2 x s + 4 x t and 6st is 6 x s x t

5. No, both the answers are wrong.
3a is actually equal to 3xa thus 3a+b≠3ab as 3ab is 3xaxb
2s+4t is actually (2s)+(4t) so it can't be 6st.

3a+b is not 3ab as 3ab is 3XaXb while 3a+b=3Xa+b.
&
2s+4t is not 6st as 2s+4t is 2Xs+4Xt and 6st is 6Xx+6Xt.

7. Both of her answers are wrong. 3a & b are not being multiplied so it should be 3a+b. 2s & 4t are of different 'base' so it should be 2s+4t

8. Both are wrong
3ab=3xaxb and 3a+b=3a+b
6st=6xsxt,while 2s+4t=2s+4t

9. both her answers are wrong. 3a+b= 3a+b and not 3ab = 3 x a x b. likewise, for 2s+4t = 2s + 4t ,not 6st = 6 x s x t
e.g----> assuming a= 2 and b = 3
3 x 2 x 3= 18
3 x 2 + 3= 9

10. Jane you are wrong.
3a+b is not 3ab but 3a+b as 3ab is 3 x a x b
2s + 4t is not 6st as 6st is 6 x s x t while the answer is 2s +4t

11. Both equations are wrong.
3a + b means 3 groups of a and one group of b.
2s + 4t means 2 group of s and 4 groups of t.

12. Jane is wrong.
3ab = 3 x a x b, but she puts 3a + b = 3ab, so she is wrong. 3a + b is already simplified.
2s + 4t is NOT equal to 6st because 6st = 6 x s x t. You can't add 2 and 4 together as they do not have the same variable. 2s + 4t cannot be known, unless we have the end result (solution) or the variables.

13. Jane is wrong.
3a+b will stay as 3a+b as it can't be simplified.
2s+4t will also stay the same as it also can't be simplified

14. Both equations are wrong
ab=3 x a x b
And the mistake repeats in the next equation.

15. 3a + b = 3ab: 3ab = 3 x a x b which is not equal to 3a + b. The answer is 3a + b because that is an expressions.
2s + 4t = 6st: 6st = 6 x s x t which is not equal to 2s + 4t. The answer is simply 2s + 4t because that is an expression.