## Monday, April 18, 2011

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

Given a and b are 2 unlike terms.
It is given that

• 3a + b
• 2s + 4t

Jane did the following algebraic manipulation:
• 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.
[you may substitute values for both a and  to prove your case]

1. This comment has been removed by the author.

2. No jane is wrong. For example
a=2 and b=4
3(2) + 4 = 6+4 = 10 and not 6x4=24
The same for the second one..
s=3 and t=5
3(3) + 4(5) = 9+20 and not 9x20

3. No, I do not think that she is correct for both algebraic manipulations.
In the first example, a and b are two different terms altogether, so they cannot be 'combined' together to form ab. ab gives a whole different meaning altogether. It means that the two terms are multiplied together, not added up. This concept is also applied to the other manipulations.

4. No,she is not correct.
3a+b are 2 different algebric expressions,so they cannot be added together they can only be multiplied.
For example if I take a to be 3 and b to be 7
3(3)+(7)=3(10)
which is wrong if I take it as Jane's way
So Jane's concept is wrong.
9+7=16

Her errors are both the similar in concept.

5. No Jane is wrong. She can only do this if it is multiplication, not addition. e.g. 3a x b = 3ab. For example, let a be 2 and b be 3. 3a + b = 3 x 2 + 3 = 6 + 3 = 9. 3ab = 3 x 2 x 3 = 18. So Jane is wrong.

6. No she is not.
For example
a=2
b=3
3a + b = 3X2+3=9
while
3a + b = 3ab = 3X2X3=18
S=2
T=3
2s + 4t = 2X2+4X3=16
WHILE
2s + 4t = 6st =6X2X3=36

7. No,she is wrong
The answer that Jane gave is not the sum of the numbers but it i the product .

These numbers can only be added if one of the values ( a or b ) is given.

For Example , Take a as 1 and b as 2

A=1
B=2

3a + b = 3+2
=5

3ab on the other hand is 3x1x2 which is 6 so the answer is wrong

This proves that jane is wrong

8. No, she is not correct. Both a and b are stated that they are unlike terms, which means they are of different values. Hence, you cannot add them up and get ab. You can only multiply to get ab.
Hence, you should not get 3a + b = 3ab.
Since you cannot add them up, 3a + b = 3a + b

9. No, she is wrong.
Assuming A is 2 and B is 4.
3a + b= 10
3ab =24
Therefore, she is incorrect

10. Jane is wrong.
As she puts it,
3a + b = 3ab
2s + 4t = 6st
but,
3ab=3 x a x b
so, 3a+b is not 3ab
And you can use the same concept for the second example Jane did.
Example: a=3, b=4
3a + b= 3 x 3 + 4 = 9+4 =13
3ab= 3 x 3 x 4 = 9 x 4 = 36
Therefore Jane is wrong.

11. No she is not correct. Both expressions are unlike terms so they have different values and cannot be put together.
For example, a=4 and b=3
In Jane's case, she did this:
3(4)+3= 3(4x3)
= 3(12)
= 36
However if we simplify before putting together, the answer will be different:

3(4)+3=12+3
=15
If we see it in another way, a=marshmallows and b=beef strips. A marshmallow and a beef strip are different and can never be the same.
It is the same for the other equation.

12. Jane is wrong.
for example, a=2 and b is 3
In my way of interpreting the question, its
(2x3)+3=9
(2x2)+(4x3)=16

in jane's case,
its 3x2x3=18
6x2x3=36

13. Lindsay Oliver4/19/2011 04:13:00 PM

No she is not.
For example a=2 b=3
3a+b=(3x2)+3=9
S=2 T=3
2s+4t=(2x2)+(3x4)=16

14. No, she is not correct.

For instance, a = 5, b = 10
The correct equation should be, 3a+b=(3x5)+10=25
However, Jane's equation was, 3ab = 3x(5+10)= 150

For instance, s=5 and t=10
The correct equation should be, 2s+4t=(2x5)+(4x10)=50
However, her equation was 6st=6x(5+10)=300

15. Jane is incorrect.

a and b are both unlike terms, and ab cannot be derived from adding.
If I substitute
a = 5
b = 2
3a + b = 15 + 2 = 17
Jane's manipulation was 3ab, which was:
3ab = 3 x (5x2) = 30.

She made the same mistake for the second question.
If I substitute
s = 5
t = 2
2s + 4t = 2(5) + 4(2) = 10 + 8 = 18
6st = 6(5x2) = 72

16. No, she is wrong. For example, a=4, b=3
Jane saw the equation as
3(4) + 3= 3(4x3)
= 3(12)
= 36
When it should have been
3(4) + 3= 12 + 3
= 15
This is because they are unlike terms and have different values

17. She is wrong for both. She did not follow the 'Commutative Property of Addition' for algebra. This means that changing the order of the addends will not affect the sum. Example: a + b = b + a

18. She is wrong for both.
1) She saw it as 3a + b = 3ab. That is wrong because they are two different algebraic expressions and they can only be combined when it is multiplication.It should be 3a + b = 3a + b as they cannot be combined.

2) She saw it as 2s + 4t = 6st.The same rule applies here as well as they are both different algebraic expressions.

19. No.
1) a and b are different variables, thus we cannot combine both variables together. Note that 3a+b = 3xa+b, while 3ab = 3xaxb. This shows that both expressions does not equate.

2) Similarly, s and t are different variables, thus we cannot combine them.
2s+4t = 2s+4t, while 6st = 6xsxt. This shows that both expressions does not equate.