Expressions, when to add and when not to!

[JeffM]

OK guys you should not be so hard on me. I did point out at the beginning that I'd not had any examples of how to do these types of problems, and I did provide an example of how I did the problem, even though it was wrong, I did ask for advice. Please remember also I'm learning this on my own.

So here I have had another go at it now based on your replies above. Please advise how I'm doing this time...

We have;

[MATH]{4s}\times\frac{1}{2}\times rst-{2}(-\frac{1}{2}s)[/MATH]
Now if I look at the expression in two sections and work out each section one at a time, hopefully this will be correct, so here goes;

[MATH]{4s}\times\frac{1}{2}\times rst[/MATH]
I see this as [MATH]({4s}\times rst\times\frac{1}{2})=\frac{4}{2}r{s^2}t=2r{s^2}t[/MATH]
Now if I look at;

[MATH]{-2}(-\frac{1}{2}s)={s}[/MATH]
[MATH]={2}{r}{s^2}{t}+{s}[/MATH]

Looks good BUT notice that you could have simplified your answer. Furthermore, you have not done as I suggested, whiich is to test your result by substituting specific numbers and seeing whether they work. Part of the discipline of math is checking your work.

 

[Probability]

Hi. I quoted your first post, so that's your typing. (In this forum, one can use the link at the top of a quote to be taken to the source.)

You wrote -2a - (-4a) = -6a

That is not correct. Subtracting a negated quantity is the same as adding the opposite quantity. In other words:

-2 - (-4) = -2 + 4

I'm thinking the subtraction of -4a is a typo because your first expression adds -4a instead of subtracting -4a.

?

Your correct, yes that is a typo from my notes. It took some finding that did

 

[Probability]

Looks good BUT notice that you could have simplified your answer. Furthermore, you have not done as I suggested, whiich is to test your result by substituting specific numbers and seeing whether they work. Part of the discipline of math is checking your work.

I fully agree with you JeffM I really do, but please bare with me on this as it is a learning curve from first principles and the only guidance I've had is from this forum and you good members. I will get there.

 

[Probability]

OK JeffM here goes;

[MATH]{4s}\times\frac{1}{2}\times{r}{s}{t}-{2}-\frac{1}{2}\times{s}[/MATH]
[MATH]{4}\times{2}\times\frac{1}{2}\times{4}\times{2}\times{3}-{2}-\frac{1}{2}\times{2}={98}[/MATH]
and

[MATH]{2}{r}{s^2}{t}+{s}=[/MATH]
[MATH]{2}\times{4}\times{2^2}\times{3}+{2}={98}[/MATH]

 

[JeffM]

Perfect. Well done.

A note. Do not use 0 or 1 as test numbers. Why? Because 0 and 1 are very unusual numbers

a * 0 = 0. It is not generally true that a * b = b.
a * 1 = a. It is not generally true a * b = a.
a + 0 = a. It is not generally true that a + b = a.

0 and 1 may give results that would not occur with any other numbers.

A 2nd note. Try to include a negative number in your tests. Sometimes something is true just for non-negative numbers. Example

[MATH]a > b \text { and } ab \ne 0 \implies \dfrac{1}{a} < \dfrac{1}{b}[/MATH]
is FALSE. But if you test only with numbers of the same sign, you will conclude that it is true. The true statement is

[MATH]a > b \text { and } ab > 0 \implies \dfrac{1}{a} < \dfrac{1}{b}[/MATH]