Can someone break this down further please?

P

predondo

New member
Joined
Jul 27, 2021
Messages
7
I'm taking an online algebra course for college credit and working through the textbook. This is an example in the textbook that I'm having trouble understanding:
(4t - 5/4s) - (2/3t + 2s) becomes somehow through the distributive property? :
4t - 4(t - 5/4s) - (2/3t + 2s) or maybe this is the step with the distributive property?
4t - 5/4s - 2/3t - 2s at this point I can understand how the commutative property gets used to obtain
4t - 2/3t - 5/4s - 2s and then just simplify (I'll skip that step here)
it's the first two steps that I'm having trouble wrapping my head around, any help is greatly appreciated.
 
predondo said:
I'm taking an online algebra course for college credit and working through the textbook. This is an example in the textbook that I'm having trouble understanding:
(4t - 5/4s) - (2/3t + 2s) becomes somehow through the distributive property? :
4t - 4(t - 5/4s) - (2/3t + 2s) or maybe this is the step with the distributive property?
4t - 5/4s - 2/3t - 2s at this point I can understand how the commutative property gets used to obtain
4t - 2/3t - 5/4s - 2s and then just simplify (I'll skip that step here)
it's the first two steps that I'm having trouble wrapping my head around, any help is greatly appreciated.
Click to expand...
I think your original problem is:

4(t - 5/4s) - (2/3t + 2s)...................... you may have misplaced the first "("

Can you take a photo of the worked-out problem and post it?

Please let us know....
 
predondo said:
(4t - 5/4s) - (2/3t + 2s) becomes somehow through the distributive property? :
4t - 4(t - 5/4s) - (2/3t + 2s) or maybe this is the step with the distributive property?
Click to expand...
Can you please check that you have typed this out correctly? Those expressions are NOT equal.
 
Distributive property: a(b + c) = ab + ac
[imath]4 \left ( t - \dfrac{t}{4} s \right ) = 4t - 4 \cdot \dfrac{5}{4}s = 4t- 5s[/imath]

Commutative property: a + b = b + a
[imath]- \dfrac{5}{4}s - \dfrac{2}{3}t = - \left ( \dfrac{5}{4}s + \dfrac{2}{3}t \right ) = - \left ( \dfrac{2}{3}t + \dfrac{5}{4}s \right ) = - \dfrac{2}{3}t- \dfrac{5}{4}s[/imath]

-Dan
 
Dr.Peterson said:
In their answers, they copy the original expression on the left-hand side and then work on that. But the LHS for (c) does not match the problem.

If you just replace that with the original expression, then everything makes sense. This is just a printing error.
Click to expand...
Thank you, it's something so small and simple! That's what I get for trusting authority (the textbook)
 
Last edited:
Dr.Peterson said:
In their answers, they copy the original expression on the left-hand side and then work on that. But the LHS for (c) does not match the problem.

If you just replace that with the original expression, then everything makes sense. This is just a printing error.
Click to expand...
Good catch!

-Dan
 
topsquark said:
Distributive property: a(b + c) = ab + ac
[imath]4 \left ( t - \dfrac{t}{4} s \right ) = 4t - 4 \cdot \dfrac{5}{4}s = 4t- 5s[/imath]

Commutative property: a + b = b + a
[imath]- \dfrac{5}{4}s - \dfrac{2}{3}t = - \left ( \dfrac{5}{4}s + \dfrac{2}{3}t \right ) = - \left ( \dfrac{2}{3}t + \dfrac{5}{4}s \right ) = - \dfrac{2}{3}t- \dfrac{5}{4}s[/imath]

-Dan
Click to expand...
Hello. I am using the same book and was stumped on this same thing. But I don't understand your answer though. I normally get the distributive property, but not here.

In the line describing ditributive, there is nothing I see like that in the equation, so i cannot see how
[imath]4 \left ( t - \dfrac{t}{4} s \right )[/imath]

relates to

[imath](4t - \dfrac{5}{4} s \right )[/imath] --the original

I substituted 2=t and 3-s like my instructor told me to do when in doubt, but I come up with different answers.

This book and problem have me all confused now and I suddenly don't think I understand anything.
 
Last edited:
stilltryin said:
Hello. I am using the same book and was stumped on this same thing. But I don't understand your answer though. I normally get the distributive property, but not here.

In the line describing ditributive, there is nothing I see like that in the equation, so i cannot see how
[imath]4 \left ( t - \dfrac{t}{4} s \right )[/imath]

relates to

[imath]\left(4t - \dfrac{5}{4} s \right )[/imath] --the original

I substituted 2=t and 3-s like my instructor told me to do when in doubt, but I come up with different answers.

This book and problem have me all confused now and I suddenly don't think I understand anything.
Click to expand...
Did you read post #7? Other answers failed to notice that what was printed is not what they intended. What you observe as wrong is, in fact, wrong!
 
Yes, I read that the book is in error. My question is regarding what topsquark provided as an answer. He wrote 4(t− t/t * s) and I do not see how he gets this from the original problem.

But then I can't see the original equation as being under distributive at all. I've only seen it where the term is already outside the brackets or it's apparent in ab + ac that ab and ac are now multiples of a.
 
Last edited:
stilltryin said:
Yes, I read that the book is in error. My question is regarding what topsquark provided as an answer. He wrote 4(t− t/t * s) and I do not see how he gets this from the original problem.

But then I can't see the original equation as being under distributive at all. I've only seen it where the term is already outside the brackets or it's apparent in ab + ac that ab and ac are now multiples of a.
Click to expand...

Surely you can see that topsquark, too, typed the LHS incorrectly! He meant to type this:
topsquark said:
Distributive property: a(b + c) = ab + ac
[imath]4 \left ( t - \dfrac{{\color{red}5}}{4} s \right ) = 4t - 4 \cdot \dfrac{5}{4}s = 4t- 5s[/imath]
Click to expand...

And that expression comes from the (mistyped) LHS in the provided solution (or perhaps from the attempted correction in post #2):

1654030584381.png​

When you know there are errors in a question, you need to look very carefully to find what's correct! Perhaps this whole thread should have been deleted, since it is so misleading.

Don't forget that the RHS in the solution agrees with the original problem, not the LHS of the solution.
 
So two errors, I understand this now.
It gets difficult when you're a learner and you know you have to trust an authority (book, instructor, whomever...), but you yourself can't identify the error because the subject is still above your head.

My main issue is still that, in the original problem --not the shown work-- how the distributive works for (4t - 5/4 s)
 
stilltryin said:
So two errors, I understand this now.
It gets difficult when you're a learner and you know you have to trust an authority (book, instructor, whomever...), but you yourself can't identify the error because the subject is still above your head.

My main issue is still that, in the original problem --not the shown work-- how the distributive works for (4t - 5/4 s)
Click to expand...
I like to think there's a 1 and -1 being multiplied by the parentheses.
\(\displaystyle 1\left(4t-\frac{5}{4}s\right)-1\left(\frac{2}{3}t+2s\right)\)

Distribute the +1 and -1:
\(\displaystyle 4t-\frac{5}{4}s-\frac{2}{3}t-2s=\frac{10}{3}t-\frac{13}{4}s\)
 
stilltryin said:
So two errors, I understand this now.
It gets difficult when you're a learner and you know you have to trust an authority (book, instructor, whomever...), but you yourself can't identify the error because the subject is still above your head.

My main issue is still that, in the original problem --not the shown work-- how the distributive works for (4t - 5/4 s)
Click to expand...
Are you talking about this step?

4 * [t - (5/4) * s] = 4 * t - 4*(5/4) * s = 4 * t - 5 * s

The 4 is getting distributed over multiplication.
 
What I understand from how I learned, is that inorder to break out the 4 from the brackets, you need both expressions to be multiples of 4.
4t is 4 *t that's okay. But 5/4s is not a multiple of 4.

I was taught BEDMAS is immutable and something cannot be taken out of brackets unless you can take it out of all every expression inside the brackets.

I mean, how can you take the 4 out of (4t - 5/4 * s) without needing to do anything to the -5/4*s?
 
stilltryin said:
My main issue is still that, in the original problem --not the shown work-- how the distributive works for (4t - 5/4 s)
Click to expand...

Here is what the work is supposed to look like:

1654089566396.png​

There is no distribution needed for (4t - 5/4 s); there you just have to drop the parentheses, which do nothing. The distribution they refer to is presumably for -(2/3 t + 2s), where they distribute the negative (that is, multiplication by -1).
 
So simple.
Distributive only affected the RHS as -1.
My brain feels unfried.
Thank you.
 
If you want to factor out a 4 from 5s/4, you can think of 5s/4 as 4*5s/(4*4) = 4(5s/16). Another words, you can factor out any quantity you want (other than 0)!
 
You must log in or register to reply here.
Top