Problem 24: If P/Q = R/S, which of the following is NOT true?

[happiness]

Problem 24. Is the answer letter d?

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[Dr.Peterson]

Problem 24. Is the answer letter d?

Can you tell us why you think the answer is d? That will give us a chance to have a more useful dialog to help you improve your style of thinking.

 

[happiness]

Actually I think it's C because they switched the fractions horizontally. I know it has something to do with means and extremes. I think.

Can you tell us why you think the answer is d? That will give us a chance to have a more useful dialog to help you improve your style of thinking.

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[Dr.Peterson]

Actually I think it's C because they switched the fractions horizontally. I know it has something to do with means and extremes. I think.

Yes, your answer is right, and one approach to the problem is to rewrite each equation in terms of "product of means equals product of extremes" (which is also expressed as "cross-multiplication"). All but C are equivalent in that form.

Another way to think of it is like what you say in your first sentence. I think of it this way: if you put a proportion into the form of a table,

P R
Q S

any form in which the same pairs (pr, qs, pq, rs in any order) appear in rows or columns, like

S Q
R P

or

S R
Q P

is an equivalent proportion. If any pairs are broken up (so that they are diagonal rather than in a row or column), then it is not equivalent.

But the cross-multiplication is probably easier.

 

[Steven G]

Problem 24. Is the answer letter d?

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Why is a valid? If two (non-zero) quantities are equal, then their reciprocals are equals. Ex: 2/3 =2/3 so 3/2 = 3/2.

Why is b valid? If A=B, then B=A

Why is d valid? If you multiply both sides by QS, choice d follows.

Why is c invalid? Counter example. We know 2/3 = 4/6 but 2*4 \(\displaystyle \neq\) 3*6, that is 8 \(\displaystyle \neq\) 18

 

[happiness]

I don't know if that can answer your question. I have never seen a problem like this.

Actually I think it's C because they switched the fractions horizontally. I know it has something to do with means and extremes. I think.

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[happiness]

Sorry, didn't read why you said it was C. Ignore my response, big thanks for your help Dr.Peterson

I don't know if that can answer your question. I have never seen a problem like this.

Sent from my LGMS210 using Tapatalk

Sent from my LGMS210 using Tapatalk

 

[happiness]

Yes, your answer is right, and one approach to the problem is to rewrite each equation in terms of "product of means equals product of extremes" (which is also expressed as "cross-multiplication"). All but C are equivalent in that form.

Another way to think of it is like what you say in your first sentence. I think of it this way: if you put a proportion into the form of a table,

P R
Q S

any form in which the same pairs (pr, qs, pq, rs in any order) appear in rows or columns, like

S Q
R P

or

S R
Q P

is an equivalent proportion. If any pairs are broken up (so that they are diagonal rather than in a row or column), then it is not equivalent.

But the cross-multiplication is probably easier.

Thanks, I understand now.

Sent from my LGMS210 using Tapatalk

 

[happiness]

Why is a valid? If two (non-zero) quantities are equal, then their reciprocals are equals. Ex: 2/3 =2/3 so 3/2 = 3/2.

Why is b valid? If A=B, then B=A

Why is d valid? If you multiply both sides by QS, choice d follows.

Why is c invalid? Counter example. We know 2/3 = 4/6 but 2*4 \(\displaystyle \neq\) 3*6, that is 8 \(\displaystyle \neq\) 18

Got it.