You are very resistant aren't you? ?
The method you have followed is not that which I have tried to encourage you to use but you seem to be determined to persevere with yours even though it is producing the wrong answers (principally due to the 'early rounding' that I tried to warn you against) so I will go over what you say and try to show you again how to simplify the process. Both of the answers in your post are out by a sixteenth of an inch. Not much, perhaps, but, since you are determined to work to that level of 'accuracy', I trust you will agree that even that small(?) error is not really acceptable?
As @Dr.Peterson and I have both shown you, the correct answer is "8 feet, 9 1/8 inches" (courtesy of DrP in Post #8) or "8 ft 9\(\displaystyle \frac{2}{16}\) in" which I showed you (in detail) how to calculate my easy way in Post #9.
No, no, no, no!
What you should be "working with" is:-
\(\displaystyle \frac{77}{1,136}=\frac{342}{h}\)
The two fractions you have constructed are equivalent to each other (hence the = sign); they are not to be multiplied!
So rearranging, you get: \(\displaystyle \frac{77}{1,136}=\frac{342}{h}\Rightarrow h=\frac{1,136 × 342}{77}\)
Which (somehow) you did arrive at! (Perhaps you are just writing in the wrong arithmetic operator but somehow 'know' what you're trying to do?)
Now this is where you are going wrong! I have repeatedly tried to encourage you NOT to approximate/round until you get to your very last calculation result!
I have absolutely no idea what you are doing in those two lines!
So, lets see if we can get the right answer (your way).
For the remainder of this section, all the numbers are just what are displayed on my calculator; I am not writing them down anywhere or re-entering them into the calculator, all the calculations shown just follow on from each other on the calculator!
If we start with the rearranged fraction equivalence...
\(\displaystyle h=\frac{1,136 × 342}{77}=5045.61039\) (sixteenths of an inch!)
So, 5045.61039 ÷ 16 = 315.3506494 inches.
Subtracting the 315, we can do 0.350649351 × 16 = 5.610389616 ≈ 6 (sixteenths of an inch) which is the remaining (fractional) part of the inches figure.
[Note how the “.3506494” (2 lines above) ‘changes to “.350649351” (1 line above) because the calculator works to a greater degree of accuracy than it displays!]
Now we can do: 315 ÷ 12 = 26.25 feet.
and subtracting the 26, 0.25 × 12 = 3 inches to give us the final answer of: 26 ft 3\(\displaystyle \frac{6}{16}\) in (correct to the nearest sixteenth of an inch).
I wanted to continue in this post to show you again my way of doing this in an attempt to illustrate how much simpler it is but the site is 'playing up’ (very badly) and I’ve had to bounce all around the world (using a VPN) to get this far! So I will just post what I’ve written so far and continue in a new post once the site has settled down again either in the next hour or so or tomorrow (for me) if it still isn’t working properly.
I think one problem that I have that is also a problem that you are having with me is that I have forgotten so much in terms of mathematics. Literally, aside from the basic arithmetic of addition, subtraction, multiplication, and division, ratios are the most advanced application of mathematics that I can remember. And what I remember was taught to me back in Middle School or so. What little I can remember of those classes was the following:
I have the first ratio:
1
___
4
and the second ratio that I need to solve for:
5
____
h
To find out h I needed to multiply the denominator of the first ratio with the numerator of the second ratio, and then divide that answer by the numerator of the first ratio.
So:
1 5
____ * _____
4 h
or
(4 * 5) / 1 = 20 / 1 = 20
Therefore, If 1 is equal to 4 than 5 is equal to 20.
Another problem that you and I might be facing is our intent in things. I guess to peel back the curtain, maybe it's time to tell you what this is for.
I have 2 action figures in my collection, one with a rather large "pompadour" shall we say, and one that's just flat out WYSIWYG. On a day of way too little to do and way too much introspection, I was wondering, if the pompadoured figure was scaled to a point where the top of its face was at the same height as mine, 5 Foot 11 Inches, how tall would the scaled up figure be if I were to measure to the top of its pompadour. Then, because my autistic mind couldn't stand to leave well enough alone, I also wondered what the height of my tallest figure in my collection would be if it were to be scaled up porportionally according to the results I got with the first figure.
So I used the only tape measure I could find in my house that measured only in feet and inches. Now because this is something as inconsequental as scaling up the size of stupid action figures, and not a question in an exam book or a job, or something like life or death, I look at being just a sixteenth of an inch off in my final result as hey, that came to be pretty damn close.
A third issue is the way I am typing out some of these equations. I have no idea how to make the fraction 4/5 look like the way you've got your fractions displayed. So that 315 5/16 that you are going "Huh???" about is supposed to be displayed as the whole number of 315 followed by the fraction of 5/16, corresponding to the measurement of 315 and 5/16ths of an inch.
However, if you say that the correct answer to my ultimate question is 26 Feet and 3 6/16 of an Inch and the answer that I came up with 26 Feet and 3 5/16 Inches, then I must have learned something from you as before I made this thread, I had NO idea how to even begin finding out the answer to this question using my own pen and paper.
You were also correct about something else. I am indeed a stubborn idiot. I haven't used my mind really at all in the past decade and a half. I used to be fairly intelligent, but over a decade and a half of not exersizing my brain has left my mind in a state where ratios are the most complicated thing I can remember and even that is getting a little foggy for me now. Couple that with my autism and you've got a perfect storm of stubborness and idocy. I'm sorry if I stressed you out at all. I really do thank you for getting me to this point because, as I said before, I needed to register on this forum because I simply didn't know how to structure my question in a way that would get me to the starting point of solving it. But thanks to you, I was able to come away with an answer that is only 1/16th of an inch off. That's awesome, and you DID teach me something or else, I wouldn't have been able to get that answer. I do graciously thank you VERY much for your patience and understanding. You did indeed help me.
