Ratio's

Probability said:
I have various makes of calculators such as the CASIO fx-85GT Plus and a more advanced Texas Instruments TI-83 graphics type. I have various books on these calculators but at time of writing this I have not managed to find the manufacturer book on the TI-83.

I like learning using pen and paper and find it interesting to work out solutions to problems, and when I have some misunderstandings (as I have a good few of), good members like yourself on this forum help me understand a great deal, which is very much appreciated. The calculator would provide me a solution to a problem that I could use to check my understanding from pen and paper, and when I make mistakes, errors in my understanding, hopefully I'd be able to see it and work it out more quickly if the calculator could provide an answer!
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TI-83 Plus / TI-83 Plus Silver Edition Guidebook
 
Probability said:
Sorry if I'm not being clear in my explanations, but will a calculator solve those types of ratios as you have just completed?

A ratio such as 12:18 I can enter as a fraction which will = [MATH]\frac{2}{3}[/MATH] but entering 12:18:24 will not provide the correct answer in my experience using a calculator, unless there is a specific method to follow!
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No!, 2:3 is 2/5 or 3/5 Not 2/3!
 
Thank you very much Subhotosh Khan

Looking again at the ratio [MATH]{12}:{18}:{24}[/MATH] when I enter that ratio into the TI 83 Graphics Calculator with reference to page 70 of the guide book, the calculator displays a result of [MATH]\frac{1}{36}[/MATH]
If I simplify the ratios[MATH]{12}:{18}:{24}[/MATH] manually [MATH]{2}:{3}:{4}[/MATH] then if I enter that ratio into the TI 83 calculator and press MATH (1) the calculator shows the simplified result [MATH]\frac{8}{9}[/MATH].

This is a really good improvement for me because now after cancelling fractions and ratios I can check my work and see if I got it correct.

A BIG thank you to this forum, its staff and members.
 
Jomo said:
No!, 2:3 is 2/5 or 3/5 Not 2/3!
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Jomo, I don't understand your reasoning sorry. A ratio of [MATH]{12}:{18} =\frac{2}{3}[/MATH] when simplified. A ratio of [MATH]{2}:{3}[/MATH] in its simplified result cannot be [MATH]\frac{2}{5}or\frac{3}{5}[/MATH] I'm not sure where you are going with your explanations!!
 
You have 5 items. 2 goes to person A and 3 goes to person B.

A gets 2/5 of the items and B gets 3/5 of the items.
 
Probability said:
Jomo, I don't understand your reasoning sorry. A ratio of [MATH]{12}:{18} =\frac{2}{3}[/MATH] when simplified. A ratio of [MATH]{2}:{3}[/MATH] in its simplified result cannot be [MATH]\frac{2}{5}or\frac{3}{5}[/MATH] I'm not sure where you are going with your explanations!!
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See post #7.
 
I understand that yes, but its not in context with the ratios I was talking about, which is why it came across confusing, to me at least.
 
Probability said:
I did and I was;

Are you totally confused now?
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Well I am confused as well. If you want to express the ratio among parts as fractions, e.g.

[MATH]12:18:24[/MATH],

why do you even need a calculator?

[MATH]\dfrac{18}{12} = \dfrac{3}{2}, \ \dfrac{24}{12} = \dfrac{2}{1}, \text { and } \dfrac{24}{18} \dfrac{4}{3}.[/MATH]
I am not sure what the value of that transformation is, but it is basically given by the ratio presentation itself.

If, as is more likely to be meaningful, you want to express the ratio of the parts to the whole, that too is simple.

[MATH]12 + 18 + 24 = 54.[/MATH]
[MATH]\dfrac{12}{54} = \dfrac{2}{9}, \ \dfrac{18}{54} = \dfrac{1}{3}, \text { and } \dfrac{24}{54} = \dfrac{4}{9}.[/MATH]
You can check that computation: the fractions need to add up to 1.

I think that what is confusing many of us is why any of this is problematic to you. Calculators are irrelevant. It is arithmetic learned in the third or fourth grade.
 
JeffM said:
why do you even need a calculator?

I think that what is confusing many of us is why any of this is problematic to you. Calculators are irrelevant. It is arithmetic learned in the third or fourth grade.
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Well JeffM, let's assume you had a really good life in your childhood and had plenty of parental help along the way, your school would have given you good reports and you would have been a good student.

Suppose then in your childhood you had a bad parent who from around 6 years old was always saying you were think and stupid. Suppose you were also hit and abused every week of your childhood life. Today you could go to the authorities and sort that problem out immediately, but in the 1960's and 70's that were not possible. I started to get a little insight into the subject of maths about 15 years old, and one day I came home from school with homework and I started to complete it at the kitchen table, and then my dad came in and asked, what are you doing! I said my maths homework, and he abruptly said you are doing it wrong, and I said my teacher told me to do it this way, and my dad said, your teacher is wrong do it this way. My work was wrong, the teacher marked it wrong and I was punished for being wrong. I spent about fifteen years of my life in that environment and left school with no exam passes. I started work in a manual job and when I started college I was at some point presented with maths and could not do them, and in the exams I just ignored anything to do with maths, yes I scraped through but I'd never had any professional help with the subject of maths. As years went by maths were increasing becoming common in my training for the trade I'm in, so I decided to start looking into the subject, but I have to learn it one step at a time, I have nobody that can help except forums. This is a interest to me that is very much a scientific part of the trade I'm in, and I'm choosing to learn it myself for my own benefit, so when you see I ask questions about the basics, please don't be offended and look down on me, you've had a good schooling where I have not. We've lead very different lives and sometimes not by choice.
 
Probability said:
Well JeffM, let's assume you had a really good life in your childhood and had plenty of parental help along the way, your school would have given you good reports and you would have been a good student.

Suppose then in your childhood you had a bad parent who from around 6 years old was always saying you were think and stupid. Suppose you were also hit and abused every week of your childhood life. Today you could go to the authorities and sort that problem out immediately, but in the 1960's and 70's that were not possible. I started to get a little insight into the subject of maths about 15 years old, and one day I came home from school with homework and I started to complete it at the kitchen table, and then my dad came in and asked, what are you doing! I said my maths homework, and he abruptly said you are doing it wrong, and I said my teacher told me to do it this way, and my dad said, your teacher is wrong do it this way. My work was wrong, the teacher marked it wrong and I was punished for being wrong. I spent about fifteen years of my life in that environment and left school with no exam passes. I started work in a manual job and when I started college I was at some point presented with maths and could not do them, and in the exams I just ignored anything to do with maths, yes I scraped through but I'd never had any professional help with the subject of maths. As years went by maths were increasing becoming common in my training for the trade I'm in, so I decided to start looking into the subject, but I have to learn it one step at a time, I have nobody that can help except forums. This is a interest to me that is very much a scientific part of the trade I'm in, and I'm choosing to learn it myself for my own benefit, so when you see I ask questions about the basics, please don't be offended and look down on me, you've had a good schooling where I have not. We've lead very different lives and sometimes not by choice.
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I don't think anybody looks down on you. It's just not clear why you are bringing up calculators. If you don't understand how to do something calculators won't help. They are generally used when you know what to do but the numbers are such that it would take a long time to do the calculations in your head or in paper. So, if you clarify why you need them in this situation, it would help.
 
Probability said:
Well JeffM, let's assume you had a really good life in your childhood and had plenty of parental help along the way, your school would have given you good reports and you would have been a good student.

Suppose then in your childhood you had a bad parent who from around 6 years old was always saying you were think and stupid. Suppose you were also hit and abused every week of your childhood life. Today you could go to the authorities and sort that problem out immediately, but in the 1960's and 70's that were not possible. I started to get a little insight into the subject of maths about 15 years old, and one day I came home from school with homework and I started to complete it at the kitchen table, and then my dad came in and asked, what are you doing! I said my maths homework, and he abruptly said you are doing it wrong, and I said my teacher told me to do it this way, and my dad said, your teacher is wrong do it this way. My work was wrong, the teacher marked it wrong and I was punished for being wrong. I spent about fifteen years of my life in that environment and left school with no exam passes. I started work in a manual job and when I started college I was at some point presented with maths and could not do them, and in the exams I just ignored anything to do with maths, yes I scraped through but I'd never had any professional help with the subject of maths. As years went by maths were increasing becoming common in my training for the trade I'm in, so I decided to start looking into the subject, but I have to learn it one step at a time, I have nobody that can help except forums. This is a interest to me that is very much a scientific part of the trade I'm in, and I'm choosing to learn it myself for my own benefit, so when you see I ask questions about the basics, please don't be offended and look down on me, you've had a good schooling where I have not. We've lead very different lives and sometimes not by choice.
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I am not offended, nor did I intend any hint of personal disparagement. Nor have I supplied literally thousands of answers on this and other fora because I am unsympathetic to those striving to learn. I said I was confused. Why am I confused?

First, learning how to use a specific model of calculator is useful if you own that model, but it no more teaches mathematics than does learning how to use a specific model of electric coffee maker. We can talk about that if you want.

Second, early in this thread, I gave a rather lengthy answer that said (a) how ratios are presented does not lead to a meaningful understanding of mathematics, (b) what the arithmetic of ratios is, and (c) why ratios have great practical utility even for, maybe especially for, those with little mathematical training. I got a response giving a joke, but no substantive engagement with an answer that I had spent considerable putting together.

Third, the follow-up questions tended to wander from one mechanical issue to another. We have no idea what specific type of practical problem you think a calculator would help with nor what specific conceptual issues you want to understand better.
 
lev888 said:
I don't think anybody looks down on you. It's just not clear why you are bringing up calculators. If you don't understand how to do something calculators won't help. They are generally used when you know what to do but the numbers are such that it would take a long time to do the calculations in your head or in paper. So, if you clarify why you need them in this situation, it would help.
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Calculators can be used to check answers to maths like fractions, where the fraction answer is displayed in the simplified terms. While learning ratios and fractions if I suspect I've made an error the calculator is like a tutor, who can give guidance, the calculator shows the answer in simplified terms and if I've made an error I can see immediately a difference that is drawn to my attention.
 
JeffM said:
I am not offended, nor did I intend any hint of personal disparagement. Nor have I supplied literally thousands of answers on this and other fora because I am unsympathetic to those striving to learn. I said I was confused. Why am I confused?

First, learning how to use a specific model of calculator is useful if you own that model, but it no more teaches mathematics than does learning how to use a specific model of electric coffee maker. We can talk about that if you want.

Second, early in this thread, I gave a rather lengthy answer that said (a) how ratios are presented does not lead to a meaningful understanding of mathematics, (b) what the arithmetic of ratios is, and (c) why ratios have great practical utility even for, maybe especially for, those with little mathematical training. I got a response giving a joke, but no substantive engagement with an answer that I had spent considerable putting together.

Third, the follow-up questions tended to wander from one mechanical issue to another. We have no idea what specific type of practical problem you think a calculator would help with nor what specific conceptual issues you want to understand better.
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I'm sorry if I came across wrong to the reply to your post previously. I didn't provide a response in the way you wanted because I didn't understand it. Please remember there is no balance between an expert with a lifetime of experience in something like maths, and me learning the subject from first principles with a lack of professional experience. I just take maths one step at a time until I understand the particular topic being discussed.

I would like to point out that the methods you used to provide the fractional type answers to the ratio 12:18:24 was very well received and understood by me. Thank you very much for that.
 
Probability said:
I'm sorry if I came across wrong to the reply to your post previously. I didn't provide a response in the way you wanted because I didn't understand it. Please remember there is no balance between an expert with a lifetime of experience in something like maths, and me learning the subject from first principles with a lack of professional experience. I just take maths one step at a time until I understand the particular topic being discussed.

I would like to point out that the methods you used to provide the fractional type answers to the ratio 12:18:24 was very well received and understood by me. Thank you very much for that.
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I say to the kids that I tutor, "It is my responsibility to give an understandable explanation, but it is your responsibility to tell me out loud when I fail."

Do not be afraid to ask follow-on questions about anything you do not understand. Otherwise, we are likely to assume that you have understood it. Chaos then ensues.
 
JeffM said:
I say to the kids that I tutor, "It is my responsibility to give an understandable explanation, but it is your responsibility to tell me out loud when I fail."

Do not be afraid to ask follow-on questions about anything you do not understand. Otherwise, we are likely to assume that you have understood it. Chaos then ensues.
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See my thread in algebra
 
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