# Conversion factors in pre-algebra....ARRGHHHH!!!!!!

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We're doing LoF pre-algebra 2 and having such a struggle with conversion factors. Even *I* have problems with it. We're never sure where the numbers go. Could it be that LoF isn't explaining it the way our brain works, do we need more practice....what, what, what?????????? I'm going crazy with it and dd learns JUST like me, so there are tears! What can I do?

I'm not great at math...do I need to switch programs, and if so, what is going to be VERY self-explanatory throughout high school?

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Are you saying you aren't sure which number goes in the numerator and which goes in the denominator? Since you are cross canceling labels you want the label you are going to cancel to be in the opposite position in the conversion factor. Here you can see how it works in the first problem when the numbers are in the right spot so the labels can cross cancel and how it doesn't work when they aren't because you can't cross cancel.

2.5 days X 24 hours = 60 hours

xxx1xxxxxxxxx1 day

2.5 days X xx1 dayxx = 2.5 days squared

xxx1xxxxxxxx24 hoursxxxxxx24 hours

It's also important to remember that a conversion factor is just multiplying times 1 so the factors need to equal each other. 1 day = 24 hours.

We found it to be very straightforward but we'd also already learned conversion factors in MUS first. Are you at the beginning of where conversion factors are introduced? If I remember correctly there is more instruction as you work through it. If this continues to be a problem (especially if it's with more than just conversion factors) you might need a math.

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Are you saying you aren't sure which number goes in the numerator and which goes in the denominator? Since you are cross canceling labels you want the label you are going to cancel to be in the opposite position in the conversion factor. Here you can see how it works in the first problem when the numbers are in the right spot so the labels can cross cancel and how it doesn't work when they aren't because you can't cross cancel.

2.5 days X 24 hours = 60 hours

xxx1xxxxxxxxx1 day

2.5 days X xx1 dayxx = 2.5 days squared

xxx1xxxxxxxx24 hoursxxxxxx24 hours

It's also important to remember that a conversion factor is just multiplying times 1 so the factors need to equal each other. 1 day = 24 hours.

My son is working with these in Saxon Algebra 1/2 and also Apologia Physical Science. I remember doing this in highschool Chemistry and stumbling along. I think I know why I was stumbling. I just realized, in teaching my son, that the reason you can multiply by 1 day over 24 hours is because 1 day is the same as 24 hours and therefore equals 1 just like the pp said AND you can switch it around and it still equals 1. That was the part that confused me as a student. How can the fraction be correct one way and just as correct upside down? :001_huh: After all 4/5 is NOT the same as 5/4. I just didn't get it. But I would put it upside down if I needed to so that I could cancel out the units properly but I didn't understand until just a few weeks ago WHY the fraction works equally both ways. I love those lightbulb moments. :001_smile:

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Are you saying you aren't sure which number goes in the numerator and which goes in the denominator? Since you are cross canceling labels you want the label you are going to cancel to be in the opposite position in the conversion factor. Here you can see how it works in the first problem when the numbers are in the right spot so the labels can cross cancel and how it doesn't work when they aren't because you can't cross cancel.

2.5 days X 24 hours = 60 hours

xxx1xxxxxxxxx1 day

2.5 days X xx1 dayxx = 2.5 days squared

xxx1xxxxxxxx24 hoursxxxxxx24 hours

It's also important to remember that a conversion factor is just multiplying times 1 so the factors need to equal each other. 1 day = 24 hours.

We found it to be very straightforward but we'd also already learned conversion factors in MUS first. Are you at the beginning of where conversion factors are introduced? If I remember correctly there is more instruction as you work through it. If this continues to be a problem (especially if it's with more than just conversion factors) you might need a math.

Sometimes it's not knowing which numbers go in the numerator vs. denominator, and sometimes it's just not knowing which numbers to plug in. I had that lightbulb moment today that sometimes it's just as easy as 1 day = 24 hours, but then sometimes what I'm multiplying it by can be tricky. Sigh. You mention I might need a math... I don't think you finished the sentence. I'm thinking you're saying I might need a math tutor. Are you free??? ;)

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Sometimes it's not knowing which numbers go in the numerator vs. denominator, and sometimes it's just not knowing which numbers to plug in. I had that lightbulb moment today that sometimes it's just as easy as 1 day = 24 hours, but then sometimes what I'm multiplying it by can be tricky. Sigh. You mention I might need a math... I don't think you finished the sentence. I'm thinking you're saying I might need a math tutor. Are you free??? ;)

Oops, I had to change a diaper and think I didn't finish editing before posting:001_huh::lol: I meant to say that if that continues you may need a different math curricula. Many find conversion facts confusing so I wouldn't switch just yet but would continue and see if other concepts taught in LoF are confusing as well.

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Oops, I had to change a diaper and think I didn't finish editing before posting:001_huh::lol: I meant to say that if that continues you may need a different math curricula. Many find conversion facts confusing so I wouldn't switch just yet but would continue and see if other concepts taught in LoF are confusing as well.

LOL...I was thinking of switching to TT Algebra once the LoF pre-algebra books are finished. I'm crossing my fingers that it'll be what helps my child!!!

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Ds did LoF Pre-Algebra w/Biology over the summer. Conversions took him longer than any other section. It just takes awhile to sink in and get it. He finally made it through and is happily zooming through MUS Pre-Algebra now (I always have him do both).

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FWIW, the conversion factors were the only thing that tripped us up as well.

It was our only issue with LOF--so I wouldn't give up on it based on that--but we do use it only as a supplement for pre-alg.

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Cheryl has a nice explanation. I also like this one from Dr. Math,http://mathforum.org/library/drmath/view/62176.html

This is something worth spending time on. Conversion factors are very important in math and science. In science, especially physics, the units give you a ton of information and a great way to check your answer, but only if you do your conversion properly. If you don't do your conversion properly, you get a whole lot of nonsense because you multiplied by something other than 1.

If you find yourself trying to memorize conversion factors and don't really get how the units cancel out or why you are allowed to multiply by 12inches/1ft or by 1ft/12inches (because since 12inches=1ft you are multiplying by 1 and in the process converting the units) then you are going to have trouble later. Math should not be about memorizing seemingly arbitrary rules and neither should science. I'm not saying that it is for you because obviously you are trying to make sense of it. But some end up relying on memorization and this is an important point because all of those arbitrary rules will be lost from your brain but understanding how to make 1's and cancel units will stay. I really can't stress enough how important this concept is for science, especially physics. This is the mathematical foundation that makes the difference between memorizing a ton of formula for physics or learning some laws of physics and deriving the formula that you need. I would stay on this topic until it makes sense. Use other sources if they help.

I don't have Fred pre-algebra but my son is doing Fred Algebra and I have found that sometimes he glosses over an important topic without really spelling it out sufficiently. But this can be remedied if you pick up another source and then put it down again until you need it. I think the benefits of Fred make this effort worthwhile if you can make Fred work for you.

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Sometimes it's not knowing which numbers go in the numerator vs. denominator, and sometimes it's just not knowing which numbers to plug in. I had that lightbulb moment today that sometimes it's just as easy as 1 day = 24 hours, but then sometimes what I'm multiplying it by can be tricky. Sigh. You mention I might need a math... I don't think you finished the sentence. I'm thinking you're saying I might need a math tutor. Are you free??? ;)

I didn't read the other replies very carefully, so someone may already have suggested this. Simply think about what you want unit you want to end with and put that in the numerator, then work for how you get from the units you are given to the units you need to end up with. Conversions are simply mlutiplying by fractions that equal 1.

For example say you are given 1 mile and you want to end up with inches. You know that you need inches to end up in the numerator and you were given miles which begins in the numerator.

2 mi/1...................inches/?

How do I get there with units I know?

2 mi/1 X 5280 ft/mi (that way the miles cross eliminate. Now I am left with 5280 ft.

2*5280 ft/1 X 12 in/ft and now ft cross reduces and you are left with inches in the numerator and now you simply need to multiply.

In simple conversion terms, it would look like this:

2 mi/1 x 5280 ft/1 mi x 12 in/1ft All the units factor out with the exception of inches. All that is left to do is multiply 2 * 5280 * 12 inches.

Does that help?

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If people are using LoF pre-alegbra as a supplement what else are you using? Someone said MUS...what else? Should I maybe move from completing LoF Pre-A to TT pre-algebra...or will dd be ready for TT Algebra once LoF pre is done?

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Simply think about what you want unit you want to end with and put that in the numerator, then work for how you get from the units you are given to the units you need to end up with. Conversions are simply mlutiplying by fractions that equal 1.

For example say you are given 1 mile and you want to end up with inches. You know that you need inches to end up in the numerator and you were given miles which begins in the numerator.

2 mi/1...................inches/?

How do I get there with units I know?

2 mi/1 X 5280 ft/mi (that way the miles cross eliminate. Now I am left with 5280 ft.

2*5280 ft/1 X 12 in/ft and now ft cross reduces and you are left with inches in the numerator and now you simply need to multiply.

In simple conversion terms, it would look like this:

2 mi/1 x 5280 ft/1 mi x 12 in/1ft All the units factor out with the exception of inches. All that is left to do is multiply 2 * 5280 * 12 inches.

Does that help?

Ok, after writing down what you wrote again and looking it over it make sense. But I will admit...

....that I wouldn't have thought in a conversion factor to put it from miles to feet then to inches. I would have sat there thinking how the conversion factor would look with just miles to inches. See what I mean? So in a problem, I'm not considering EVERYTHING I need to consider. But once it's broken down for me like you did, it makes sense...of course you'd do it like that! LOL Thanks.

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Cheryl has a nice explanation. I also like this one from Dr. Math,http://mathforum.org/library/drmath/view/62176.html

This is something worth spending time on. Conversion factors are very important in math and science. In science, especially physics, the units give you a ton of information and a great way to check your answer, but only if you do your conversion properly. If you don't do your conversion properly, you get a whole lot of nonsense because you multiplied by something other than 1.

If you find yourself trying to memorize conversion factors and don't really get how the units cancel out or why you are allowed to multiply by 12inches/1ft or by 1ft/12inches (because since 12inches=1ft you are multiplying by 1 and in the process converting the units) then you are going to have trouble later. Math should not be about memorizing seemingly arbitrary rules and neither should science. I'm not saying that it is for you because obviously you are trying to make sense of it. But some end up relying on memorization and this is an important point because all of those arbitrary rules will be lost from your brain but understanding how to make 1's and cancel units will stay. I really can't stress enough how important this concept is for science, especially physics. This is the mathematical foundation that makes the difference between memorizing a ton of formula for physics or learning some laws of physics and deriving the formula that you need. I would stay on this topic until it makes sense. Use other sources if they help.

I don't have Fred pre-algebra but my son is doing Fred Algebra and I have found that sometimes he glosses over an important topic without really spelling it out sufficiently. But this can be remedied if you pick up another source and then put it down again until you need it. I think the benefits of Fred make this effort worthwhile if you can make Fred work for you.

I understand what you're saying and totally agree...this is why I'm so concerned and I wrote the thread...I just KNOW if we're not getting this, it's going to bite us in the butt really badly once we move on! Thanks!

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Ok, after writing down what you wrote again and looking it over it make sense. But I will admit...

....that I wouldn't have thought in a conversion factor to put it from miles to feet then to inches. I would have sat there thinking how the conversion factor would look with just miles to inches. See what I mean? So in a problem, I'm not considering EVERYTHING I need to consider. But once it's broken down for me like you did, it makes sense...of course you'd do it like that! LOL Thanks.

The entire point of conversions is to move along steps of what you easily know to get from one unit to another.

For example if I want to know how many seconds are in 10 centuries, it really isn't hard to solve as long as you just plug along step by step with common knowledge (and I am going to ignore the fact that leap yrs exist!)

10 centuries/1..............secs/? (more than likely mins, right?)

10 centuries/1 x 100 yrs/century x 365 days/1yr x 24 hr/1 day x 60 mins/ 1hr x 60 secs/1 min

All I did was think about how to get rid of my numerator's units in a logical progression toward the units that I wanted to end up with.

Does that help? (The key is to focus on the units you want to eliminate and create the fraction that equals 1......12ft/1 in, 365 days/1yr, 100 mm/1 m, etc.

Edited by 8FillTheHeart
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The entire point of conversions is to move along steps of what you easily know to get from one unit to another.

For example if I want to know how many seconds are in 10 centuries, it really isn't hard to solve as long as you just plug along step by step with common knowledge (and I am going to ignore the fact that leap yrs exist!)

10 centuries/1..............secs/? (more than likely mins, right?)

10 centuries/1 x 100 yrs/century x 365 days/1yr x 24 hr/1 day x 60 mins/ 1hr x 60 secs/1 min

All I did was think about how to get rid of my numerator's units in a logical progression toward the units that I wanted to end up with.

Does that help? (The key is to focus on the units you want to eliminate and create the fraction that equals 1......12ft/1 in, 365 days/1yr, 100 mm/1 m, etc.

Oh man, a lightbulb moment. Ok, really stupid admission....I never really thought I was CONVERTING things, just trying to figure out a number. But you're right...I've got to along a line to CONVERT one thing to another...roflolol. What an idiot I am. I better go back to LoF's first pre-algebra book and see how he explains it. Somehow that was completely lost on me. Thanks!

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