Need help with working out really easy algebra fraction question

[FranzPattison]

Hey, so I know this is an easy solution, but it's been years since I've done any real math, so I just can't remember the rules on how to work out the formula. This is a basic fuel economy calculation where I essentially want to swap from km/100L to L/km.

So I set up:

7.1L = x km
100km 1 L (somehow I seem to recall you should invert the units across the equals sign like that)


And I know the answer is 100/7.1 = 14.08 = x (from just trying different combinations of division), but I couldn't figure out how to do all the fraction work, cross multiplying with the variable and the units and whatnot, and it's frustrating me because I know it's a simple process but over time I've just forgotten the rules for working with fractions, units, and variables across an equal sign, all together.

Can anybody explain how I begin with the above setup and actually properly arrive at the answer step by step? (multiply both sides by ____, etc...) Because it's making me feel old and dull that the info is missing from my mind. Thanks!

 

[Steven G]

Especially after years you have done math you need to do it in a way that makes sense, not something that your teacher told you or something that you remembered from years ago.

You just have to remember if you want to change the way something looks like then you multiply by 1. Also recall that there are many ways to write 1.

1 = 3/3 = 1day/(24hrs) = 12in/1ft = ...etc .................................. corrected

Now [math] \dfrac{100km}{7.1L} = \dfrac{100km}{7.1L} * \dfrac{100}{100} = \dfrac{14.08km}{L} *\dfrac{100}{100} = \dfrac{1408km}{100L}[/math]
So you have that [math]\dfrac{100L}{1408km}[/math]
It would make more sense to start with [math] \dfrac{7.1L}{100km} = \dfrac{7.1L}{100km} *\dfrac{100}{100} = \dfrac{L}{14.08km} *\dfrac{100}{100} = \dfrac{100L}{1408km}[/math]

 

[Dr.Peterson]

Hey, so I know this is an easy solution, but it's been years since I've done any real math, so I just can't remember the rules on how to work out the formula. This is a basic fuel economy calculation where I essentially want to swap from km/100L to L/km.

So I set up:

7.1L = x km
100km 1 L (somehow I seem to recall you should invert the units across the equals sign like that)


And I know the answer is 100/7.1 = 14.08 = x (from just trying different combinations of division), but I couldn't figure out how to do all the fraction work, cross multiplying with the variable and the units and whatnot, and it's frustrating me because I know it's a simple process but over time I've just forgotten the rules for working with fractions, units, and variables across an equal sign, all together.

Can anybody explain how I begin with the above setup and actually properly arrive at the answer step by step? (multiply both sides by ____, etc...) Because it's making me feel old and dull that the info is missing from my mind. Thanks!

You can't start the way you did, because it is impossible for L/km to be equal to km/L. It isn't a proportion (as you wrote it), so cross-multiplication doesn't work. But you could do something similar and easier.

Take your [MATH]\frac{7.1\text{ L}}{100\text{ km}}[/MATH] and flip it to get [MATH]\frac{100\text{ km}}{7.1\text{ L}}[/MATH], then do your division to get 14.08 km/L. There's the answer.

What Jomo did is the more formal way, which I would follow for anything more complicated than your problem; both approaches focus on watching the units; not doing so is the mistake you made.

 

[HallsofIvy]

somehow I seem to recall you should invert the units across the equals sign like that

OUCH! That violates the whole point of what "equal" means! If A= B then A and B are the same. The same numeric value, the same units. \(\displaystyle \frac{2}{3}= \frac{2}{3}\), not \(\displaystyle \frac{3}{2}\)!

 

[Otis]

1 = 2/3

 

[Steven G]

No no, it looks like a three but it is really a 2. I have terrible handwriting.