I cant spot my mistake i make.

[Niek89]

I keep getting stuck on converting gallons to liters, to Cad, to quartes etc.

Because of the answer in the book I know that have 90% correct but always end up switching one at the wrong side. But I keep looking and in my mind I think it makes so much sense that I put everything on the good side.
But the answer in the book keeps forcing me to switch one of them while that makes it to me to the wrong side.

*i am not sure how to call this type of mathematics. The books tells me to do a trick which basically says:
Multiply all the left side with each other. And multiple all the right side with each other. In the end u divide the 2 total sums with each other.*

Let me try to show you one question on the way I do it. And hopefully you can spot my mistake and explain why I should switch it.

For example: In California Gasoline sells for $1.99 US per gallon. In BC gasoline is currently selling for $0.729 CDN per liter. Convert the Canadian price per liter to US dollars per gallon. Is the price of gasoline cheaper in California or in BC?

The information I get:
$1 US = $1.5644 CDN
1 Liter = 1.0567 Quarts
1 Gallon = 4 Quarts

My first question would be where do I start (Does it really matter where I start)?
$1.99 US = 1 gallon
OR because of the question it asks me to convert the CAD price per liter to US Dollar I could start I think at (so far I used both and still came to the same wrong answer):
1.5644 CDN = $1 US

If I choose the first option I would continue like this:
$1.99 US = 1 gallon
1 Gallon = 4 Quarts
1.0567 Quarts = 1 Liter
1 Liter = 0.729 CDN
1.5644 CDN = $1 US

1.99 *(multiply) 1 * 1.0567 * 1 * 1.5644 = 3.289671945
Divided by:
1 * 4 * 1 * 0.729 CAD * 1 = 2.916

So in the end I should do 3.289... divided 2.916 = 1.1279...

The right answer is 1.76

Second Question: In my mind, every step I take makes totally sense. Where am I going wrong? And why I need to change the steps I took?

Niek

 

[Dr.Peterson]

It appears that you are being taught to follow a routine without thinking. That is a recipe for (at least occasional) failure.

What are you, or the book, claiming that the answer you get MEANS? It's a yes-or-no question, so neither 1.1279 nor 1.76 answers the question. And neither means anything without a unit and a definition.

What you should be getting, presumably, is the ratio of one price per unit to the other. But to make use of that, you need to know what the order is.

What I would have done is similar to your work, but more intentional: Convert one of the prices to the units of the other, and compare them.

To convert the Canadian price to American form:

$0.729 CDN / L * 1 L / 1.0567 qt * 4 qt / 1 gal * $1 US / $1.5644 CDN = $1.763957 US / 1 gal
​

That is:

\(\displaystyle \dfrac{$0.729\ \text{CDN}}{1\ \text{L}} \cdot\dfrac{1\ \text{L}}{1.0567\ \text{qt}} \cdot\dfrac{4\ \text{qt}}{1\ \text{gal}} \cdot\dfrac{$1\ \text{US}}{$1.5644\ \text{CDN}} = \dfrac{$1.763957\ \text{US}}{1\ \text{gal}}\)
​

That, apparently, is what they did. Since this is less than the California price, Canadian is cheaper. The ratio of the prices, 1.99:1.76, is 1.128:1; that is what you calculated, and could have led to the right answer if you knew what you had done!

Your mistake was not asking what it is that you wanted to calculate, and not interpreting the result.

 

[Niek89]

It appears that you are being taught to follow a routine without thinking. That is a recipe for (at least occasional) failure.

What are you, or the book, claiming that the answer you get MEANS? It's a yes-or-no question, so neither 1.1279 nor 1.76 answers the question. And neither means anything without a unit and a definition.

What you should be getting, presumably, is the ratio of one price per unit to the other. But to make use of that, you need to know what the order is.

What I would have done is similar to your work, but more intentional: Convert one of the prices to the units of the other, and compare them.

To convert the Canadian price to American form:

$0.729 CDN / L * 1 L / 1.0567 qt * 4 qt / 1 gal * $1 US / $1.5644 CDN = $1.763957 US / 1 gal
​

That is:

\(\displaystyle \dfrac{$0.729\ \text{CDN}}{1\ \text{L}} \cdot\dfrac{1\ \text{L}}{1.0567\ \text{qt}} \cdot\dfrac{4\ \text{qt}}{1\ \text{gal}} \cdot\dfrac{$1\ \text{US}}{$1.5644\ \text{CDN}} = \dfrac{$1.763957\ \text{US}}{1\ \text{gal}}\)
​

That, apparently, is what they did. Since this is less than the California price, Canadian is cheaper. The ratio of the prices, 1.99:1.76, is 1.128:1; that is what you calculated, and could have led to the right answer if you knew what you had done!

Your mistake was not asking what it is that you wanted to calculate, and not interpreting the result.

That seems helpful already although i cant seem to understand the last part.
$1 US / $1.5644 CDN
Why u choose specifically 1 US / 1.5644 CDN
And not 1.5644 CDN / 1 US. That would have mean the answer would be different.

Could you explain that to me?