Question

People in Japan on average eat 3 ounces of fish per day. How many pounds of fish is this per week?

Answer 1

`5.6875/1("pound")/("week") -> 5.6875" pounds per week"`

Explanation:

`color(brown)("Did you know that you cam manipulate units of measurement")` `color(brown)("the same way you can numbers")`

First lets count this in ounces per week

Consider just the units of measurement to start with.

We need ounces per week `->("ounces")/("week")`

We have got: `("ounces")/("day")` so we need to change this by replacing the unit of day with the unit of week.

`("ounces")/(cancel("day"))xx(cancel("days"))/("week") = ("ounces")/("week")`
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`color(brown)("We do the same thing with the numbers")`

`[13/1 ("ounces")/(cancel("day"))]xx[7/1 (cancel("days"))/("week")] = 91/1 ("ounces")/("week")" "..Eqn(1)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Converting this to pounds")`

There are 16 ounces in 1 pound `->16/1 ("ounces")/("pound")" "..Eqn(2)`

So to covert `("ounces")/("week")` into `("pounds")/("week")` we can turn `Eqn(2)` upside

down and multiply. Like this:

`color(white)("d")Eqn(1)color(white)("dddd")xxcolor(white)("ddd")1/(Eqn(2))`

`91/1 (cancel("ounces"))/("week")color(white)("d")xxcolor(white)("d")1/16 ("pounds")/(cancel("ounces")) color(white)("d")=color(white)("d")91/16 ("pound")/("week")`

But we need 1 week. So divide both top and bottom by 16

`(91-:16)/(16-:16) ("pound")/("week") color(white)("dddd")=color(white)("dddd") 5.6875/1("pound")/("week")`