Quante once sono in 1/4 di gallone?

YES I KNOW THIS IS PREALGEBRA!!

16 oz = 1 pint
8 pints = 1 gallon

Let the word ounces be represented by #z#
Let the word pints be represented by #p#
Let the word gallons be represented by #g#

So every time you see #z# it means the word ounces
So every time you see #p# it means the word pint
So every time you see #g# it means the word gallon
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#color(blue)("Answering the question")#

Using ratio

We can write the ounces to pints ratio as #z:p#

I much prefer to use the fraction format and you will see why.

We can write the ounces to gallons ratio as #z/p ........ Ratio(1)#
We can write the pints to gallons ratio as #p/g........... Ratio(2)#

#color(brown)("Our target is to get the ratio of ounces to gallons "->z/g)#

Look what happens when we have #Ratio(1)xxRatio(2)#

#z/pxxp/g color(white)("ddd")->color(white)("ddd") (zxxp)/(pxxg)larr("ounces "xx" pints")/("pints "xx" gallons")#

Utilizzando un esempio: #2xx3 " gives the same answer as "3xx2#
So we can swap things round when multiplying

Thus we have:

#(zxxp)/(pxxg)color(white)("d")->color(white)("d")(zxxp)/(gxxpcolor(white)("d")) ->color(white)("d")z/gxxp/p = z/g#

The #p/p# is the equivalent of 1 and anything multiplied by 1 does not change in value.

Use the same approach as above on the numbers:

#z/pxxp/g color(white)("dddd") ->color(white)("dddd")(16z)/(1p)xx(8p)/(1g) #

#color(white)("ddddddddd") ->color(white)("dddd")(16z)/(1cancel(p))xx(8cancel(p))/(1g) #

#color(white)("ddddddddd") ->color(white)("dddd")(16zxx8)/(1xx1g) #

#("ounces")/("gallons")color(white)("dd") ->color(white)("dddd")(128z)/(1g) #

So for a quater of a gallon we have:

#("ounces")/("gallons")color(white)("dd") ->color(white)("dddd")(128zxx1/4)/(1gxx1/4) = (32z)/(color(white)("d") 1/4gcolor(white)("d"))#
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#color(blue)("Check")#

#1/4(16xx8)=16xx2=32#