# Quante once sono in 1/4 di gallone?

#### Risposta:

Did you know you can manipulate units of measurement in the same way you can numbers. Use this as a guide on how to do the calculation.

32 Fluid ounces in 1/4 gallone

#### Spiegazione:

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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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"))
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Check")

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