# How many ounces are in 1/4 of a gallon?

Mar 11, 2018

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 $\frac{1}{4}$ gallon

#### Explanation:

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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$\textcolor{b l u e}{\text{Answering the question}}$

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 $\frac{z}{p} \ldots \ldots . . R a t i o \left(1\right)$
We can write the pints to gallons ratio as $\frac{p}{g} \ldots \ldots \ldots . . R a t i o \left(2\right)$

$\textcolor{b r o w n}{\text{Our target is to get the ratio of ounces to gallons } \to \frac{z}{g}}$

Look what happens when we have $R a t i o \left(1\right) \times R a t i o \left(2\right)$

$\frac{z}{p} \times \frac{p}{g} \textcolor{w h i t e}{\text{ddd")->color(white)("ddd") (zxxp)/(pxxg)larr("ounces "xx" pints")/("pints "xx" gallons}}$

Using an example: $2 \times 3 \text{ gives the same answer as } 3 \times 2$
So we can swap things round when multiplying

Thus we have:

$\frac{z \times p}{p \times g} \textcolor{w h i t e}{\text{d")->color(white)("d")(zxxp)/(gxxpcolor(white)("d")) ->color(white)("d}} \frac{z}{g} \times \frac{p}{p} = \frac{z}{g}$

The $\frac{p}{p}$ is the equivalent of 1 and anything multiplied by 1 does not change in value.

Use the same approach as above on the numbers:

$\frac{z}{p} \times \frac{p}{g} \textcolor{w h i t e}{\text{dddd") ->color(white)("dddd}} \frac{16 z}{1 p} \times \frac{8 p}{1 g}$

$\textcolor{w h i t e}{\text{ddddddddd") ->color(white)("dddd}} \frac{16 z}{1 \cancel{p}} \times \frac{8 \cancel{p}}{1 g}$

$\textcolor{w h i t e}{\text{ddddddddd") ->color(white)("dddd}} \frac{16 z \times 8}{1 \times 1 g}$

$\left(\text{ounces")/("gallons")color(white)("dd") ->color(white)("dddd}\right) \frac{128 z}{1 g}$

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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$\textcolor{b l u e}{\text{Check}}$

$\frac{1}{4} \left(16 \times 8\right) = 16 \times 2 = 32$