Question

How many ounces are in $\dfrac{1}{4}$ of a gallon?

Answer 1

Hint:
For solving this, like we manipulate the numbers sometimes to get to the result in the same way we can manipulate the units of measurements to get the required result. So by using some measurement units we are going to solve this.

Complete Step by Step Solution:
As we know that $16oz$ equals to $1{\text{ pint}}$ and similarly $8{\text{ pints}}$equals to $1{\text{ gallon}}$.
Now let us assume the word ounces are denoted by $z$ , the word pints are represented by $p$ and the word gallon will be represented by $g$ .
So by using the ratios, we can write the ounce to pints ratio and it will be
$ \Rightarrow z:p$
Similarly, the ratio of ounces to gallons will be $\dfrac{z}{p}$ , named equation $1$
And the ratio of pints to gallons will be $\dfrac{p}{g}$ , named it equation $2$
So our focus is to get the ratio of ounces to gallons, and it can be written as $\dfrac{z}{g}$
So doing the multiplication of equation $1$ and equation $2$ , we get
$ \Rightarrow \dfrac{z}{p} \times \dfrac{p}{g}$
And it can be written as
$ \Rightarrow \dfrac{{z \times p}}{{p \times g}}$
And on reversing the units in the denominator we get
$ \Rightarrow \dfrac{{z \times p}}{{g \times p}}$
So we will separate the units in a single fraction and will be equal to
$ \Rightarrow \dfrac{z}{g} \times \dfrac{p}{p}$
So using the same approach as above, and substituting the values, we get
\[ \Rightarrow \dfrac{z}{p} \times \dfrac{p}{g} = \dfrac{{16z}}{{1p}} \times \dfrac{{8p}}{{1g}}\]
On solving it we get
$ \Rightarrow \dfrac{{128z}}{{1g}}$
So for a quarter of a gallon, we will get
$ \Rightarrow \dfrac{{ounces}}{{gallons}} = \dfrac{{128z \times \dfrac{1}{4}}}{{1g \times \dfrac{1}{4}}}$
And on solving it, we get
$ \Rightarrow \dfrac{{ounces}}{{gallons}} = \dfrac{{32}}{{\dfrac{1}{4}g}}$

Therefore, there will be $32$ ounces in $\dfrac{1}{4}$ of a gallon.

Note:
When we have to measure a liquid like milk, then it is being measured in gallons or quarts whereas an ounce is also used for measuring the weight. So to describe the capacity of an object these measuring units are used.