Question

How many cups are in ${\displaystyle \frac{1}{2}}$ a gallon?

Answer 1

Hint: For converting the gallon to cups we need a relation between them. As we know that the conversion factor of a gallon to cups will be as $1$ gallon will be equal to $16$ cups. Hence, by using this we will be able to get the required converted value in cups.

Complete step-by-step answer:
So we have the values of a gallon given as ${\displaystyle \frac{1}{2}}$ and we have to convert this into the number of cups. So from the hint, we know that
$\Rightarrow 1gallon=16cups$ , and we will name it equation $1$
So we have to find the number of cups in ${\displaystyle \frac{1}{2}}$ a gallon. So for this, we will multiply both the side of the equation by ${\displaystyle \frac{1}{2}}$ and it will be equal to
$\Rightarrow {\displaystyle \frac{1}{2}}\times 1\text{ gallon = }{\displaystyle \frac{1}{2}}\times 16\text{ cups}$
And on solving the multiplication and division of both the sides, we get
$\Rightarrow {\displaystyle \frac{1}{2}}\times \text{gallon = 8 cups}$
So we can write the above equation as
$\Rightarrow {\displaystyle \frac{1}{2}}\text{gallon = 8 cups}$
Therefore, there are $8$ cups in ${\displaystyle \frac{1}{2}}$ a gallon.

Additional information:
Generally, it is seen that most people use gallon when they have larger quantities, and when they have smaller quantities they use paints, cups, quarts, and many more. So when there is a problem for solving or converting the liquid present in the container then we use the unit conversion and with this, we need to convert those units from one to another.

Note: So while solving such a type of question where they asked to convert it from something to a different thing, we always need to focus on the units. As if we don’t write the unit after the conversion then it will be considered as wrong .