Question

How do you write 13 quarts to 4 gallons in fractional notation in lowest terms?

Answer 1

Hint: Here, this question belongs to the conversion topic that is we have to convert the quarters to gallons. We need to make the units of measurement the same. So they either have to be all in gallons or quarts. One gallon is equal to four quarters on further simplification we get the required solution.

Complete step by step solution:
The gallon is a unit of measurement for volume and fluid capacity in both the US customary units and the British imperial systems of measurement. Which is equal to four quarts, the U.S. standard gallon being equal to 231 cubic inches (3.7853 liters), and the British imperial gallon to 277.42 cubic inches (4.546 liters). It can be abbreviated as gal.
Now select gallons as the common units
As we know one gallon is equal to four quarters i.e.,
1 quatres = \[\dfrac{1}{4}\] gallon
In the given question we have 13 quatres, we have convert in to the gallon by multiplying \[\dfrac{1}{4}\] , then
13 quarters = \[13 \times \dfrac{1}{4}\] gallons.
Now we have to write the fraction form of 13 quarts to 4 gallons. In fractional notation 4 gallons is the lowest terms, it can be expressed as by multiplying \[\dfrac{{13}}{4}\] into the \[\dfrac{1}{4}\] , we get the required solution. i.e.,
 \[ \Rightarrow \dfrac{{13}}{4} \times \dfrac{1}{4}\]
On multiplying the fraction, we get
 \[ \Rightarrow \dfrac{{13}}{{16}}\]
Hence, it’s a required solution.
So, the correct answer is “ \[ \dfrac{{13}}{{16}}\] ”.

Note: Remember when we need to represent the different units in the same unit. Here in the above question, we converted unit quart to gallon. We have to know 1 gallon has divided into four equivalent parts i.e., half as represented as \[\dfrac{1}{2}\] similarly quarter is represented as \[\dfrac{1}{4}\] and the three quarters represented as \[\dfrac{3}{4}\] and mainly we know the how to multiply the fraction.