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# How many quarters are there in $18\dfrac{3}{4}$ ?

Last updated date: 13th Jun 2024
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Hint: Quarter means "fourth". A quarter is a quantity which is $\dfrac{1}{4}{th}$ in magnitude.
Observe that there are 4 quarters in 1 unit, i.e. $\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}=1$ .
$\dfrac{3}{4}$ can be written as $\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}$ .

The number $18\dfrac{3}{4}$ is a mixed fraction which actually represents a value of:
= $18+\dfrac{3}{4}$
Equating the denominators and adding, we get:
= $\dfrac{18\times 4}{4}+\dfrac{3}{4}$
= $\dfrac{72}{4}+\dfrac{3}{4}$
= $\dfrac{75}{4}$
= $75\times \dfrac{1}{4}$
So, there are 75 quarters in $18\dfrac{3}{4}$ .

Note: The question can also be solved by using the fact that there are 4 quarters in every 1.
So, there are $18\times 4=72$ quarters in 18, and there are 3 quarters in $\dfrac{3}{4}$ .
Overall, there are $72+3=75$ quarters.
$\dfrac{1}{2}$ of something is also called "a half" and $\dfrac{1}{4}$ of something is also called "a quarter". There are 2 halves of each 1, and there are 2 quarters in each half.
A "quart" is a common unit of capacity in the FPS system. It is equal to $\dfrac{1}{4}{th}$ of a gallon (3.7853 liters in U.S. and 4.546 liters in U.K.).