Question

How many quarters are there in $18{\displaystyle \frac{3}{4}}$ ?

Answer 1

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

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

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 ${\displaystyle \frac{3}{4}}$ .
Overall, there are $72+3=75$ quarters.
 ${\displaystyle \frac{1}{2}}$ of something is also called "a half" and ${\displaystyle \frac{1}{4}}$ 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 ${\displaystyle \frac{1}{4}}th$ of a gallon (3.7853 liters in U.S. and 4.546 liters in U.K.).