Question

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

Answer 1

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} $ .

Complete step-by-step answer:
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.).