Question

A room measures $5\dfrac{1}{3}\text{ yd}$ by $3\dfrac{3}{4}\text{ yd}$. How many square yards of the floor?

Answer 1

Hint: We start solving this question by assuming the length of room to be \[l=5\dfrac{1}{3}\text{ yd}\] and width of room to be $b=3\dfrac{3}{4}\text{ yd}$. Now, we know that the room is rectangular in shape so we will use the formula of area of rectangle to find the area of floor. The area of the rectangle is given by $length\times width$. By substituting the values and simplifying the obtained equations we get the desired answer.

Complete step by step solution:
We have been given that a room measures $5\dfrac{1}{3}\text{ yd}$ by $3\dfrac{3}{4}\text{ yd}$.
We have to find the area of the floor.
Now, let us assume that the length of room is \[l=5\dfrac{1}{3}\text{ yd}\] and width of room is $b=3\dfrac{3}{4}\text{ yd}$.
Now, we know that the room is rectangular in shape and the area of the rectangle is given as $length\times width$.

Now, substituting the values in the above formula we will get
$\Rightarrow 5\dfrac{1}{3}\text{ yd}\times 3\dfrac{3}{4}\text{ yd}$
Now, simplifying the above obtained equation we will get
$\Rightarrow \dfrac{16}{3}\text{ yd}\times \dfrac{15}{4}\text{ yd}$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow \dfrac{16\times 15}{3\times 4}\text{ sq}\text{. yd} \\
 & \Rightarrow \dfrac{240}{12}\text{ sq}\text{. yd} \\
 & \Rightarrow 20\text{ sq}\text{. yd} \\
\end{align}$
Thus the area of the rectangle is equal to the area of the floor.
Hence the area of the floor is $20\text{ sq}\text{. yd}$.

Note: In this type of question be careful about the units. The units of all quantities must be the same, if the units are different and we solve the question without converting the units we get the incorrect answer. Also students must know the conversion of mixed fraction into improper fraction.