Question

Find the ratio of 4 weeks to 18 days.

Answer 1

Hint: We know that a ratio indicates how many times one number contains another number. We can also say that the simplest fractional form which indicates how many times one number contains another number. It is also a dimensionless quantity. Let us assume the value of x is equal to 4 weeks. Now we have to convert weeks into days. Now we will consider this as equation (1). Let us also assume the value of y is equal to 18 days. Now let us consider this as equation (2). Now by using equation (1) and equation (2), we can find the value of the ratio of 4 weeks and 18 days.

Complete step-by-step answer:
Before solving the question, we know that a ratio indicates how many times one number contains another number. We can also say that the simplest fractional form which indicates how many times one number contains another number. It is also a dimensionless quantity.
The ratio of x and y is said to be equal to \[a:b\] where \[a:b\] is the simplest ratio possible.
Let us assume the value of x is equal to 4 weeks.
\[x=\text{4 weeks}\]
We know that 1 week is 7 days.
\[\begin{align}
  & \Rightarrow \text{x=4(7) days} \\
 & \Rightarrow \text{x=28 days}.....\text{(1)} \\
\end{align}\]
Let us also assume the value of y is equal to 18 days.
\[y=18\text{ days}......\text{(2)}\]
Now by using equation (1) and equation (2), we can find the ratio of x and y.
\[\Rightarrow \dfrac{x}{y}=\dfrac{28}{18}\]
\[\Rightarrow \dfrac{x}{y}=\dfrac{14}{9}......(3)\]
Finally, from equation (3) we have obtained the ratio of x and y.
So, the ratio of 28 weeks and 18 weeks is equal to \[14:9\].


Note: Before solving the question, we know that a ratio indicates how many times one number contains another number. We can also say that the simplest fractional form which indicates how many times one number contains another number. It is also a dimensionless quantity.
The ratio of x and y is said to be equal to \[a:b\] where \[a:b\] is the simplest ratio possible.
Let us assume the value of x is equal to 4 weeks.
\[x=\text{4 weeks}......\text{(1)}\]
Let us also assume the value of y weeks is equal to 18 days.
We know that 1 week is 7 days.
By criss-cross method, we get
\[\begin{align}
  & y\to 18 \\
 & 1\to 7 \\
\end{align}\]
\[\begin{align}
  & \Rightarrow 7y=18 \\
 & \Rightarrow y=\dfrac{18}{7}weeks....(2) \\
\end{align}\]
Now by using equation (1) and equation (2), we can find the ratio of x and y.
\[\begin{align}
  & \Rightarrow \dfrac{x}{y}=\dfrac{4}{\left( \dfrac{18}{7} \right)} \\
 & \Rightarrow \dfrac{x}{y}=\dfrac{28}{18} \\
\end{align}\]
\[\Rightarrow \dfrac{x}{y}=\dfrac{14}{9}......(3)\]
Finally, from equation (3) we have obtained the ratio of x and y.
So, the ratio of 28 weeks and 18 weeks is equal to \[14:9\].