Question

Find the ratio of following:
(1) 30 minutes to 45 minutes
(2) 10 minutes to 1 hour

Answer 1

Hint: We solve this problem by using the definition of ratios.
The representation of ratio \[a\] to \[b\] is given as \[a:b\]
We have the definition of ratios that is
\[a:b=\dfrac{a}{b}\]
By using the above definition we find the required ratio after converting the numbers into the same units.
We use the conversion of time that is
\[1hour=60\text{minutes}\]

Complete step by step answer:
(1) We are asked to find the ratio of 30 minutes to 45 minutes
Let us assume that the ratio of 30 minutes to 45 minutes as \[x\]
We know that the condition that the representation of ratio \[a\] to \[b\] is given as \[a:b\]
By using the above condition we get
\[\Rightarrow x=30:45\]
We know that the definition of ratios that is
\[a:b=\dfrac{a}{b}\]

By using the above definition we get the required ratio as
\[\begin{align}
  & \Rightarrow x=\dfrac{30}{45} \\
 & \Rightarrow x=\dfrac{2}{3} \\
\end{align}\]
Now, again by using the definition of ratios we get the required ratio as
\[\Rightarrow x=2:3\]
Therefore, we can conclude that the ratio of 30 minutes to 45 minutes is \[2:3\]
(2) We are asked to find the ratio of 10 minutes to 1 hour.
We know that we use the ratios only for the same units.
We know that the conversion of time as
\[1hour=60\text{minutes}\]
By using the above conversion we get the required ratio as 10 minutes to 60 minutes.
Let us assume that the ratio as \[y\]
By using the definition of ratio we get the required ratio as
\[\begin{align}
  & \Rightarrow y=\dfrac{10}{60} \\
 & \Rightarrow y=\dfrac{1}{6} \\
\end{align}\]
Now, again by using the definition of ratios we get the required ratio as
\[\Rightarrow y=1:6\]
Therefore, we can conclude that the ratio of 10 minutes to 1 hour is \[1:6\]

Note:
 students may do mistakes in the representation of the ratio.
We use the representation of ratio \[a\] to \[b\] is given as \[a:b\]
But students may do mistake and take the representation of ratio \[a\] to \[b\] is given as \[b:a\]
This gives the wrong answer because the ratio \[a\] to \[b\] considers that \[a\] comes first then followed by \[b\]
We also note that we use the ratios of two quantities only when the two quantities are of the same units