Question

What is the ratio between \[1\dfrac{1}{4}\] hours and \[25\] minutes?

Answer 1

Hint: We have to find the ratio of the given two measurements of time. We solve this question using the concept of the conversion of the mixed fraction into a simple fraction. We should have the knowledge of the conversion of the units of measurements of hour to minutes. And the concept of the formation of ratios. First, we will change the value of the mixed fraction into a simple fraction and then use the relation of the conversion of the time in hours to the time in minutes. We will change the value of both times into a common system of units and then dividing one by the other, we will obtain the ratio of the both given values of time.

Complete step-by-step answer:
Given:
The ratio between \[1\dfrac{1}{4}\] hours and \[25\] minutes.
Let us consider that the two times \[1\dfrac{1}{4}\] hours and \[25\] minutes are \[a\] and \[b\] respectively.
So, we get the values as:
\[a = 1\dfrac{1}{4}\;hours\]
\[a = 1.25\;hours\]
And \[b = 25\;minutes\]
Now, we also know that the relation for the measurement of time in hours and minutes is given as:
\[1hour = 60\;minutes\]
Using the relation, we can write the expression for time as:
\[a = 1.25 \times 60\]
\[a = 75\;minutes\]
Also, we know that we can the write the ratio as:
\[a:b = \dfrac{a}{b}\]
So, we can write the ratio of the two times as:
\[\dfrac{a}{b} = \dfrac{{75}}{{25}}\]
Simplifying, the ratio we get the value of ratio as:
\[\dfrac{a}{b} = \dfrac{3}{1}\]
Hence, we find that the ratio between \[1\dfrac{1}{4}\] hours and \[25\] minutes is \[3:1\].
So, the correct answer is “ \[3:1\]”.

Note: We wrote the value of time \[1\dfrac{1}{4}\] as \[1.25\]. As using the property of writing the mixed fraction into simple fraction and then exact value.
The mixed fraction can be written as:
\[1\dfrac{1}{4} = \dfrac{{1 \times 4 + 1}}{4}\]
\[1\dfrac{1}{4} = \dfrac{5}{4}\]
And on solving, we get the value as:
\[1\dfrac{1}{4} = 1.25\]
The ratio of two numbers can be written as:
\[a:b = \dfrac{a}{b}\]