Question

How do you find the ratio $ 140 $ minutes to $ 9 $ hours in simplest form?

Answer 1

Hint: As we know that comparison of two quantities of the same kind by division is called ratio. Or we can say that the ratio is the number that can be used to express one quantity as a fraction of the other ones. It is denoted by. In this question we have two different units so we have to convert one of them in the same quantity as the other and then solve it.

Complete step-by-step answer:
As per the question we have $ 140 $ minutes and $ 9 $ hours, so we will convert the hour into minutes.
We know that in $ 1 $ hour, there are $ 60 $ minutes. So in $ 9 $ hours there are $ 9 \times 60 = 540 $ minutes.
Now we have both the quantities in the same units , so the required ratio is $ \dfrac{{140}}{{540}} $ .
It can be written as $ \dfrac{{140}}{{540}} = \dfrac{7}{{27}} $ .
Hence the required ratio is $ 7:27. $
So, the correct answer is “ $ 7:27 $ ”.

Note: We should know that a fraction is said to be written in the simplest form if the numerator and the denominator will not have a common factor except $ 1 $ . So we have to simplify the above fraction as small as possible and based on this definition, the simplest form can be found. We should also note that the question is asked to be in simplest form, not to convert into decimal i.e. $ \dfrac{7}{{27}} = 0.25 $ .