Question

The ratio of \[{\text{35}}\] minutes to \[{\text{45}}\] second in the simplest form is
A. \[{\text{35:45}}\]
B. \[{\text{7:9}}\]
C. \[{\text{2100:45}}\]
D. \[{\text{140:3}}\]

Answer 1

Hint: First of all calculate both the quantities into the same units so it will be easy for us to compare the ratio of both the quantities. As \[{\text{1minute = 60 second}}\], apply proper unit conversion method. We need to find the ratio of the given quantities only after having them in the same unit means to convert the unit of either of the term and then calculate it’s ratio.

Complete step by step answer:

First let us convert the minute quantity into seconds by using \[{\text{1minute = 60 second}}\] so \[{\text{35}}\] minutes will be
\[
  {\text{1minute = 60 second}} \\
  {\text{35minute = 35 $\times$ 1minute}} \\
  {\text{ = 35 $\times$ 60 second}} \\
  {\text{ = 2100second}} \\
 \]
And other parameter is of \[{\text{45}}\] second in order to find the simplest ratio of both we need to divide both the quantities
\[{\text{ = }}\dfrac{{{\text{2100}}}}{{{\text{45}}}}\]
As now further also we can simplify the above ratio, as we have a common factor among both numerator and denominator.
So,
\[
  {\text{ = }}\dfrac{{{\text{2100}}}}{{{\text{45}}}} \\
  {\text{ = }}\dfrac{{{\text{700}}}}{{{\text{15}}}}{\text{(factor:3)}} \\
  {\text{ = }}\dfrac{{{\text{140}}}}{{\text{3}}}{\text{(factor:5)}} \\
 \]
As it cannot be further simplified. so, our correct answer will be an option (d).

Note: One can also think that option (C) is also the correct option as it matches the ratio, but here we are told to find the simplest ratio so we go with option (D). A ratio in the simplest form is also called the ratio in the lowest terms. Example: The ratio \[{\text{32:48}}\] is not in the simplest form, because \[16\] is a common factor of its numerator and denominator both. The simplest form of this ratio is \[{\text{2:3}}\].