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
$$a:b={\displaystyle \frac{a}{b}}$$
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
$$a:b={\displaystyle \frac{a}{b}}$$

By using the above definition we get the required ratio as
$$\begin{array}{rl}& \Rightarrow x={\displaystyle \frac{30}{45}}\\ & \Rightarrow x={\displaystyle \frac{2}{3}}\end{array}$$
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
$$\begin{array}{rl}& \Rightarrow y={\displaystyle \frac{10}{60}}\\ & \Rightarrow y={\displaystyle \frac{1}{6}}\end{array}$$
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