Question

Find the ratio of the following: 40 cm to 1.5 m?

Answer 1

Hint: We start solving the problem by converting both the given measurements into a same unit of measurement. We use the fact that 1 metre (m) is equal to 100 centimetres (cm) to convert 1.5 m into the centimetres. After converting to centimetres, we take the ratio of both the measurements using the fact that the ratio of ‘a’ to ‘b’ is $a:b=\dfrac{a}{b}$. We then make the necessary calculations to get the required answer.

Complete step by step answer:
According to the problem, we need to find the ratio: 40 cm to 1.5m.
Let us convert both the given measurements into the same unit of measurement.
We know that 1 metre (m) is equal to 100 centimetres (cm). i.e., $1m=100cm$.
So, we get $1.5m=1.5\times 100=150cm$.
Now, we need to find the ratio of 40 cm to 150 cm. Let us assume the ratio is ‘d’.
We know that ratio of ‘a’ to ‘b’ is defined as $a:b=\dfrac{a}{b}$. Let us use this concept to find the ratio of 40 cm to 150 cm.
So, we get $d=\dfrac{40}{150}$.
$\Rightarrow d=\dfrac{4}{15}$.

So, we have found the ratio of 40 cm to 1.5m as $\dfrac{4}{15}$.

Note: We should not directly take the ratio as $\dfrac{40}{1.5}=\dfrac{80}{3}$, which is wrong as they were not in similar units. We can also solve this problem by converting 40 cm into the metres using the conversion $1cm=0.01m$ and take the ratio which will also give us the same answer. We should know that ratio should be provided in the form of $\dfrac{p}{q}\left( q\ne 0 \right)$. Similarly, we can expect problems to find the ratio of 4 mm to 1 m.