Question

Find the ratio of the first quantity with the second in its simplest form,
2.40 cm to 1.44 cm, is the ratio equal to 5 : 3?
(a) True
(b) False

Answer 1

Hint: We have to check if the ratio 2.40 cm to 1.44 cm is equal to 5 : 3, so first of all we will convert the decimal numbers 2.40 and 1.44 into the fractional form and after that, we will take the ratio of the obtained two numbers and then we will express it in the fraction form and simplify it and check whether the obtained ratio is equal to 5 : 3 or not if it is equal then true otherwise answer is false.

Complete step-by-step solution:
We are given two numbers i.e. 2.40 and 1.44 and we have to find their ratio so first, we will convert these decimal numbers into the fractional form,
This we will do as follows,
2.40
 $\begin{align}
  & =\dfrac{240}{100} \\
 & =\dfrac{5\times 4\times 12}{5\times 5\times 4} \\
 & =\dfrac{12}{5} \\
\end{align}$
Similarly for 1.44, we get
$\begin{align}
  & =\dfrac{144}{100} \\
 & =\dfrac{4\times 36}{4\times 25} \\
 & =\dfrac{36}{25} \\
\end{align}$
Now we have the ratio as,
$\dfrac{12}{5}:\dfrac{36}{25}$
Converting this to fractional form we get,
\[\begin{align}
  & =\dfrac{12\times 25}{5\times 36} \\
 & =\dfrac{5\times 5\times 12}{3\times 5\times 12} \\
\end{align}\]
$=\dfrac{5}{3}$
Hence the ratio is equal to 5:3 so
We get the option (a) as the correct answer i.e. TRUE

Note: While solving the problems related to the ratio you should first make sure to make the units of the numerator and the denominator same and then proceed further and also go through the mentioned method to convert the decimal numbers to the fractional numbers for more problems like this. Students can also take the ratio of 2.40 to 1.44 in fraction form. Then they can multiply both denominator and numerator by 100 and simplify further.