Question

The weight of an empty gas cylinder is $ 16\dfrac{4}{5} $ kg and it contains $ 14\dfrac{2}{3} $ kg of gas. What is the weight of the cylinder filled with gas?

Answer 1

Hint: Here, to get the weight of the cylinder filled with gas is the sum of the weight of an empty gas cylinder and the contents of the gas. First of all we will convert the mixed fraction in the form of simple fractions and then simplify the fractions for the required resultant value.

Complete step-by-step answer:
Given that: The weight of an empty gas cylinder is $ = 16\dfrac{4}{5} $ kg
Convert it in the form of the simple fractions, fractions are expressed as the term numerator upon the denominator.
The weight of an empty gas cylinder is $ = \dfrac{{84}}{5} $ kg …… (A)
Now, the contains of the gas cylinder is $ = 14\dfrac{2}{3} $ kg gas
Convert it in the form of the simple fractions –
The contents of the gas cylinder is $ = \dfrac{{44}}{3} $ kg gas …… (B)
The total weight of the cylinder filled with gas $ = \dfrac{{84}}{5} + \dfrac{{44}}{3} $
Take the LCM (least common multiples) for the above expression and then simplify the numerator.
The total weight of the cylinder filled with gas $ = \dfrac{{84(3) + 44(5)}}{{5(3)}} $
Simplify the numerator finding the product of the terms –
 $ = \dfrac{{252 + 220}}{{15}} $
Add the terms in the numerator –
 $ = \dfrac{{472}}{{15}} $
Convert the above expression in the form of the mixed fraction –
 $ = 31\dfrac{7}{{15}} $
Hence, the total weight of the cylinder filled with gas is $ 31\dfrac{7}{{15}} $ kg
So, the correct answer is “ $ 31\dfrac{7}{{15}} $ kg”.

Note: Mixed fraction is the fraction expressed with the integer. Fraction is expressed as the part of the whole and it is the ratio numerator upon the denominator. Do not get confused between the fraction and the percentage. Percentage is the fraction where numerator upon the hundred.