Question

A film show lasted for $3\dfrac{1}{3}$​ hours. Out of this time, ​ $1\dfrac{3}{4}$ hours was spent on advertisements. What was the actual duration of the film?

Answer 1

Hint: In order to solve this question by calculating the actual duration of the film , We are given with the information that a film show is of $3\dfrac{1}{3}$hours. Also the time spent on advertisements is $1\dfrac{3}{4}$ , So, to calculate the actual duration of the film , we need to determine the difference of the hours the film show is played and the advertisements played. But for making our calculations easier we need to convert the given data as mixed fraction into the fraction form. A mixed fraction can be stated as the number consisting of a whole number and a proper fraction or it can be said as the fraction which is represented with its quotient and remainder.

Complete step-by-step solution:
We have the data given to us which are as follows –
The total time of the show lasted for = $3\dfrac{1}{3}$hours
The total no. of hours spent on advertisements = $1\dfrac{3}{4}$
But for making our calculations easier we need to convert the given data as mixed fraction into the fraction form.
We can convert the mixed fraction into improper fraction as follows –
We will first multiply the whole number by the denominator of the given mixed fraction.
Then add the multiplied answer to the numerator of the fraction.
The sum is going to be the numerator of the fraction.
The denominator will be as it is.
Now , here the total time of the show given in the mixed number should be converted to the fraction as follows =
 We will first multiply the whole number 3 by the denominator 3 of the given mixed fraction. $3 \times 3 9$
Then add the multiplied answer 9 to the numerator 1 of the fraction. $9 + 1 = 10$
The sum is going to be the numerator 10 of the fraction.
The denominator 3 will be as it is.
So , the fraction form of the $3\dfrac{1}{3}$ is $\dfrac{{10}}{3}$.
Similarly , the fraction form of the $1\dfrac{3}{4}$ is $\dfrac{7}{4}$.
To calculate the actual time of film we will subtract the time spent on advertisements from the total time of the show.
Actual time of the show = $\dfrac{{10}}{3} - \dfrac{7}{4}$= $\dfrac{{40 - 21}}{{12}}$=$\dfrac{{19}}{{12}}$.

Therefore , Actual time of the film show = $\dfrac{{19}}{{12}}$=$1\dfrac{7}{{12}}$.

Note: Remember the formula of \[{\mathbf{Dividend}}{\text{ }} = {\text{ }}{\mathbf{Quotient}} \times {\mathbf{Divisor}}{\text{ }} + {\text{ }}{\mathbf{Remainder}}.\]
-Conversion from the mixed fraction to the improper fraction must be known.
-Conversion from the improper fraction to the mixed fraction must be known.
Proper fraction is the form of fraction when the denominator is greater than the numerator.
The fraction when the denominator is greater than the numerator is a fraction that is less than 1.