Question

A car covers $641\dfrac{1}{4}$ KM in $43\dfrac{1}{8}$ liters of fuel. How much distance can this cover on this car in a liter of fuel?

Answer 1

Hint: First we shall learn about the topic fraction. A fraction is just a numerical value which denotes the equal parts of a whole (or collection). We may apply the fraction in our daily life. For example, when we slice a guava, it will split into two or four and so on.
Example:$\dfrac{1}{2},\dfrac{1}{4},\dfrac{2}{3}$
Here, the number above the line is usually called the numerator and the number below the line is called the denominator.

Complete step-by-step solution:
 In our question, we need to convert the mixed fraction into an improper fraction.
Example:
We need to convert $5\dfrac{1}{4}$ into an improper fraction.
First step is to multiply the denominator value with the whole part (i.e.$5 \times 4 = 20$)
Then, add the resulting value with a numerator (i.e.$20 + 1 = 21$). Finally, write the resulted number in the numerator place and there is no change in the denominator (i.e.$\dfrac{{21}}{4}$ is the required fraction)
It is given that the distance covered by a car in $43\dfrac{1}{8}$ liters of fuel= $641\dfrac{1}{4}$ KM
To find: Distance covered in a liter of fuel
We shall convert the mixed fractions.
$43\dfrac{1}{8} = \dfrac{{345}}{8}$
Also,
$641\dfrac{1}{4} = \dfrac{{2565}}{4}$
Hence, the distance covered by a car in $\dfrac{{345}}{8}$ liters of fuel= $\dfrac{{2565}}{4}$ KM
Distance covered in a liter of fuel
$ = \dfrac{{2565}}{4} \times \dfrac{8}{{345}}$
$ = \dfrac{{513}}{1} \times \dfrac{2}{{69}}$
$ = \dfrac{{171}}{1} \times \dfrac{2}{{23}}$
$ = \dfrac{{342}}{{23}}$
Therefore, Distance covered in a liter of fuel $ = \dfrac{{342}}{{23}}$Km
Now, convert the above improper fraction into mixed fraction.
First divide the numerator by the denominator. Write the quotient value as the whole number and remainder as the new numerator and there is no change in the denominator.
So, $\dfrac{{342}}{{23}} = 14\dfrac{{20}}{{23}}$
Therefore, Distance covered in a liter of fuel $14\dfrac{{20}}{{23}}$Km

Note: Fractions are classified into many types. Among them, the three important types of fraction are as follows.
> Proper fraction: It is a fraction in which the numerator is less than the denominator.
 Example:$\dfrac{4}{5}$
> Improper fraction: It is a fraction in which the numerator is more than or equal to the denominator.
Example:$\dfrac{7}{4},\dfrac{3}{3}$
> Mixed fraction: It is a fraction containing both the integral part and a proper fraction.
Example:$5\dfrac{1}{4}$