Question

The cost of $2\dfrac{1}{2}$ meters of cloth is Rs. $78\dfrac{3}{4}$. Find the cost of cloth per meter.

Answer 1

Hint: First convert the time from mixed fraction to improper fraction by multiplying the whole number part with the denominator and adding the numerator with the resultant. Then, divide the cost of the cloth by the quantity to get the cost of cloth per meter. After that convert the cost into a mixed fraction.

Complete step by step answer:
Given, the cost of $2\dfrac{1}{2}$ meters of cloth is Rs. $78\dfrac{3}{4}$.
Let the cost of cloth be $x$.
Now, change the amount from mixed fraction to improper fraction by multiplying the whole number part with the denominator and adding numerator with the resultant,
$\Rightarrow 78\dfrac{3}{4} = \dfrac{{78 \times 4 + 3}}{4}$
Multiply and add the terms,
$\Rightarrow 78\dfrac{3}{4} = \dfrac{{315}}{4}$
Now, change the cloth size from mixed fraction to improper fraction by multiplying the whole number part with the denominator and adding numerator with the resultant,
$\Rightarrow 2\dfrac{1}{2} = \dfrac{{2 \times 2 + 1}}{2}$
Multiply and add the terms,
$\Rightarrow 2\dfrac{1}{2} = \dfrac{5}{2}$
For the cost of cloth per meter divide the total cost of cloth by total size,
$\Rightarrow x = \dfrac{{\dfrac{{315}}{4}}}{{\dfrac{5}{2}}}$
Multiply and divide the terms on the right side,
$\Rightarrow x = \dfrac{{630}}{{20}}$
Cancel out the common terms,
$\Rightarrow x = \dfrac{{63}}{2}$
Now convert the improper fraction into a mixed fraction by dividing the numerator by denominator and write down the whole number and remainder as the numerator.
$\Rightarrow x = \dfrac{{62}}{2} + \dfrac{1}{2}$
Cancel out the common factor,
$\Rightarrow x = {\text{Rs}}{\text{. }}31\dfrac{1}{2}$

Hence, the cost of cloth per meter is ${\text{Rs}}{\text{. }}31\dfrac{1}{2}$.

Note:
The students might make mistakes by not converting the mixed fraction into improper fraction which will lead to wrong or lengthy calculation.
The word fraction derives from the Latin word “Fractus” meaning broken. It represents a part of a whole, consisting of several equal parts out of a whole.
There are 3 types of fractions:-
Proper fractions: - It represents a part of a whole. The numerator is smaller than the denominator.
Improper fractions: - It has a numerator that is greater than or equal to the denominator.
Mixed fractions: - It is a combination of a whole number and a proper fraction.