Question

Roma gave a wooden board of length \[150\dfrac{1}{4}{\rm{cm}}\] to a carpenter for making a shelf. The carpenter sawed a piece of \[40\dfrac{1}{5}{\rm{cm}}\] from it. What is the length of the remaining piece?

Answer 1

Hint:
Here we will firstly convert the given lengths that are given in the mixed fraction into the improper fraction. Then we will subtract the length of the sawed piece from the total length of the wooden board to get the length of the remaining piece.

Complete Step by Step Solution:
According to the question:
Total length of the wooden board \[ = 150\dfrac{1}{4}{\rm{cm}}\]
We will convert this length into the improper fraction as it is given in the mixed fraction form. Therefore, we get
Total length of the wooden board \[ = 150\dfrac{1}{4} = \dfrac{{\left( {150 \times 4} \right) + 1}}{4} = \dfrac{{601}}{4}{\rm{cm}}\]
Now it is also given that the carpenter sawed a piece of \[40\dfrac{1}{5}{\rm{cm}}\] from it. Therefore
The length of the sawed piece \[ = 40\dfrac{1}{5}{\rm{cm}}\]
We will convert this length into the improper fraction. Therefore, we get
Sawed length \[ = 40\dfrac{1}{5}{\rm{cm}} = \dfrac{{\left( {40 \times 5} \right) + 1}}{5} = \dfrac{{201}}{5}{\rm{cm}}\]
Now we will subtract the sawed piece length from the total length of the wooden board to get the length of the remaining piece. Therefore, we get
Length of the remaining piece \[ = \dfrac{{601}}{4} - \dfrac{{201}}{5}\]
Taking LCM, we get
\[ \Rightarrow \] Length of the remaining piece \[ = \dfrac{{\left( {601 \times 5} \right) - \left( {201 \times 4} \right)}}{{4 \times 5}}\]
\[ \Rightarrow \] Length of the remaining piece \[ = \dfrac{{3005 - 804}}{{20}}\]
Subtracting the terms in the denominator, we get
\[ \Rightarrow \] Length of the remaining piece \[ = \dfrac{{2201}}{{20}}\]
We will now write it in the mixed fraction form. Therefore, we get
\[ \Rightarrow \] Length of the remaining piece \[ = 110\dfrac{1}{{20}}{\rm{cm}}\]

Hence, the length of the remaining piece is equal to \[110\dfrac{1}{{20}}{\rm{cm}}\]

Note:
Here, we need to remember that when we find the remaining amount or piece of something then we subtract the used amount or piece from the total amount or piece.
Here the lengths are given in mixed fraction and we cannot mathematically operate the fraction. Therefore, we converted it to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equals to the denominator, then it is known as an improper fraction. A mixed Fraction is the combination of a natural number and fraction. It is basically an improper fraction.