Question

Question 118.
Roma gave a wooden board of length $150\frac{1}{4}$ cm to a carpenter for making a shelf. The Carpenter sawed off a piece of $40\frac{1}{5}$ cm from it.What is the length of the remaining piece?

Answer 1

Given that

The total length of the wooden board given by Roma to the carpenter = $150\frac{1}{4}$ cm
The length of the wooden board the carpenter sawed off = $40\frac{1}{5}$ cm

The total length of the wooden board = The length of the wooden board the carpenter sawed off + Length of the remaining piece

Length of the remaining piece = The total length of the wooden board - The length of the wooden board the carpenter sawed off

On substituting the values we get:
Length of the remaining piece =$150\frac{1}{4}-40\frac{1}{5}$ cm

We can express a mixed fraction as an improper fraction as $\frac{(\text{Whole}\times \text{Denominator})\text{+ Numerator}}{\text{Denominator}}$.

$\therefore$ Length of the remaining piece =$\frac{150\times 4+1}{4}-\frac{40\times 5+1}{5}$ cm
$\Rightarrow$ Length of the remaining piece =$\frac{601}{4}-\frac{201}{5}$ cm

Now, the LCM of the denominator of the fractions $\frac{601}{4}$ and $\frac{201}{5}$ i.e. the LCM of 4 and 5 is 20.

$\therefore$ Length of the remaining piece =$\frac{601\times 5}{4\times 5}-\frac{201\times 4}{5\times 4}$ cm
$\Rightarrow$ Length of the remaining piece =$\frac{3005}{20}-\frac{804}{20}=\frac{2201}{20}$ cm

We can express an improper fraction as a mixed fraction by dividing the numerator by denominator to obtain the quotient and the remainder.

Then the mixed fraction will be written as $\text{Quotient}\frac{\text{Remainder}}{\text{Divisor}}$.

$\left[\begin{array}{c}\because 20\left)2201\right(110\\ \frac{20}{20}\\ \frac{20}{1}\end{array}\right]$

$\therefore$ Length of the remaining piece =$110\frac{1}{20}cm$
So, the length of the remaining piece is $110\frac{1}{20}cm.$