Question

One roll of kitchen tissues is \[15\dfrac{3}{4}\] long. Shreya has three complete rolls and \[\dfrac{2}{3}\] of a roll. How many meters of kitchen tissue does Shreya have?

Answer 1

Hint:
Here, we will first be rewriting the fraction in normal form and then we will multiply the length of one roll by 3 to find the length of three complete rolls and multiply the length of one complete roll by \[\dfrac{2}{3}\] to find the remaining length Shreya has. Then we will add the length of 3 complete rolls with the length of \[\dfrac{2}{3}\] of one roll to find the total length Shreya has.

Complete step by step solution:
We are given that one roll of kitchen tissues is \[15\dfrac{3}{4}\] long.
Rewriting the given fraction in normal form, we get
\[ \Rightarrow \dfrac{{63}}{4}\]
So we will multiply the length of one roll by 3 to find the length of three complete rolls, we get
\[
   \Rightarrow 3 \times \dfrac{{63}}{4} \\
   \Rightarrow \dfrac{{189}}{4} \\
 \]
Now we will multiply the length of one complete roll by \[\dfrac{2}{3}\] to find the remaining length Shreya has, we get
\[
   \Rightarrow \dfrac{2}{3} \times \dfrac{{63}}{4} \\
   \Rightarrow \dfrac{{21}}{2} \\
 \]
Adding the length of 3 complete rolls with the length of \[\dfrac{2}{3}\] of one roll to find the total length Shreya has, we get
\[ \Rightarrow \dfrac{{189}}{4} + \dfrac{{21}}{2}\]
Taking common denominator in the above equation, we get
\[
   \Rightarrow \dfrac{{189}}{4} + \dfrac{{42}}{4} \\
   \Rightarrow \dfrac{{231}}{2} \\
 \]
Rewriting the given fraction in the mixed form, we get
\[ \Rightarrow 115\dfrac{1}{2}{\text{ m}}\]

Thus, the \[115\dfrac{1}{2}\] meters of kitchen tissue Shreya had.

Note:
This is a really simple problem, everything is written in the question. We will find the final fraction by dividing the 231 by 2.

Writing it into the mixed fraction, \[{\text{Quotient}}\dfrac{{{\text{Remainder}}}}{{{\text{Divisor}}}}\] to match with the options, we get
\[115\dfrac{1}{2}\]