Question

A bundle of 500 sheets of paper has a net weight of $23\dfrac{3}{10}$ kg. Find the weight of 1 sheet of paper.\[\]

Answer 1

Hint: Use the unitary method to solve the problem. First convert the given mixed fraction to improper fraction and then divide by the total number of sheets get the weight of 1 sheet.\[\]

Complete step by step answer:
We will solve the problem with unitary method. The unitary method is used when information about a group of things are given and we have to find the information about a single unit by division. \[\]

As given in the question that there are 500 sheets of paper which has a net weight $23\dfrac{3}{10}$ kg.
We see the weight is given in mixed fraction. Let us first convert it to improper fraction. We know that a mixed fraction of the type $a\dfrac{b}{c}$ is converted to improper fraction as $\dfrac{c\times a+b}{c}$ where $a,b,c$ are positive integers. . So the weight of 500 sheets in improper fraction is $\dfrac{10\times 23+3}{10}=\dfrac{233}{10}$kg.\[\]

We are given the information about 500 sheets and we have found the information about 1 sheet. So we divide using unitary method to find the weight of 1 sheet,
So the weight of 1 sheet is $\dfrac{233}{10}\div 500$. We know that to divide $\dfrac{233}{10}$ by 500 we need to multiply $\dfrac{233}{10}$ with the reciprocal of 500. The reciprocal of a fraction of the type $\dfrac{a}{b}$ is $\dfrac{b}{a}$ where $a,b$ are positive integers. The reciprocal of 500 whose denominator is 1 is $\dfrac{1}{500}$. Now we do the division
\[\dfrac{233}{10}\div 500=\dfrac{233}{10}\times \dfrac{1}{500}\]
 So we multiply two fractions numerator by numerator and denominator by denominator.We have
\[\dfrac{233}{10}\div 500=\dfrac{233}{10}\times \dfrac{1}{500}=\dfrac{233\times 1}{500\times 10}=\dfrac{233}{5000}\]

So the weight of 1 sheet is $\dfrac{233}{5000}$ kg. \[\]

Note: The key in this question to divide total weight by total numbered sheets not the opposite. You can also convert the obtained fraction to decimals first dividing by 5 and then by 1000. We show it as $\dfrac{233}{5000}=\dfrac{233}{5\times 1000}=\dfrac{233}{5}\times \dfrac{1}{1000}=\dfrac{46.6}{1000}=0.0466$.