Question

What is ${\displaystyle \frac{1}{8}}$ divided by ${\displaystyle \frac{1}{4}}$ ?

Answer 1

Hint: In this problem, we have to find the value when one number is divided by another number. Thus, we will use the basic mathematical rule and the reciprocal method, to get the accurate solution. Now, we will first convert the language statement into the mathematical statement, that is if $a$ is divided by $b$ , then we write it as ${\displaystyle \frac{a}{b}}$ , where $a$ is equal to ${\displaystyle \frac{1}{8}}$ and $b$ is equal to ${\displaystyle \frac{1}{4}}$ . After that, we will take the reciprocal of the denominator. In the end, we will make the necessary calculations, to get the required solution for the problem.

Complete step by step solution:
According to the problem, we have to find the value when one number is divided by another number.
Thus, we will use the basic mathematical rule and the reciprocal method.
The statement given to us is ${\displaystyle \frac{1}{8}}$ divided by ${\displaystyle \frac{1}{4}}$
Now, we will first convert the language statement into mathematical statement, that is when $a$ is divided by $b$ , then we write it as ${\displaystyle \frac{a}{b}}$ , where $a={\displaystyle \frac{1}{8}}$ and $b={\displaystyle \frac{1}{4}}$ , thus we get
$\Rightarrow {\displaystyle \frac{{\displaystyle \frac{1}{8}}}{{\displaystyle \frac{1}{4}}}}$
Now, we will take the reciprocal of the denominator in the above expression, we get
$\Rightarrow {\displaystyle \frac{1}{8}}\times {\displaystyle \frac{4}{1}}$
Now, we will make the necessary calculations in the above expression, we get
$\Rightarrow {\displaystyle \frac{1}{2}}$ which is the required solution
Therefore, when ${\displaystyle \frac{1}{8}}$ is divided by ${\displaystyle \frac{1}{4}}$ , then we get ${\displaystyle \frac{1}{2}}$ as a solution.

Note: While solving this problem, do mention all the steps properly to avoid mathematical errors. Do not write the mathematical statement as ${\displaystyle \frac{b}{a}}$ , because this means $b$ is divided by $a$ and not $a$ is divided by $b$ .