Question

How do you write three different complex fractions that simplify to $\dfrac{1}{4}$ ?

Answer 1

Hint: A complex fraction can be defined as a fraction in which the denominator and numerator or both contain fraction. An example of a complex fraction is $\left( \dfrac{8}{4} \right)\left( \dfrac{9}{10} \right)$. Hence to get three different complex fractions that simplify to $\dfrac{1}{4}$ just multiply numerator and denominator by the same number monomial polynomial or may be a complex number.

Complete step-by-step answer:
As per the question we have to write three complex fraction that simplify to $\dfrac{1}{4}$
Complex fractions are bigger fractions that can be simplified into smaller fractions.
To get three different complex fractions that simplify to $\dfrac{1}{4}$ we have to just multiply. Numerator and denominator by the same number and you will get the fraction. Here the numerator is $1$ and the denominator is $4$.
The first number we will take i.e. $\dfrac{7}{11}$.
Multiply numerator i.e. $1$ and denominator i.e. $4$ by the number $\dfrac{7}{11}$
$=\dfrac{1\times \dfrac{7}{11}}{4\times \dfrac{7}{11}}=\dfrac{\dfrac{7}{11}}{\dfrac{28}{11}}$
The first complex fraction is $\dfrac{\dfrac{7}{11}}{\dfrac{28}{11}}$
The second number will take $\dfrac{13}{16}$.
Multiply numerator i.e. $1$ and denominator i.e. $4$ by the number $\dfrac{13}{16}$
$\dfrac{1}{4}=\dfrac{1\times \dfrac{13}{16}}{4\times \dfrac{13}{16}}=\dfrac{\dfrac{13}{16}}{\dfrac{13}{4}}$
The second complex fraction is \[\dfrac{\dfrac{13}{16}}{\dfrac{13}{4}}\] which will simplify to $\dfrac{1}{4}$.
The third number we will take $\dfrac{15}{4}3\dfrac{3}{4}$
Multiply numerator i.e. $1$ and denominator i.e. $4$by the number $3\dfrac{3}{4}$
$\dfrac{1}{4}=\dfrac{1\times 3\dfrac{3}{4}}{4\times 3\dfrac{3}{4}}=\dfrac{\dfrac{1}{1}\times \dfrac{15}{4}}{4\times \dfrac{15}{4}}=\dfrac{\dfrac{15}{4}}{15}$
The third complex fraction which will simplify to $\dfrac{1}{4}$ is $\dfrac{\dfrac{15}{4}}{15}$
There are many possible answers.

There are infinite complex fractions that can be simplified to $\dfrac{1}{4}$.

Additional Information:
As per the question we have to write $3$ complex fraction which will simplify to $\dfrac{1}{4}$. For this you must know here to simplify the complex fraction. Because when you select a number or complex fraction after selecting a number or complex fraction after simplifying. You will get to know that the answer will come $\dfrac{1}{4}$ or not. If we will get $\dfrac{1}{4}$ or not. If we will get $\dfrac{1}{4}$ after simplifying then we can consider the complex fraction. There are two methods of simplifying complex fractions. The procedures are following.
Method 1: first generate a single fraction both in the denominator and the numerator after that employ the division rule by multiplying the top of the fraction by the reciprocal of the bottom. After that simplify the fraction to its lowest term possible.
Step 1: Start by finding the least common multiple of all the denominators in the complex fractions.
Step 2: Multiply the both the numerator and denominator of the complex fractions by this L.C.M.
Step 3: Simplify the result to the lowest term possible.

Note:
A complex fraction must contain a fraction in numerator and denominator. As given in the question, write complex fractions which simplifies to $\dfrac{1}{4}$.