Question

Which of the following is a complex fraction?
(A) $${\displaystyle \frac{6{\displaystyle \frac{1}{3}}}{9}}$$
(B) $${\displaystyle \frac{4}{9}}$$
(C) $${\displaystyle \frac{5}{9}}$$
(D) $${\displaystyle \frac{8}{9}}$$

Answer 1

Hint: We are given a question asking us to find the options which represent a complex fraction. A fraction refers to the ratio of a numerator and a denominator and is represented as, $${\displaystyle \frac{a}{b}}$$. Here, ‘a’ is the numerator and ‘b’ is the denominator. Complex fraction would mean that the expression will not exactly appear to be a usual fraction. It might be in the form of a mixed fraction, which is represented as, $$2{\displaystyle \frac{1}{3}}$$, etc. But when resolved or simplified, it takes the usual appearance of a fraction. We will check each of the options for this anomaly and we will have the appropriate option.

Complete step by step solution:
According to the given question, we are asked to find from the given options, a particular option that is a complex fraction.
A fraction is usually referred to a ratio which is represented as, $${\displaystyle \frac{a}{b}}$$ where ‘a’ is the numerator and ‘b’ is the denominator.
A complex fraction here would mean that its representation would be somewhat different from the usual fraction. So it can be a mixed fraction, which is $$2{\displaystyle \frac{1}{3}}$$, or a ratio of mixed fractions or a ratio of mixed fraction and a number.
We will check each of the options given and determine the required.
(A) $${\displaystyle \frac{6{\displaystyle \frac{1}{3}}}{9}}$$
Here, the numerator is a mixed fraction. So, it’s a ratio of a mixed fraction and a number. In order to make it look as a usual fraction, we just have to simplify and we will have the fraction.
$$\Rightarrow {\displaystyle \frac{{\displaystyle \frac{19}{3}}}{9}}$$
$$\Rightarrow {\displaystyle \frac{19}{27}}$$
(B) $${\displaystyle \frac{4}{9}}$$
Here, we have the numerator as 4 and the denominator as 9. And so the given expression is a simple fraction.
(C) $${\displaystyle \frac{5}{9}}$$
Here, we have the numerator as 5 and the denominator as 9. And so the given expression is a simple fraction.
(D) $${\displaystyle \frac{8}{9}}$$
Here, we have the numerator as 8 and the denominator as 9. And so the given expression is a simple fraction.
Therefore, Option (A) $${\displaystyle \frac{6{\displaystyle \frac{1}{3}}}{9}}$$ is a complex fraction.

Note: The fractions can be of three different types: Proper fraction, Improper fraction and Mixed fraction. Proper fraction refers to a fraction which is represented as, $${\displaystyle \frac{a}{b}}$$ where $$a<b$$ and is generally used mostly in all fields. Next, we have the improper fraction, which is shown as, $${\displaystyle \frac{b}{a}}$$ where $$a<b$$, that is, the denominator is less than the numerator. Mixed fractions are represented as $$c{\displaystyle \frac{a}{b}}$$. For example - $$2{\displaystyle \frac{1}{3}}$$.