Answer
Verified
378.3k+ views
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, \[\dfrac{a}{b}\]. 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, \[2\dfrac{1}{3}\], 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, \[\dfrac{a}{b}\] 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 \[2\dfrac{1}{3}\], 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) \[\dfrac{6\dfrac{1}{3}}{9}\]
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.
\[\Rightarrow \dfrac{\dfrac{19}{3}}{9}\]
\[\Rightarrow \dfrac{19}{27}\]
(B) \[\dfrac{4}{9}\]
Here, we have the numerator as 4 and the denominator as 9. And so the given expression is a simple fraction.
(C) \[\dfrac{5}{9}\]
Here, we have the numerator as 5 and the denominator as 9. And so the given expression is a simple fraction.
(D) \[\dfrac{8}{9}\]
Here, we have the numerator as 8 and the denominator as 9. And so the given expression is a simple fraction.
Therefore, Option (A) \[\dfrac{6\dfrac{1}{3}}{9}\] 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, \[\dfrac{a}{b}\] where \[a< b\] and is generally used mostly in all fields. Next, we have the improper fraction, which is shown as, \[\dfrac{b}{a}\] where \[a< b\], that is, the denominator is less than the numerator. Mixed fractions are represented as \[c\dfrac{a}{b}\]. For example - \[2\dfrac{1}{3}\].
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, \[\dfrac{a}{b}\] 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 \[2\dfrac{1}{3}\], 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) \[\dfrac{6\dfrac{1}{3}}{9}\]
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.
\[\Rightarrow \dfrac{\dfrac{19}{3}}{9}\]
\[\Rightarrow \dfrac{19}{27}\]
(B) \[\dfrac{4}{9}\]
Here, we have the numerator as 4 and the denominator as 9. And so the given expression is a simple fraction.
(C) \[\dfrac{5}{9}\]
Here, we have the numerator as 5 and the denominator as 9. And so the given expression is a simple fraction.
(D) \[\dfrac{8}{9}\]
Here, we have the numerator as 8 and the denominator as 9. And so the given expression is a simple fraction.
Therefore, Option (A) \[\dfrac{6\dfrac{1}{3}}{9}\] 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, \[\dfrac{a}{b}\] where \[a< b\] and is generally used mostly in all fields. Next, we have the improper fraction, which is shown as, \[\dfrac{b}{a}\] where \[a< b\], that is, the denominator is less than the numerator. Mixed fractions are represented as \[c\dfrac{a}{b}\]. For example - \[2\dfrac{1}{3}\].
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE