Question

How do you write \[6\dfrac{7}{8}\] as an improper fraction?

Answer 1

Hint: We know that fraction is a part of whole. Here we are given with a mixed fraction. We have to convert this into an improper fraction. For that we will multiply the denominator with the whole number and then add it to the numerator this is the process. And when we write this this denominator is the same.
Mixed fraction to improper fraction
\[ \Rightarrow \dfrac{{{\text{denominator} \times \text{whole number + numerator}}}}{{{\text{denominator}}}}\]

Complete step-by-step answer:
Given that is a mixed fraction \[6\dfrac{7}{8}\] .
While converting into the improper fraction we will use the formula mentioned above.
Mixed fraction to improper fraction
\[ \Rightarrow \dfrac{{{\text{denominator} \times \text{whole number + numerator}}}}{{{\text{denominator}}}}\]
 \[6\dfrac{7}{8} \Rightarrow \dfrac{{{\text{8}} \times {\text{6 + 7}}}}{8}\]
On solving this we get,
 \[6\dfrac{7}{8} \Rightarrow \dfrac{{{\text{48 + 7}}}}{8}\]
On adding the numbers in numerator
 \[6\dfrac{7}{8} \Rightarrow \dfrac{{55}}{8}\]
This is our final answer \[\dfrac{{55}}{8}\] .
So, the correct answer is “$\dfrac{{55}}{8}$”.

Note: Note that denominator doesn’t change. Also we can cross verify that the answer so obtained has a numerator greater than denominator so that is an improper fraction. Also remember mixed fractions are never converted into proper fractions because the denominator is always less than the numerator.
Mixed fraction: It is a combination of whole number and fraction. It is written as \[a\dfrac{b}{c}\] where \[a\] is the whole number part and the fraction is \[\dfrac{b}{c}\]
Improper fraction: It is the type of fraction having numerator greater than denominator.
Proper fraction: It is the type of fraction having numerator less than denominator.
Fractions are involved in mathematics and in the calculation part at the most. Percentage is one big concept totally dependent on fractions.