Question

Convert \[8\dfrac{7}{9}\] into improper fraction.

Answer 1

Hint: In any mixed fraction of the form \[a\dfrac{b}{c}\] the improper fraction is given by the form \[\dfrac{{(c \times a) + b}}{c}\]. Using this we will get our required solution.

Complete Step by Step Solution:
A fraction in which the numerator is greater than the denominator, such as \[\dfrac{5}{4}\] is called an improper fraction. As given in the hint we will use the same formula for \[8\dfrac{7}{9}\] where \[a = 8,b = 7,c = 9\]
Now putting it in the form \[\dfrac{{(c \times a) + b}}{c}\]
We get,
\[\begin{array}{l}
 = \dfrac{{(9 \times 8) + 7}}{7}\\
 = \dfrac{{72 + 7}}{7}\\
 = \dfrac{{79}}{7}
\end{array}\]
\[\therefore \dfrac{{79}}{7}\] is the improper fraction we are told to find.

Note: Do not change the denominator while converting from mixed fraction to improper fraction students often make this mistake and thus, penalised. One also must note that \[8\dfrac{7}{9} \ne 8 \times \dfrac{7}{9}\] this mistake often means lack of concept and thus provides a very negative impact on the examiner checking your copy.