Answer
Two rational numbers of the form \[\frac{a}{b}\]and \[\frac{c}{d}\] can be multiplied by dividing the product of numerators from the product of denominators. This can be shown as follows:
\[\frac{a}{b}\times \frac{c}{d}=\frac{a\cdot c}{b\cdot d}\]
The product of the two rational numbers thus gives:
\[\begin{align}
& \frac{13}{4}\times \frac{13}{9}=\frac{13\times 13}{4\times 9} \\
& =\frac{169}{36}
\end{align}\]
Two rational numbers\[\frac{a}{b}\]and \[\frac{c}{d}\] can be added by first finding the least common multiple of their denominators also known as least common denominator. The rational numbers are then multiplied by a rational number of the form \[\frac{e}{e}\] so that the denominator of both the rational numbers becomes the least common denominators as found earlier.
The least common denominator of the rational numbers \[\frac{13}{4},\frac{13}{9}\]is \[36\].
Thus, the addition oftwo rational numbers can be shown as:
\[\begin{align}
& \frac{13}{4}+\frac{13}{9}=\frac{13}{4}\times \frac{9}{9}+\frac{13}{9}\times \frac{4}{4} \\
& =\frac{13\times 9+13\times 4}{36} \\
& =\frac{169}{36}
\end{align}\]
We conclude that \[\frac{13}{4}+\frac{13}{9}\] and \[\frac{13}{4}\times \frac{13}{9}\]give the same answer.
