Converting Unlike fractions into like fraction

Example (1) : Convert $LaTeX: \frac{5}{6}$ $\frac{5}{6}$ and $LaTeX: \frac{7}{9}$ $\frac{7}{9}$ into like fractions .

Here , we must find a common multiple for the numbers 6 and 9 .

Multiples of 6 :6,12,18,24,30,36,..........

Multiples of 9 : 9,18,27,36,45,..........

Here, the number 18 is a multiple of both 6 and 9 . So ,let us make 18 the denominator of both the fractions.

$LaTeX: \frac{5}{6}=\frac{5\times3}{6\times3}=\frac{15}{18}\:\:\:\:\:\:\frac{7}{9}=\frac{7\times2}{9\times2}=\frac{14}{18}$ $\frac{5}{6}=\frac{5\times3}{6\times3}=\frac{15}{18}\:\:\:\:\:\:\frac{7}{9}=\frac{7\times2}{9\times2}=\frac{14}{18}$

Thus, $LaTeX: \frac{15}{18}\:$ $\frac{15}{18}\:$ and $LaTeX: \frac{14}{18}\:$ $\frac{14}{18}\:$ are like fractions.

Example (2) : Convert $LaTeX: \frac{4}{8}\:$ $\frac{4}{8}\:$ and $LaTeX: \frac{5}{16}\:$ $\frac{5}{16}\:$ into like fractions .

As 16 is twice 8 , it is easy to make 16 the common denominator .

$LaTeX: \frac{4}{8}=\frac{4\times2}{8\times2}=\frac{8}{16}\:\:$ $\frac{4}{8}=\frac{4\times2}{8\times2}=\frac{8}{16}\:\:$ . Thus , $LaTeX: \frac{8}{16}\:$ $\frac{8}{16}\:$ and $LaTeX: \frac{5}{16}\:$ $\frac{5}{16}\:$ are the required like fractions .