To make this a little clearer, let's give the pairs of inequalities the same denominator:
Question 1:
[tex] \frac{11}{15} [/tex] ? [tex] \frac{5}{7} [/tex]
First, apply the common denominator to the first fraction:
[tex] (\frac{11}{15})7 \\ \frac{11}{15} * \frac{7}{7} \\ \frac{11*7}{15*7} \\ \frac{77}{105} [/tex]
Do the same for the second:[tex]15( \frac{5}{7}) \\ \frac{5}{7}* \frac{15}{15} \\ \frac{5*15}{7*15} \\ \frac{75}{105} [/tex]
Nest, compare the two fractions:
[tex] \frac{77}{105} \ \textgreater \ \frac{75}{105} [/tex]
Therefore:
[tex] \frac{11}{15} [/tex] > [tex] \frac{5}{7} [/tex]
Question Two:
[tex] \frac{5}{9} [/tex] ? [tex] \frac{7}{13} [/tex]
Apply the common denominator to fraction one:
[tex]13( \frac{5}{9}) \\ \frac{5}{9} * \frac{13}{13} \\ \frac{5*13}{9*13} \\ \frac{65}{117} [/tex]
Fraction two:
[tex] 9(\frac{7}{13}) \\ \frac{7}{13} * \frac{9}{9} \\ \frac{7*9}{13*9} \\ \frac{63}{117} [/tex]
Evaluate:
[tex] \frac{65}{117} [/tex] > [tex]\frac{63}{117} [/tex]
Therefore:
[tex] \frac{5}{9} [/tex] > [tex] \frac{7}{13} [/tex]
Hope this helps!
