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