Property 9
Sorting Rational Numbers
The numerator or the denominate is made equal by expanding the given rational numbers with suitable numbers.
If the denominators are equal, the number with the biggest numerator is bigger.
If the numerators are equal, the number with the smallest denominator is bigger.
\(\samefrac{1}{5}<\samefrac{3}{5}<\samefrac{4}{5}\quad,\quad\samefrac{2}{7}>\samefrac{2}{9}>\samefrac{2}{11}\)
Sorting Rational Numbers
If the difference between the numerator and the denominator are equal, then the number with larger numerator is closer to 1.
\(a=\samefrac{13}{11}\quad b=\samefrac{15}{13}\quad c=\samefrac{17}{15}\)
\(a=1+\samefrac{2}{11}\quad b=1+\samefrac{2}{13}\quad c=1+\samefrac{2}{15}\)
\(c<b<a\)
\(a=\samefrac{11}{13}\quad b=\samefrac{13}{15}\quad c=\samefrac{15}{17}\)
\(a=1-\samefrac{2}{13}\quad b=1-\samefrac{2}{15}\quad c=1-\samefrac{2}{17}\)
\(a<b<c\)
Sorting Rational Numbers
If negative rational numbers are being ordered, they are ordered as if they were positive numbers, and then the obtained sorting is reversed.
1.
\(a=\samefrac{3}{7}\quad b=\samefrac{2}{7}\quad c=\samefrac{6}{7}\)
\(\Rightarrow ?<?<?\)
2.
\(a=-\samefrac{8}{11}\quad b=-\samefrac{4}{11}\quad c=-\samefrac{7}{11}\)
\(\Rightarrow ?<?<?\)
3.
\(a=\samefrac{7}{9}\quad b=\samefrac{7}{12}\quad c=\samefrac{7}{10}\)
\(\Rightarrow ?<?<?\)
4.
\(a=-\samefrac{5}{6}\quad b=-\samefrac{5}{12}\quad c=-\samefrac{5}{8}\)
\(\Rightarrow ?<?<?\)
5.
\(a=\samefrac{5}{6}\quad b=\samefrac{3}{4}\quad c=\samefrac{7}{12}\)
\(\Rightarrow ?<?<?\)
6.
\(a=\samefrac{1}{2}\quad b=\samefrac{2}{5}\quad c=\samefrac{3}{7}\)
\(\Rightarrow ?<?<?\)
7.
\(a=\samefrac{3}{4}\quad b=\samefrac{1}{2}\quad c=\samefrac{4}{5}\)
\(\Rightarrow ?<?<?\)