Consider two fractions [tex]\dfrac{10}{21}[/tex] and [tex]\dfrac{15}{28}.[/tex]
1. Approximate first fraction by [tex]\dfrac{10}{20}.[/tex] You know that
[tex]\dfrac{10}{20}=\dfrac{1}{2}[/tex] and comparing two fractions with the same numerators, we compare their denominators. Since [tex]21>20,[/tex] then
[tex]\dfrac{10}{21}<\dfrac{10}{20},\\ \\\dfrac{10}{21}<\dfrac{1}{2}.[/tex]
2. Approximate the second fraction by [tex]\dfrac{14}{28}.[/tex] You know that
[tex]\dfrac{14}{28}=\dfrac{1}{2}[/tex] and comparing two fractions with the same denominators, we compare their numerators. Since [tex]15>14,[/tex] then
[tex]\dfrac{15}{28}>\dfrac{14}{28},\\ \\\dfrac{15}{28}>\dfrac{1}{2}.[/tex]
You have two fractions, the first one is less than [tex]\dfrac{1}{2}[/tex] and the second one is greater than [tex]\dfrac{1}{2}.[/tex] Thus,
[tex]\dfrac{10}{21}<\dfrac{15}{28}.[/tex]
Answer: [tex]\dfrac{10}{21}<\dfrac{15}{28}.[/tex]
