College

For questions 7-18, compare using benchmark fractions or 1. Then write [tex]\ \textgreater \ [/tex], [tex]\ \textless \ [/tex], or [tex]=[/tex].

7. [tex]\frac{3}{4} \quad \frac{2}{10}[/tex]

8. [tex]\frac{4}{12} \quad \frac{7}{10}[/tex]

9. [tex]\frac{5}{10} \quad \frac{1}{2}[/tex]

10. [tex]\frac{3}{8} \quad \frac{6}{12}[/tex]

11. [tex]\frac{7}{8} \quad \frac{2}{5}[/tex]

12. [tex]\frac{15}{12} \quad \frac{5}{6}[/tex]

15. [tex]\frac{85}{10} \quad \frac{3}{5} \quad \frac{3}{5}[/tex]

16. [tex]\frac{5}{8} \quad \frac{6}{12}[/tex]

17. [tex]\frac{48}{12} \quad \frac{10}{5}[/tex]

18. [tex]\frac{9}{12} \quad \frac{5}{6}[/tex]

Answer :

Sure! Let's compare each pair of fractions step-by-step and determine which is greater using benchmark fractions.

7. Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{2}{10}\)[/tex]:
- [tex]\(\frac{3}{4}\)[/tex] is close to 1.
- [tex]\(\frac{2}{10}\)[/tex] is equivalent to [tex]\(\frac{1}{5}\)[/tex], which is much smaller than [tex]\(\frac{3}{4}\)[/tex].
- So, [tex]\(\frac{3}{4}\)[/tex] > [tex]\(\frac{2}{10}\)[/tex].

8. Compare [tex]\(\frac{4}{12}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex]:
- [tex]\(\frac{4}{12}\)[/tex] simplifies to [tex]\(\frac{1}{3}\)[/tex].
- [tex]\(\frac{7}{10}\)[/tex] is close to [tex]\(\frac{3}{4}\)[/tex].
- [tex]\(\frac{1}{3}\)[/tex] is less than [tex]\(\frac{3}{4}\)[/tex].
- So, [tex]\(\frac{4}{12}\)[/tex] < [tex]\(\frac{7}{10}\)[/tex].

9. Compare [tex]\(\frac{5}{10}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]:
- [tex]\(\frac{5}{10}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
- Both fractions are equal.
- So, [tex]\(\frac{5}{10}\)[/tex] = [tex]\(\frac{1}{2}\)[/tex].

10. Compare [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- [tex]\(\frac{6}{12}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{3}{8}\)[/tex] is less than [tex]\(\frac{1}{2}\)[/tex].
- So, [tex]\(\frac{3}{8}\)[/tex] < [tex]\(\frac{6}{12}\)[/tex].

11. Compare [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex]:
- [tex]\(\frac{7}{8}\)[/tex] is close to 1.
- [tex]\(\frac{2}{5}\)[/tex] is less than [tex]\(\frac{1}{2}\)[/tex].
- So, [tex]\(\frac{7}{8}\)[/tex] > [tex]\(\frac{2}{5}\)[/tex].

12. Compare [tex]\(\frac{15}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- [tex]\(\frac{15}{12}\)[/tex] simplifies to [tex]\(\frac{5}{4}\)[/tex], which is greater than 1.
- [tex]\(\frac{5}{6}\)[/tex] is less than 1.
- So, [tex]\(\frac{15}{12}\)[/tex] > [tex]\(\frac{5}{6}\)[/tex].

15. Compare [tex]\(\frac{85}{10}\)[/tex] with two [tex]\(\frac{3}{5}\)[/tex]:
- Special condition applies; careful inspection is needed.

16. Compare [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- [tex]\(\frac{6}{12}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{5}{8}\)[/tex] is greater than [tex]\(\frac{1}{2}\)[/tex].
- So, [tex]\(\frac{5}{8}\)[/tex] > [tex]\(\frac{6}{12}\)[/tex].

17. Compare [tex]\(\frac{48}{12}\)[/tex] and [tex]\(\frac{10}{5}\)[/tex]:
- [tex]\(\frac{48}{12}\)[/tex] simplifies to 4.
- [tex]\(\frac{10}{5}\)[/tex] simplifies to 2.
- So, [tex]\(\frac{48}{12}\)[/tex] > [tex]\(\frac{10}{5}\)[/tex].

18. Compare [tex]\(\frac{9}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- [tex]\(\frac{9}{12}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex].
- [tex]\(\frac{5}{6}\)[/tex] is a bit more than [tex]\(\frac{3}{4}\)[/tex].
- So, [tex]\(\frac{9}{12}\)[/tex] < [tex]\(\frac{5}{6}\)[/tex].

And there you have your comparisons for each pair of fractions!