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!
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!
