Answer :
Certainly! Let's compare each pair of fractions step by step and determine the correct relationship using symbols [tex]\(>\)[/tex], [tex]\(<\)[/tex], or [tex]\(=\)[/tex].
1. Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{2}{10}\)[/tex]:
- [tex]\(\frac{3}{4}\)[/tex] is close to the benchmark fraction of 1.
- [tex]\(\frac{2}{10}\)[/tex] is equivalent to [tex]\(\frac{1}{5}\)[/tex], which is much smaller.
- Conclusion: [tex]\(\frac{3}{4} > \frac{2}{10}\)[/tex]
2. Compare [tex]\(\frac{4}{12}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex]:
- Simplify [tex]\(\frac{4}{12}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex].
- [tex]\(\frac{7}{10}\)[/tex] is much larger than [tex]\(\frac{1}{3}\)[/tex].
- Conclusion: [tex]\(\frac{4}{12} < \frac{7}{10}\)[/tex]
3. Compare [tex]\(\frac{5}{10}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]:
- Both fractions simplify to [tex]\(\frac{1}{2}\)[/tex].
- Conclusion: [tex]\(\frac{5}{10} = \(\frac{1}{2}\)[/tex]
4. Compare [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- Simplify [tex]\(\frac{6}{12}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{3}{8}\)[/tex] is less than [tex]\(\frac{1}{2}\)[/tex].
- Conclusion: [tex]\(\frac{3}{8} < \(\frac{6}{12}\)[/tex]
5. Compare [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex]:
- [tex]\(\frac{7}{8}\)[/tex] is larger than [tex]\(\frac{2}{5}\)[/tex].
- Conclusion: [tex]\(\frac{7}{8} > \(\frac{2}{5}\)[/tex]
6. Compare [tex]\(\frac{15}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- Simplify [tex]\(\frac{15}{12}\)[/tex] to [tex]\(\frac{5}{4}\)[/tex].
- [tex]\(\frac{5}{4}\)[/tex] is larger than [tex]\(\frac{5}{6}\)[/tex].
- Conclusion: [tex]\(\frac{15}{12} > \(\frac{5}{6}\)[/tex]
7. Compare [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex]:
- Both are equal to 1.
- Conclusion: [tex]\(\frac{5}{5} = \(\frac{4}{4}\)[/tex]
8. Compare [tex]\(\frac{4}{6}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- Simplify [tex]\(\frac{4}{6}\)[/tex] to [tex]\(\frac{2}{3}\)[/tex].
- [tex]\(\frac{2}{3}\)[/tex] is larger than [tex]\(\frac{1}{3}\)[/tex].
- Conclusion: [tex]\(\frac{4}{6} > \(\frac{1}{3}\)[/tex]
9. Compare [tex]\(\frac{8}{10}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- Simplify both: [tex]\(\frac{8}{10}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].
- [tex]\(\frac{4}{5}\)[/tex] is larger than [tex]\(\frac{3}{5}\)[/tex].
- Conclusion: [tex]\(\frac{8}{10} > \(\frac{3}{5}\)[/tex]
10. Compare [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- Simplify [tex]\(\frac{6}{12}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{5}{8}\)[/tex] is larger than [tex]\(\frac{1}{2}\)[/tex].
- Conclusion: [tex]\(\frac{5}{8} > \(\frac{6}{12}\)[/tex]
11. Compare [tex]\(\frac{48}{12}\)[/tex] and [tex]\(\frac{10}{5}\)[/tex]:
- Simplify both: [tex]\(\frac{48}{12}\)[/tex] is 4, and [tex]\(\frac{10}{5}\)[/tex] is 2.
- 4 is larger than 2.
- Conclusion: [tex]\(\frac{48}{12} > \(\frac{10}{5}\)[/tex]
12. Compare [tex]\(\frac{9}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- Simplify [tex]\(\frac{9}{12}\)[/tex] to [tex]\(\frac{3}{4}\)[/tex].
- [tex]\(\frac{3}{4}\)[/tex] is less than [tex]\(\frac{5}{6}\)[/tex].
- Conclusion: [tex]\(\frac{9}{12} < \(\frac{5}{6}\)[/tex]
That's the complete set of comparisons!
1. Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{2}{10}\)[/tex]:
- [tex]\(\frac{3}{4}\)[/tex] is close to the benchmark fraction of 1.
- [tex]\(\frac{2}{10}\)[/tex] is equivalent to [tex]\(\frac{1}{5}\)[/tex], which is much smaller.
- Conclusion: [tex]\(\frac{3}{4} > \frac{2}{10}\)[/tex]
2. Compare [tex]\(\frac{4}{12}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex]:
- Simplify [tex]\(\frac{4}{12}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex].
- [tex]\(\frac{7}{10}\)[/tex] is much larger than [tex]\(\frac{1}{3}\)[/tex].
- Conclusion: [tex]\(\frac{4}{12} < \frac{7}{10}\)[/tex]
3. Compare [tex]\(\frac{5}{10}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]:
- Both fractions simplify to [tex]\(\frac{1}{2}\)[/tex].
- Conclusion: [tex]\(\frac{5}{10} = \(\frac{1}{2}\)[/tex]
4. Compare [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- Simplify [tex]\(\frac{6}{12}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{3}{8}\)[/tex] is less than [tex]\(\frac{1}{2}\)[/tex].
- Conclusion: [tex]\(\frac{3}{8} < \(\frac{6}{12}\)[/tex]
5. Compare [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex]:
- [tex]\(\frac{7}{8}\)[/tex] is larger than [tex]\(\frac{2}{5}\)[/tex].
- Conclusion: [tex]\(\frac{7}{8} > \(\frac{2}{5}\)[/tex]
6. Compare [tex]\(\frac{15}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- Simplify [tex]\(\frac{15}{12}\)[/tex] to [tex]\(\frac{5}{4}\)[/tex].
- [tex]\(\frac{5}{4}\)[/tex] is larger than [tex]\(\frac{5}{6}\)[/tex].
- Conclusion: [tex]\(\frac{15}{12} > \(\frac{5}{6}\)[/tex]
7. Compare [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex]:
- Both are equal to 1.
- Conclusion: [tex]\(\frac{5}{5} = \(\frac{4}{4}\)[/tex]
8. Compare [tex]\(\frac{4}{6}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- Simplify [tex]\(\frac{4}{6}\)[/tex] to [tex]\(\frac{2}{3}\)[/tex].
- [tex]\(\frac{2}{3}\)[/tex] is larger than [tex]\(\frac{1}{3}\)[/tex].
- Conclusion: [tex]\(\frac{4}{6} > \(\frac{1}{3}\)[/tex]
9. Compare [tex]\(\frac{8}{10}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- Simplify both: [tex]\(\frac{8}{10}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].
- [tex]\(\frac{4}{5}\)[/tex] is larger than [tex]\(\frac{3}{5}\)[/tex].
- Conclusion: [tex]\(\frac{8}{10} > \(\frac{3}{5}\)[/tex]
10. Compare [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- Simplify [tex]\(\frac{6}{12}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{5}{8}\)[/tex] is larger than [tex]\(\frac{1}{2}\)[/tex].
- Conclusion: [tex]\(\frac{5}{8} > \(\frac{6}{12}\)[/tex]
11. Compare [tex]\(\frac{48}{12}\)[/tex] and [tex]\(\frac{10}{5}\)[/tex]:
- Simplify both: [tex]\(\frac{48}{12}\)[/tex] is 4, and [tex]\(\frac{10}{5}\)[/tex] is 2.
- 4 is larger than 2.
- Conclusion: [tex]\(\frac{48}{12} > \(\frac{10}{5}\)[/tex]
12. Compare [tex]\(\frac{9}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- Simplify [tex]\(\frac{9}{12}\)[/tex] to [tex]\(\frac{3}{4}\)[/tex].
- [tex]\(\frac{3}{4}\)[/tex] is less than [tex]\(\frac{5}{6}\)[/tex].
- Conclusion: [tex]\(\frac{9}{12} < \(\frac{5}{6}\)[/tex]
That's the complete set of comparisons!
