Answer :
Sure! Let's compare each pair of fractions step by step. We'll use benchmark fractions or 1 to help us decide which fraction is larger, smaller, or if they are equal.
7. Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{2}{10}\)[/tex]:
- [tex]\(\frac{3}{4}\)[/tex] is close to 1, as [tex]\(\frac{3}{4} = 0.75\)[/tex].
- [tex]\(\frac{2}{10}\)[/tex] is [tex]\(\frac{1}{5} = 0.2\)[/tex].
- Since 0.75 is greater than 0.2, [tex]\(\frac{3}{4} > \frac{2}{10}\)[/tex].
8. Compare [tex]\(\frac{4}{12}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex]:
- [tex]\(\frac{4}{12}\)[/tex] simplifies to [tex]\(\frac{1}{3} \approx 0.333\)[/tex].
- [tex]\(\frac{7}{10} = 0.7\)[/tex].
- Since 0.333 is less than 0.7, [tex]\(\frac{4}{12} < \frac{7}{10}\)[/tex].
9. Compare [tex]\(\frac{5}{10}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]:
- [tex]\(\frac{5}{10} = \frac{1}{2} = 0.5\)[/tex].
- Both fractions are equal. So, [tex]\(\frac{5}{10} = \frac{1}{2}\)[/tex].
10. Compare [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- [tex]\(\frac{3}{8} = 0.375\)[/tex].
- [tex]\(\frac{6}{12} = \frac{1}{2} = 0.5\)[/tex].
- Since 0.375 is less than 0.5, [tex]\(\frac{3}{8} < \frac{6}{12}\)[/tex].
11. Compare [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex]:
- [tex]\(\frac{7}{8} = 0.875\)[/tex].
- [tex]\(\frac{2}{5} = 0.4\)[/tex].
- Since 0.875 is greater than 0.4, [tex]\(\frac{7}{8} > \frac{2}{5}\)[/tex].
12. Compare [tex]\(\frac{15}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- [tex]\(\frac{15}{12}\)[/tex] simplifies to [tex]\(\frac{5}{4} = 1.25\)[/tex].
- [tex]\(\frac{5}{6} \approx 0.833\)[/tex].
- Since 1.25 is greater than 0.833, [tex]\(\frac{15}{12} > \frac{5}{6}\)[/tex].
13. Compare [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex]:
- [tex]\(\frac{5}{5} = 1\)[/tex].
- [tex]\(\frac{4}{4} = 1\)[/tex].
- Both fractions are equal. So, [tex]\(\frac{5}{5} = \frac{4}{4}\)[/tex].
14. Compare [tex]\(\frac{4}{6}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- [tex]\(\frac{4}{6}\)[/tex] simplifies to [tex]\(\frac{2}{3} \approx 0.667\)[/tex].
- [tex]\(\frac{1}{3} \approx 0.333\)[/tex].
- Since 0.667 is greater than 0.333, [tex]\(\frac{4}{6} > \(\frac{1}{3}\)[/tex].
15. Compare [tex]\(\frac{8}{10}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- [tex]\(\frac{8}{10} = 0.8\)[/tex].
- [tex]\(\frac{3}{5} = 0.6\)[/tex].
- Since 0.8 is greater than 0.6, [tex]\(\frac{8}{10} > \frac{3}{5}\)[/tex].
16. Compare [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- [tex]\(\frac{5}{8} = 0.625\)[/tex].
- [tex]\(\frac{6}{12} = \frac{1}{2} = 0.5\)[/tex].
- Since 0.625 is greater than 0.5, [tex]\(\frac{5}{8} > \frac{6}{12}\)[/tex].
17. Compare [tex]\(\frac{48}{12}\)[/tex] and [tex]\(\frac{10}{5}\)[/tex]:
- [tex]\(\frac{48}{12} = 4\)[/tex].
- [tex]\(\frac{10}{5} = 2\)[/tex].
- Since 4 is greater than 2, [tex]\(\frac{48}{12} > \frac{10}{5}\)[/tex].
18. Compare [tex]\(\frac{9}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- [tex]\(\frac{9}{12}\)[/tex] simplifies to [tex]\(\frac{3}{4} = 0.75\)[/tex].
- [tex]\(\frac{5}{6} \approx 0.833\)[/tex].
- Since 0.75 is less than 0.833, [tex]\(\frac{9}{12} < \frac{5}{6}\)[/tex].
So, the results using benchmarks or 1 are as follows:
1. [tex]\(\frac{3}{4} > \frac{2}{10}\)[/tex]
2. [tex]\(\frac{4}{12} < \frac{7}{10}\)[/tex]
3. [tex]\(\frac{5}{10} = \(\frac{1}{2}\)[/tex]
4. [tex]\(\frac{3}{8} < \frac{6}{12}\)[/tex]
5. [tex]\(\frac{7}{8} > \frac{2}{5}\)[/tex]
6. [tex]\(\frac{15}{12} > \frac{5}{6}\)[/tex]
7. [tex]\(\frac{5}{5} = \(\frac{4}{4}\)[/tex]
8. [tex]\(\frac{4}{6} > \frac{1}{3}\)[/tex]
9. [tex]\(\frac{8}{10} > \frac{3}{5}\)[/tex]
10. [tex]\(\frac{5}{8} > \frac{6}{12}\)[/tex]
11. [tex]\(\frac{48}{12} > \frac{10}{5}\)[/tex]
12. [tex]\(\frac{9}{12} < \frac{5}{6}\)[/tex]
7. Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{2}{10}\)[/tex]:
- [tex]\(\frac{3}{4}\)[/tex] is close to 1, as [tex]\(\frac{3}{4} = 0.75\)[/tex].
- [tex]\(\frac{2}{10}\)[/tex] is [tex]\(\frac{1}{5} = 0.2\)[/tex].
- Since 0.75 is greater than 0.2, [tex]\(\frac{3}{4} > \frac{2}{10}\)[/tex].
8. Compare [tex]\(\frac{4}{12}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex]:
- [tex]\(\frac{4}{12}\)[/tex] simplifies to [tex]\(\frac{1}{3} \approx 0.333\)[/tex].
- [tex]\(\frac{7}{10} = 0.7\)[/tex].
- Since 0.333 is less than 0.7, [tex]\(\frac{4}{12} < \frac{7}{10}\)[/tex].
9. Compare [tex]\(\frac{5}{10}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]:
- [tex]\(\frac{5}{10} = \frac{1}{2} = 0.5\)[/tex].
- Both fractions are equal. So, [tex]\(\frac{5}{10} = \frac{1}{2}\)[/tex].
10. Compare [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- [tex]\(\frac{3}{8} = 0.375\)[/tex].
- [tex]\(\frac{6}{12} = \frac{1}{2} = 0.5\)[/tex].
- Since 0.375 is less than 0.5, [tex]\(\frac{3}{8} < \frac{6}{12}\)[/tex].
11. Compare [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex]:
- [tex]\(\frac{7}{8} = 0.875\)[/tex].
- [tex]\(\frac{2}{5} = 0.4\)[/tex].
- Since 0.875 is greater than 0.4, [tex]\(\frac{7}{8} > \frac{2}{5}\)[/tex].
12. Compare [tex]\(\frac{15}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- [tex]\(\frac{15}{12}\)[/tex] simplifies to [tex]\(\frac{5}{4} = 1.25\)[/tex].
- [tex]\(\frac{5}{6} \approx 0.833\)[/tex].
- Since 1.25 is greater than 0.833, [tex]\(\frac{15}{12} > \frac{5}{6}\)[/tex].
13. Compare [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex]:
- [tex]\(\frac{5}{5} = 1\)[/tex].
- [tex]\(\frac{4}{4} = 1\)[/tex].
- Both fractions are equal. So, [tex]\(\frac{5}{5} = \frac{4}{4}\)[/tex].
14. Compare [tex]\(\frac{4}{6}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- [tex]\(\frac{4}{6}\)[/tex] simplifies to [tex]\(\frac{2}{3} \approx 0.667\)[/tex].
- [tex]\(\frac{1}{3} \approx 0.333\)[/tex].
- Since 0.667 is greater than 0.333, [tex]\(\frac{4}{6} > \(\frac{1}{3}\)[/tex].
15. Compare [tex]\(\frac{8}{10}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- [tex]\(\frac{8}{10} = 0.8\)[/tex].
- [tex]\(\frac{3}{5} = 0.6\)[/tex].
- Since 0.8 is greater than 0.6, [tex]\(\frac{8}{10} > \frac{3}{5}\)[/tex].
16. Compare [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- [tex]\(\frac{5}{8} = 0.625\)[/tex].
- [tex]\(\frac{6}{12} = \frac{1}{2} = 0.5\)[/tex].
- Since 0.625 is greater than 0.5, [tex]\(\frac{5}{8} > \frac{6}{12}\)[/tex].
17. Compare [tex]\(\frac{48}{12}\)[/tex] and [tex]\(\frac{10}{5}\)[/tex]:
- [tex]\(\frac{48}{12} = 4\)[/tex].
- [tex]\(\frac{10}{5} = 2\)[/tex].
- Since 4 is greater than 2, [tex]\(\frac{48}{12} > \frac{10}{5}\)[/tex].
18. Compare [tex]\(\frac{9}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- [tex]\(\frac{9}{12}\)[/tex] simplifies to [tex]\(\frac{3}{4} = 0.75\)[/tex].
- [tex]\(\frac{5}{6} \approx 0.833\)[/tex].
- Since 0.75 is less than 0.833, [tex]\(\frac{9}{12} < \frac{5}{6}\)[/tex].
So, the results using benchmarks or 1 are as follows:
1. [tex]\(\frac{3}{4} > \frac{2}{10}\)[/tex]
2. [tex]\(\frac{4}{12} < \frac{7}{10}\)[/tex]
3. [tex]\(\frac{5}{10} = \(\frac{1}{2}\)[/tex]
4. [tex]\(\frac{3}{8} < \frac{6}{12}\)[/tex]
5. [tex]\(\frac{7}{8} > \frac{2}{5}\)[/tex]
6. [tex]\(\frac{15}{12} > \frac{5}{6}\)[/tex]
7. [tex]\(\frac{5}{5} = \(\frac{4}{4}\)[/tex]
8. [tex]\(\frac{4}{6} > \frac{1}{3}\)[/tex]
9. [tex]\(\frac{8}{10} > \frac{3}{5}\)[/tex]
10. [tex]\(\frac{5}{8} > \frac{6}{12}\)[/tex]
11. [tex]\(\frac{48}{12} > \frac{10}{5}\)[/tex]
12. [tex]\(\frac{9}{12} < \frac{5}{6}\)[/tex]
