Answer :
Sure! Let's go through each pair of fractions step by step and compare them using benchmark fractions, 0, or 1.
7. Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{2}{10}\)[/tex]:
- [tex]\(\frac{3}{4}\)[/tex] is close to 1 (since [tex]\(\frac{3}{4} = 0.75\)[/tex]).
- [tex]\(\frac{2}{10}\)[/tex] is close to 0 (since [tex]\(\frac{2}{10} = 0.2\)[/tex]).
- Since 0.75 > 0.2, we have [tex]\(\frac{3}{4} > \frac{2}{10}\)[/tex].
8. Compare [tex]\(\frac{4}{12}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex]:
- Simplify [tex]\(\frac{4}{12}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex] (since [tex]\(\frac{1}{3} \approx 0.333\)[/tex]).
- [tex]\(\frac{7}{10} = 0.7\)[/tex].
- Since 0.333 < 0.7, we have [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]\(2 \frac{3}{4}\)[/tex] and [tex]\(2 \frac{5}{6}\)[/tex]:
- Convert to improper fractions:
- [tex]\(2 \frac{3}{4} = \frac{11}{4}\)[/tex].
- [tex]\(2 \frac{5}{6} = \frac{17}{6}\)[/tex].
- Convert to decimals if helpful:
- [tex]\(2 \frac{3}{4} = 2.75\)[/tex].
- [tex]\(2 \frac{5}{6} \approx 2.833\)[/tex].
- Since 2.75 < 2.833, we have [tex]\(2 \frac{3}{4} < 2 \frac{5}{6}\)[/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 > 0.4, we have [tex]\(\frac{7}{8} > \(\frac{2}{5}).
12. Compare \(\frac{15}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- Simplify [tex]\(\frac{15}{12}\)[/tex] to [tex]\(\frac{5}{4} = 1.25\)[/tex].
- [tex]\(\frac{5}{6} = 0.833\)[/tex].
- Since 1.25 > 0.833, we have [tex]\(\frac{15}{12} > \frac{5}{6}\)[/tex].
13. Compare [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex]:
- Both are equal to 1, so [tex]\(\frac{5}{5} = \frac{4}{4}\)[/tex].
15. Compare [tex]\(1 \frac{1}{3}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]:
- Convert to improper fractions:
- [tex]\(1 \frac{1}{3} = \frac{4}{3}\)[/tex].
- [tex]\(\frac{2}{3} = 0.667\)[/tex].
- [tex]\(\frac{4}{3} = 1.333\)[/tex].
- Since 1.333 > 0.667, [tex]\(1 \frac{1}{3} > \frac{2}{3}\)[/tex].
16. Compare [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- [tex]\(\frac{5}{8} = 0.625\)[/tex].
- Simplify [tex]\(\frac{6}{12}\)[/tex] to [tex]\(\frac{1}{2} = 0.5\)[/tex].
- Since 0.625 > 0.5, we have [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 > 2, we have [tex]\(\frac{48}{12} > \frac{10}{5}\)[/tex].
18. Compare [tex]\(\frac{9}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- Simplify [tex]\(\frac{9}{12}\)[/tex] to [tex]\(\frac{3}{4} = 0.75\)[/tex].
- [tex]\(\frac{5}{6} = 0.833\)[/tex].
- Since 0.75 < 0.833, we have [tex]\(\frac{9}{12} < \frac{5}{6}\)[/tex].
These are the comparisons for the given fractions.
7. Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{2}{10}\)[/tex]:
- [tex]\(\frac{3}{4}\)[/tex] is close to 1 (since [tex]\(\frac{3}{4} = 0.75\)[/tex]).
- [tex]\(\frac{2}{10}\)[/tex] is close to 0 (since [tex]\(\frac{2}{10} = 0.2\)[/tex]).
- Since 0.75 > 0.2, we have [tex]\(\frac{3}{4} > \frac{2}{10}\)[/tex].
8. Compare [tex]\(\frac{4}{12}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex]:
- Simplify [tex]\(\frac{4}{12}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex] (since [tex]\(\frac{1}{3} \approx 0.333\)[/tex]).
- [tex]\(\frac{7}{10} = 0.7\)[/tex].
- Since 0.333 < 0.7, we have [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]\(2 \frac{3}{4}\)[/tex] and [tex]\(2 \frac{5}{6}\)[/tex]:
- Convert to improper fractions:
- [tex]\(2 \frac{3}{4} = \frac{11}{4}\)[/tex].
- [tex]\(2 \frac{5}{6} = \frac{17}{6}\)[/tex].
- Convert to decimals if helpful:
- [tex]\(2 \frac{3}{4} = 2.75\)[/tex].
- [tex]\(2 \frac{5}{6} \approx 2.833\)[/tex].
- Since 2.75 < 2.833, we have [tex]\(2 \frac{3}{4} < 2 \frac{5}{6}\)[/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 > 0.4, we have [tex]\(\frac{7}{8} > \(\frac{2}{5}).
12. Compare \(\frac{15}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- Simplify [tex]\(\frac{15}{12}\)[/tex] to [tex]\(\frac{5}{4} = 1.25\)[/tex].
- [tex]\(\frac{5}{6} = 0.833\)[/tex].
- Since 1.25 > 0.833, we have [tex]\(\frac{15}{12} > \frac{5}{6}\)[/tex].
13. Compare [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex]:
- Both are equal to 1, so [tex]\(\frac{5}{5} = \frac{4}{4}\)[/tex].
15. Compare [tex]\(1 \frac{1}{3}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]:
- Convert to improper fractions:
- [tex]\(1 \frac{1}{3} = \frac{4}{3}\)[/tex].
- [tex]\(\frac{2}{3} = 0.667\)[/tex].
- [tex]\(\frac{4}{3} = 1.333\)[/tex].
- Since 1.333 > 0.667, [tex]\(1 \frac{1}{3} > \frac{2}{3}\)[/tex].
16. Compare [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- [tex]\(\frac{5}{8} = 0.625\)[/tex].
- Simplify [tex]\(\frac{6}{12}\)[/tex] to [tex]\(\frac{1}{2} = 0.5\)[/tex].
- Since 0.625 > 0.5, we have [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 > 2, we have [tex]\(\frac{48}{12} > \frac{10}{5}\)[/tex].
18. Compare [tex]\(\frac{9}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
- Simplify [tex]\(\frac{9}{12}\)[/tex] to [tex]\(\frac{3}{4} = 0.75\)[/tex].
- [tex]\(\frac{5}{6} = 0.833\)[/tex].
- Since 0.75 < 0.833, we have [tex]\(\frac{9}{12} < \frac{5}{6}\)[/tex].
These are the comparisons for the given fractions.
