Answer :
Certainly! Let's walk through each problem one by one and compare the given fractions using benchmark fractions, 0, or 1. Then, we'll determine whether the fractions are greater than, less than, or equal to each other.
### Problem 7: Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{2}{10}\)[/tex]
1. Convert [tex]\(\frac{2}{10}\)[/tex] to a simpler fraction: [tex]\(\frac{2}{10} = \frac{1}{5}\)[/tex].
2. [tex]\(\frac{3}{4} = 0.75\)[/tex] and [tex]\(\frac{1}{5} = 0.2\)[/tex].
3. Since [tex]\(0.75 > 0.2\)[/tex], we have [tex]\(\frac{3}{4} > \frac{2}{10}\)[/tex].
### Problem 8: Compare [tex]\(\frac{4}{12}\)[/tex] to 0.5
1. Simplify [tex]\(\frac{4}{12}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex].
2. [tex]\(\frac{1}{3} \approx 0.333\)[/tex].
3. Since [tex]\(0.333 < 0.5\)[/tex], we have [tex]\(\frac{4}{12} < 0.5\)[/tex].
### Problem 9: Compare [tex]\(\frac{5}{10}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]
1. Simplify [tex]\(\frac{5}{10}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex].
2. Both fractions are equal, so [tex]\(\frac{5}{10} = \frac{1}{2}\)[/tex].
### Problem 10: Compare [tex]\(2 \frac{3}{4}\)[/tex] and [tex]\(2 \frac{5}{6}\)[/tex]
1. [tex]\(2 \frac{3}{4} = 2.75\)[/tex] and [tex]\(2 \frac{5}{6} \approx 2.833\)[/tex].
2. Since [tex]\(2.75 < 2.833\)[/tex], we have [tex]\(2 \frac{3}{4} < 2 \frac{5}{6}\)[/tex].
### Problem 11: Compare [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex]
1. [tex]\(\frac{7}{8} = 0.875\)[/tex] and [tex]\(\frac{2}{5} = 0.4\)[/tex].
2. Since [tex]\(0.875 > 0.4\)[/tex], we have [tex]\(\frac{7}{8} > \frac{2}{5}\)[/tex].
### Problem 12: Compare [tex]\(\frac{15}{12}\)[/tex] to 1
1. Simplify [tex]\(\frac{15}{12}\)[/tex] to [tex]\(1 \frac{1}{4} \approx 1.25\)[/tex].
2. Since [tex]\(1.25 > 1\)[/tex], we have [tex]\(\frac{15}{12} > 1\)[/tex].
### Problem 13: Compare [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex]
1. Both [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex] simplify to 1.
2. Therefore, [tex]\(\frac{5}{5} = \frac{4}{4}\)[/tex].
### Problem 14: Compare [tex]\(\frac{4}{6}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]
1. Simplify [tex]\(\frac{4}{6}\)[/tex] to [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{1}{3} = 0.333\)[/tex].
2. [tex]\(\frac{2}{3} \approx 0.667\)[/tex].
3. Since [tex]\(0.667 > 0.333\)[/tex], we have [tex]\(\frac{4}{6} > \(\frac{1}{3}\)[/tex].
### Problem 15: Compare [tex]\(1 \frac{1}{3}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]
1. [tex]\(1 \frac{1}{3} \approx 1.333\)[/tex] and [tex]\(\frac{2}{3} \approx 0.667\)[/tex].
2. Since [tex]\(1.333 > 0.667\)[/tex], we have [tex]\(1 \frac{1}{3} > \(\frac{2}{3}\)[/tex].
### Problem 16: Compare [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]
1. Simplify [tex]\(\frac{6}{12}\)[/tex] to [tex]\(\frac{1}{2} = 0.5\)[/tex].
2. [tex]\(\frac{5}{8} = 0.625\)[/tex].
3. Since [tex]\(0.625 > 0.5\)[/tex], we have [tex]\(\frac{5}{8} > \(\frac{6}{12}\)[/tex].
### Problem 17: Compare [tex]\(\frac{48}{12}\)[/tex] and [tex]\(\frac{10}{5}\)[/tex]
1. Simplify [tex]\(\frac{48}{12}\)[/tex] to 4 and [tex]\(\frac{10}{5}\)[/tex] to 2.
2. Since 4 is not equal to 2, we have [tex]\(\frac{48}{12} > \(\frac{10}{5}\)[/tex].
### Problem 18: Compare [tex]\(\frac{2}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]
1. Simplify [tex]\(\frac{2}{12}\)[/tex] to [tex]\(\frac{1}{6}\)[/tex].
2. [tex]\(\frac{1}{6} \approx 0.167\)[/tex] and [tex]\(\frac{5}{6} \approx 0.833\)[/tex].
3. Since [tex]\(0.167 < 0.833\)[/tex], we have [tex]\(\frac{2}{12} < \(\frac{5}{6}\)[/tex].
These are the comparisons for each problem. Let me know if you need any further clarification!
### Problem 7: Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{2}{10}\)[/tex]
1. Convert [tex]\(\frac{2}{10}\)[/tex] to a simpler fraction: [tex]\(\frac{2}{10} = \frac{1}{5}\)[/tex].
2. [tex]\(\frac{3}{4} = 0.75\)[/tex] and [tex]\(\frac{1}{5} = 0.2\)[/tex].
3. Since [tex]\(0.75 > 0.2\)[/tex], we have [tex]\(\frac{3}{4} > \frac{2}{10}\)[/tex].
### Problem 8: Compare [tex]\(\frac{4}{12}\)[/tex] to 0.5
1. Simplify [tex]\(\frac{4}{12}\)[/tex] to [tex]\(\frac{1}{3}\)[/tex].
2. [tex]\(\frac{1}{3} \approx 0.333\)[/tex].
3. Since [tex]\(0.333 < 0.5\)[/tex], we have [tex]\(\frac{4}{12} < 0.5\)[/tex].
### Problem 9: Compare [tex]\(\frac{5}{10}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]
1. Simplify [tex]\(\frac{5}{10}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex].
2. Both fractions are equal, so [tex]\(\frac{5}{10} = \frac{1}{2}\)[/tex].
### Problem 10: Compare [tex]\(2 \frac{3}{4}\)[/tex] and [tex]\(2 \frac{5}{6}\)[/tex]
1. [tex]\(2 \frac{3}{4} = 2.75\)[/tex] and [tex]\(2 \frac{5}{6} \approx 2.833\)[/tex].
2. Since [tex]\(2.75 < 2.833\)[/tex], we have [tex]\(2 \frac{3}{4} < 2 \frac{5}{6}\)[/tex].
### Problem 11: Compare [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex]
1. [tex]\(\frac{7}{8} = 0.875\)[/tex] and [tex]\(\frac{2}{5} = 0.4\)[/tex].
2. Since [tex]\(0.875 > 0.4\)[/tex], we have [tex]\(\frac{7}{8} > \frac{2}{5}\)[/tex].
### Problem 12: Compare [tex]\(\frac{15}{12}\)[/tex] to 1
1. Simplify [tex]\(\frac{15}{12}\)[/tex] to [tex]\(1 \frac{1}{4} \approx 1.25\)[/tex].
2. Since [tex]\(1.25 > 1\)[/tex], we have [tex]\(\frac{15}{12} > 1\)[/tex].
### Problem 13: Compare [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex]
1. Both [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex] simplify to 1.
2. Therefore, [tex]\(\frac{5}{5} = \frac{4}{4}\)[/tex].
### Problem 14: Compare [tex]\(\frac{4}{6}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]
1. Simplify [tex]\(\frac{4}{6}\)[/tex] to [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{1}{3} = 0.333\)[/tex].
2. [tex]\(\frac{2}{3} \approx 0.667\)[/tex].
3. Since [tex]\(0.667 > 0.333\)[/tex], we have [tex]\(\frac{4}{6} > \(\frac{1}{3}\)[/tex].
### Problem 15: Compare [tex]\(1 \frac{1}{3}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]
1. [tex]\(1 \frac{1}{3} \approx 1.333\)[/tex] and [tex]\(\frac{2}{3} \approx 0.667\)[/tex].
2. Since [tex]\(1.333 > 0.667\)[/tex], we have [tex]\(1 \frac{1}{3} > \(\frac{2}{3}\)[/tex].
### Problem 16: Compare [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]
1. Simplify [tex]\(\frac{6}{12}\)[/tex] to [tex]\(\frac{1}{2} = 0.5\)[/tex].
2. [tex]\(\frac{5}{8} = 0.625\)[/tex].
3. Since [tex]\(0.625 > 0.5\)[/tex], we have [tex]\(\frac{5}{8} > \(\frac{6}{12}\)[/tex].
### Problem 17: Compare [tex]\(\frac{48}{12}\)[/tex] and [tex]\(\frac{10}{5}\)[/tex]
1. Simplify [tex]\(\frac{48}{12}\)[/tex] to 4 and [tex]\(\frac{10}{5}\)[/tex] to 2.
2. Since 4 is not equal to 2, we have [tex]\(\frac{48}{12} > \(\frac{10}{5}\)[/tex].
### Problem 18: Compare [tex]\(\frac{2}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]
1. Simplify [tex]\(\frac{2}{12}\)[/tex] to [tex]\(\frac{1}{6}\)[/tex].
2. [tex]\(\frac{1}{6} \approx 0.167\)[/tex] and [tex]\(\frac{5}{6} \approx 0.833\)[/tex].
3. Since [tex]\(0.167 < 0.833\)[/tex], we have [tex]\(\frac{2}{12} < \(\frac{5}{6}\)[/tex].
These are the comparisons for each problem. Let me know if you need any further clarification!
