Let's compare the given ratios step by step:
### Part (a)
Compare the ratios [tex]\(3: 7\)[/tex] and [tex]\(7: 11\)[/tex]
1. Convert the ratios to fractions:
- [tex]\(3: 7\)[/tex] can be written as [tex]\(\frac{3}{7}\)[/tex]
- [tex]\(7: 11\)[/tex] can be written as [tex]\(\frac{7}{11}\)[/tex]
2. Compare the fractions:
- [tex]\(\frac{3}{7} \approx 0.4286\)[/tex]
- [tex]\(\frac{7}{11} \approx 0.6364\)[/tex]
Since [tex]\(0.4286 < 0.6364\)[/tex],
[tex]\[ 3:7 < 7:11 \][/tex]
### Part (b)
Compare the ratios [tex]\(3: 4\)[/tex] and [tex]\(8: 9\)[/tex]
1. Convert the ratios to fractions:
- [tex]\(3: 4\)[/tex] can be written as [tex]\(\frac{3}{4}\)[/tex]
- [tex]\(8: 9\)[/tex] can be written as [tex]\(\frac{8}{9}\)[/tex]
2. Compare the fractions:
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
- [tex]\(\frac{8}{9} \approx 0.8889\)[/tex]
Since [tex]\(0.75 < 0.8889\)[/tex],
[tex]\[ 3:4 < 8:9 \][/tex]
### Part (c)
Compare the ratios [tex]\(3: 4\)[/tex] and [tex]\(5: 6\)[/tex]
1. Convert the ratios to fractions:
- [tex]\(3: 4\)[/tex] can be written as [tex]\(\frac{3}{4}\)[/tex]
- [tex]\(5: 6\)[/tex] can be written as [tex]\(\frac{5}{6}\)[/tex]
2. Compare the fractions:
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
- [tex]\(\frac{5}{6} \approx 0.8333\)[/tex]
Since [tex]\(0.75 < 0.8333\)[/tex],
[tex]\[ 3:4 < 5:6 \][/tex]
### Part (d)
Compare the ratios [tex]\(3: 7\)[/tex] and [tex]\(2: 5\)[/tex]
1. Convert the ratios to fractions:
- [tex]\(3: 7\)[/tex] can be written as [tex]\(\frac{3}{7}\)[/tex]
- [tex]\(2: 5\)[/tex] can be written as [tex]\(\frac{2}{5}\)[/tex]
2. Compare the fractions:
- [tex]\(\frac{3}{7} \approx 0.4286\)[/tex]
- [tex]\(\frac{2}{5} = 0.4\)[/tex]
Since [tex]\(0.4286 > 0.4\)[/tex],
[tex]\[ 3:7 > 2:5 \][/tex]
### Summary:
- [tex]\(3:7 < 7:11\)[/tex]
- [tex]\(3:4 < 8:9\)[/tex]
- [tex]\(3:4 < 5:6\)[/tex]
- [tex]\(3:7 > 2:5\)[/tex]
