Answer :
To determine which of the given statements is true, we need to compare each fraction with [tex]\(\frac{3}{5}\)[/tex].
1. Compare [tex]\(\frac{30}{100}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- The fraction [tex]\(\frac{30}{100}\)[/tex] simplifies to [tex]\(\frac{3}{10}\)[/tex].
- Now, compare [tex]\(\frac{3}{10}\)[/tex] with [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[ \frac{3}{10} = 0.3 \quad \text{and} \quad \frac{3}{5} = 0.6 \][/tex]
Since [tex]\(0.3\)[/tex] is less than [tex]\(0.6\)[/tex],
[tex]\[ \frac{3}{10} < \frac{3}{5} \][/tex]
Thus, [tex]\(\frac{30}{100} < \frac{3}{5}\)[/tex].
2. Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- Convert both fractions to decimals or find a common denominator.
- [tex]\(\frac{3}{4} = 0.75\)[/tex] and [tex]\(\frac{3}{5} = 0.6\)[/tex].
- Since [tex]\(0.75\)[/tex] is greater than [tex]\(0.6\)[/tex],
[tex]\[ \frac{3}{4} > \frac{3}{5} \][/tex]
3. Compare [tex]\(\frac{3}{7}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- Convert both fractions to decimals or find a common denominator.
- [tex]\(\frac{3}{7} \approx 0.4286\)[/tex] and [tex]\(\frac{3}{5} = 0.6\)[/tex].
- Since [tex]\(0.4286\)[/tex] is less than [tex]\(0.6\)[/tex],
[tex]\[ \frac{3}{7} < \frac{3}{5} \][/tex]
4. Compare [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- Convert both fractions to decimals or find a common denominator.
- [tex]\(\frac{12}{25} = 0.48\)[/tex] and [tex]\(\frac{3}{5} = 0.6\)[/tex].
- Since [tex]\(0.48\)[/tex] is less than [tex]\(0.6\)[/tex],
[tex]\[ \frac{12}{25} < \frac{3}{5} \][/tex]
After comparing all the fractions, the only true statement is:
[tex]\[ \frac{3}{4} > \frac{3}{5} \][/tex]
1. Compare [tex]\(\frac{30}{100}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- The fraction [tex]\(\frac{30}{100}\)[/tex] simplifies to [tex]\(\frac{3}{10}\)[/tex].
- Now, compare [tex]\(\frac{3}{10}\)[/tex] with [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[ \frac{3}{10} = 0.3 \quad \text{and} \quad \frac{3}{5} = 0.6 \][/tex]
Since [tex]\(0.3\)[/tex] is less than [tex]\(0.6\)[/tex],
[tex]\[ \frac{3}{10} < \frac{3}{5} \][/tex]
Thus, [tex]\(\frac{30}{100} < \frac{3}{5}\)[/tex].
2. Compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- Convert both fractions to decimals or find a common denominator.
- [tex]\(\frac{3}{4} = 0.75\)[/tex] and [tex]\(\frac{3}{5} = 0.6\)[/tex].
- Since [tex]\(0.75\)[/tex] is greater than [tex]\(0.6\)[/tex],
[tex]\[ \frac{3}{4} > \frac{3}{5} \][/tex]
3. Compare [tex]\(\frac{3}{7}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- Convert both fractions to decimals or find a common denominator.
- [tex]\(\frac{3}{7} \approx 0.4286\)[/tex] and [tex]\(\frac{3}{5} = 0.6\)[/tex].
- Since [tex]\(0.4286\)[/tex] is less than [tex]\(0.6\)[/tex],
[tex]\[ \frac{3}{7} < \frac{3}{5} \][/tex]
4. Compare [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
- Convert both fractions to decimals or find a common denominator.
- [tex]\(\frac{12}{25} = 0.48\)[/tex] and [tex]\(\frac{3}{5} = 0.6\)[/tex].
- Since [tex]\(0.48\)[/tex] is less than [tex]\(0.6\)[/tex],
[tex]\[ \frac{12}{25} < \frac{3}{5} \][/tex]
After comparing all the fractions, the only true statement is:
[tex]\[ \frac{3}{4} > \frac{3}{5} \][/tex]
