Answer :
To determine which of the options is equal to \(\frac{5}{7}\), we need to compare \(\frac{5}{7}\) with each of the given options by evaluating each fraction.
Let's evaluate each fraction one by one and compare them with \(\frac{5}{7}\):
1. Option A: \(\frac{42}{63}\)
[tex]\[ \frac{42}{63} \approx 0.6667 \][/tex]
2. Option B: \(\frac{54}{63}\)
[tex]\[ \frac{54}{63} \approx 0.8571 \][/tex]
3. Option C: \(\frac{45}{63}\)
[tex]\[ \frac{45}{63} \approx 0.7143 \][/tex]
4. Option D: \(\frac{35}{63}\)
[tex]\[ \frac{35}{63} \approx 0.5556 \][/tex]
Next, we calculate the decimal equivalent of \(\frac{5}{7}\):
[tex]\[ \frac{5}{7} \approx 0.7143 \][/tex]
Upon comparing the calculated values:
- \(\frac{42}{63} \approx 0.6667\) which is not equal to \(\frac{5}{7}\).
- \(\frac{54}{63} \approx 0.8571\) which is not equal to \(\frac{5}{7}\).
- \(\frac{45}{63} \approx 0.7143\) which is equal to \(\frac{5}{7}\).
- \(\frac{35}{63} \approx 0.5556\) which is not equal to \(\frac{5}{7}\).
Therefore, the fraction that is equal to \(\frac{5}{7}\) is:
[tex]\[ \boxed{\frac{45}{63}} \][/tex]
Let's evaluate each fraction one by one and compare them with \(\frac{5}{7}\):
1. Option A: \(\frac{42}{63}\)
[tex]\[ \frac{42}{63} \approx 0.6667 \][/tex]
2. Option B: \(\frac{54}{63}\)
[tex]\[ \frac{54}{63} \approx 0.8571 \][/tex]
3. Option C: \(\frac{45}{63}\)
[tex]\[ \frac{45}{63} \approx 0.7143 \][/tex]
4. Option D: \(\frac{35}{63}\)
[tex]\[ \frac{35}{63} \approx 0.5556 \][/tex]
Next, we calculate the decimal equivalent of \(\frac{5}{7}\):
[tex]\[ \frac{5}{7} \approx 0.7143 \][/tex]
Upon comparing the calculated values:
- \(\frac{42}{63} \approx 0.6667\) which is not equal to \(\frac{5}{7}\).
- \(\frac{54}{63} \approx 0.8571\) which is not equal to \(\frac{5}{7}\).
- \(\frac{45}{63} \approx 0.7143\) which is equal to \(\frac{5}{7}\).
- \(\frac{35}{63} \approx 0.5556\) which is not equal to \(\frac{5}{7}\).
Therefore, the fraction that is equal to \(\frac{5}{7}\) is:
[tex]\[ \boxed{\frac{45}{63}} \][/tex]
