Answer :
To rename the fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex] using their least common denominator, follow these steps:
1. Find the Least Common Denominator (LCD):
- The denominators we have are 5 and 7.
- To find the least common denominator, we need to find the least common multiple (LCM) of these two numbers.
- The LCM of 5 and 7 is 35 because 35 is the smallest number that both 5 and 7 can divide evenly into.
2. Rename the fractions:
For [tex]\(\frac{3}{5}\)[/tex]:
- Since the LCD is 35, we convert [tex]\(\frac{3}{5}\)[/tex] to an equivalent fraction with a denominator of 35.
- We multiply both the numerator and denominator of [tex]\(\frac{3}{5}\)[/tex] by 7 (because [tex]\(35 \div 5 = 7\)[/tex]).
- [tex]\(\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}\)[/tex].
For [tex]\(\frac{6}{7}\)[/tex]:
- Similarly, convert [tex]\(\frac{6}{7}\)[/tex] to an equivalent fraction with a denominator of 35.
- We multiply both the numerator and denominator of [tex]\(\frac{6}{7}\)[/tex] by 5 (because [tex]\(35 \div 7 = 5\)[/tex]).
- [tex]\(\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}\)[/tex].
3. Conclusion:
- The fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex] can be renamed with the least common denominator of 35 as [tex]\(\frac{21}{35}\)[/tex] and [tex]\(\frac{30}{35}\)[/tex] respectively.
Therefore, the correct answer is option A, which is [tex]\(\frac{21}{35} \text{ and } \frac{30}{35}\)[/tex].
1. Find the Least Common Denominator (LCD):
- The denominators we have are 5 and 7.
- To find the least common denominator, we need to find the least common multiple (LCM) of these two numbers.
- The LCM of 5 and 7 is 35 because 35 is the smallest number that both 5 and 7 can divide evenly into.
2. Rename the fractions:
For [tex]\(\frac{3}{5}\)[/tex]:
- Since the LCD is 35, we convert [tex]\(\frac{3}{5}\)[/tex] to an equivalent fraction with a denominator of 35.
- We multiply both the numerator and denominator of [tex]\(\frac{3}{5}\)[/tex] by 7 (because [tex]\(35 \div 5 = 7\)[/tex]).
- [tex]\(\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}\)[/tex].
For [tex]\(\frac{6}{7}\)[/tex]:
- Similarly, convert [tex]\(\frac{6}{7}\)[/tex] to an equivalent fraction with a denominator of 35.
- We multiply both the numerator and denominator of [tex]\(\frac{6}{7}\)[/tex] by 5 (because [tex]\(35 \div 7 = 5\)[/tex]).
- [tex]\(\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}\)[/tex].
3. Conclusion:
- The fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex] can be renamed with the least common denominator of 35 as [tex]\(\frac{21}{35}\)[/tex] and [tex]\(\frac{30}{35}\)[/tex] respectively.
Therefore, the correct answer is option A, which is [tex]\(\frac{21}{35} \text{ and } \frac{30}{35}\)[/tex].
