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Answer :
To rename the fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex] with a common denominator, we need to find the least common denominator (LCD) and convert both fractions accordingly.
### Step 1: Find the Least Common Denominator (LCD)
- The denominators here are 5 and 7.
- The least common multiple of 5 and 7 is 35.
### Step 2: Convert [tex]\(\frac{3}{5}\)[/tex] to a fraction with a denominator of 35
- To change the denominator from 5 to 35, determine how many times 5 fits into 35. This is [tex]\(35 ÷ 5 = 7\)[/tex].
- Multiply both the numerator and the denominator of [tex]\(\frac{3}{5}\)[/tex] by 7:
[tex]\[
\frac{3 \times 7}{5 \times 7} = \frac{21}{35}
\][/tex]
### Step 3: Convert [tex]\(\frac{6}{7}\)[/tex] to a fraction with a denominator of 35
- To change the denominator from 7 to 35, determine how many times 7 fits into 35. This is [tex]\(35 ÷ 7 = 5\)[/tex].
- Multiply both the numerator and the denominator of [tex]\(\frac{6}{7}\)[/tex] by 5:
[tex]\[
\frac{6 \times 5}{7 \times 5} = \frac{30}{35}
\][/tex]
### Conclusion:
The fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex] renamed with the least common denominator of 35 are [tex]\(\frac{21}{35}\)[/tex] and [tex]\(\frac{30}{35}\)[/tex].
Thus, the correct answer is A. [tex]\(\frac{21}{35}\)[/tex] and [tex]\(\frac{30}{35}\)[/tex]
### Step 1: Find the Least Common Denominator (LCD)
- The denominators here are 5 and 7.
- The least common multiple of 5 and 7 is 35.
### Step 2: Convert [tex]\(\frac{3}{5}\)[/tex] to a fraction with a denominator of 35
- To change the denominator from 5 to 35, determine how many times 5 fits into 35. This is [tex]\(35 ÷ 5 = 7\)[/tex].
- Multiply both the numerator and the denominator of [tex]\(\frac{3}{5}\)[/tex] by 7:
[tex]\[
\frac{3 \times 7}{5 \times 7} = \frac{21}{35}
\][/tex]
### Step 3: Convert [tex]\(\frac{6}{7}\)[/tex] to a fraction with a denominator of 35
- To change the denominator from 7 to 35, determine how many times 7 fits into 35. This is [tex]\(35 ÷ 7 = 5\)[/tex].
- Multiply both the numerator and the denominator of [tex]\(\frac{6}{7}\)[/tex] by 5:
[tex]\[
\frac{6 \times 5}{7 \times 5} = \frac{30}{35}
\][/tex]
### Conclusion:
The fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex] renamed with the least common denominator of 35 are [tex]\(\frac{21}{35}\)[/tex] and [tex]\(\frac{30}{35}\)[/tex].
Thus, the correct answer is A. [tex]\(\frac{21}{35}\)[/tex] and [tex]\(\frac{30}{35}\)[/tex]
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