Question

which expression uses a common denominator to rewrite \\(\frac{1}{6} + \frac{1}{5}\\)? \\(\frac{16}{30} + \frac{15}{30}\\) \\(\frac{5}{30} + \frac{6}{30}\\) \\(\frac{1}{12} + \frac{1}{10}\\) \\(\frac{5}{5} + \frac{6}{6}\\)

Explanation:

Step1: Find common denominator

The denominators are 6 and 5. The least common denominator (LCD) of 6 and 5 is \( 6\times5 = 30 \) (since 6 and 5 are coprime).

Step2: Rewrite each fraction

For \( \frac{1}{6} \), multiply numerator and denominator by 5: \( \frac{1\times5}{6\times5}=\frac{5}{30} \).
For \( \frac{1}{5} \), multiply numerator and denominator by 6: \( \frac{1\times6}{5\times6}=\frac{6}{30} \).
So \( \frac{1}{6}+\frac{1}{5}=\frac{5}{30}+\frac{6}{30} \).

Answer:

B. \( \frac{5}{30} + \frac{6}{30} \)