Question

1. which sum is equivalent to \\(\frac{3}{5} + \frac{1}{6}\\)?

a \\(\frac{6}{10} + \frac{2}{10}\\)
b \\(\frac{12}{30} + \frac{5}{30}\\)
c \\(\frac{18}{30} + \frac{5}{30}\\)
d \\(\frac{3}{11} + \frac{4}{11}\\)

Explanation:

Step1: Find common denominator for \(\frac{3}{5}\) and \(\frac{1}{6}\)

The least common denominator of 5 and 6 is \(5\times6 = 30\).
Rewrite \(\frac{3}{5}\) with denominator 30: \(\frac{3\times6}{5\times6}=\frac{18}{30}\)
Rewrite \(\frac{1}{6}\) with denominator 30: \(\frac{1\times5}{6\times5}=\frac{5}{30}\)
So \(\frac{3}{5}+\frac{1}{6}=\frac{18}{30}+\frac{5}{30}\)

Step2: Check each option

• Option A: \(\frac{6}{10}+\frac{2}{10}=\frac{8}{10}\), \(\frac{3}{5}+\frac{1}{6}=\frac{18 + 5}{30}=\frac{23}{30}\), \(\frac{8}{10}=\frac{24}{30}

eq\frac{23}{30}\)

• Option B: \(\frac{12}{30}+\frac{5}{30}=\frac{17}{30}

eq\frac{23}{30}\)

• Option C: \(\frac{18}{30}+\frac{5}{30}=\frac{23}{30}\), which matches \(\frac{3}{5}+\frac{1}{6}\)
• Option D: \(\frac{3}{11}+\frac{4}{11}=\frac{7}{11}\approx0.636\), \(\frac{23}{30}\approx0.767\), not equal

Answer:

C. \(\frac{18}{30} + \frac{5}{30}\)