Question
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Answer
\[
\frac{2}{7} + \frac{6}{14} = \frac{5}{7}
\]
Solution
1. Simplify the second fraction:
\[
\frac{6}{14} = \frac{6 \div 2}{14 \div 2} = \frac{3}{7}
\]
2. Add the fractions with a common denominator:
\[
\frac{2}{7} + \frac{3}{7} = \frac{2+3}{7} = \frac{5}{7}
\]
Thus,
\[
\frac{2}{7}+\frac{6}{14} = \frac{5}{7}
\]
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Simplify this solution Bonus Knowledge
First, let's find a common denominator for the two fractions. The denominator of \( \frac{2}{7} \) is 7, and for \( \frac{6}{14} \), it's 14. Since 14 is a multiple of 7, we can rewrite \( \frac{2}{7} \) as \( \frac{4}{14} \) (by multiplying both the numerator and denominator by 2). Now we can add them: \[ \frac{4}{14} + \frac{6}{14} = \frac{10}{14} \] To simplify, divide both the numerator and denominator by their greatest common divisor, which is 2: \[ \frac{10 \div 2}{14 \div 2} = \frac{5}{7} \] So, \( \frac{2}{7} + \frac{6}{14} = \frac{5}{7} \).
