What is the value of \(\frac{3}{4}+\frac{5}{6}+\frac{2}{7}\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{157}{84}\)
Fractions with different denominators are added after writing each over the LCM of the denominators.
LCM of 4, 6 and 7 \(=84\)
\(\displaystyle \frac{3}{4}=\frac{3\times21}{84}=\frac{63}{84}\)
\(\displaystyle \frac{5}{6}=\frac{5\times14}{84}=\frac{70}{84}\)
\(\displaystyle \frac{2}{7}=\frac{2\times12}{84}=\frac{24}{84}\)
\(\displaystyle \text{Sum}=\frac{63+70+24}{84}=\frac{157}{84}\)