If \(\displaystyle\frac{a}{1}=\frac{b}{13}=\frac{c}{7}\), then find the value of \(\displaystyle\frac{a+b}{a+b+c}\).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{2}{3}\)
When several ratios are equal, each letter is its denominator times the same number. Calling that common value \(k\), every term of the fraction carries \(k\), which then cancels.
\(a=k\), \(b=13k\), \(c=7k\)
\(a+b=k+13k=14k\)
\(a+b+c=k+13k+7k=21k\)
\(\displaystyle\frac{a+b}{a+b+c}=\frac{14k}{21k}=\frac{2}{3}\)