If \(a:b=\displaystyle\frac{2}{3}:\frac{1}{4}\) and \(b:c=\displaystyle\frac{3}{4}:\frac{4}{5}\), then find \(a:b:c\).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 40:15:16
Turn each ratio of fractions into whole numbers, then make the common term b equal in both before joining them.
\(a:b=\frac{2}{3}:\frac{1}{4}\); multiplying both by 12: \(a:b=8:3\)
\(b:c=\frac{3}{4}:\frac{4}{5}\); multiplying both by 20: \(b:c=15:16\)
b is 3 in the first and 15 in the second; multiplying the first by 5: \(a:b=40:15\)
So \(a:b:c=40:15:16\)