If \(A:B = 2:3\) and \(B:C = 4:5\), find \(A:C\).
\(8:15\)
To combine two ratios that share the common term B, make B equal in both. In \(A:B = 2:3\), B is 3; in \(B:C = 4:5\), B is 4. The LCM of 3 and 4 is 12.
Scale the first ratio by 4: \(A:B = 8:12\). Scale the second ratio by 3: \(B:C = 12:15\).
Now B matches (12) in both, so \(A:B:C = 8:12:15\).
Hence, \(A:C = 8:15\).
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