If a : b = 9 : 5, b : c = 4 : 11. Find a : c.
36:55
To join two ratios into a single ratio, the common term \(b\) must be made the same number in both.
The given ratios are \(a : b = 9 : 5\) and \(b : c = 4 : 11\), where \(b\) appears as 5 in the first and 4 in the second.
The LCM of 5 and 4 is 20, so multiply the first ratio by 4 and the second by 5.
This gives \(a : b = 36 : 20\) and \(b : c = 20 : 55\), with \(b = 20\) in both.
Now the three quantities are \(a : b : c = 36 : 20 : 55\), so \(a : c = 36 : 55\).
Key concept: chained ratios are combined by scaling each so the shared term matches, after which the outer terms can be read directly.
Hence \(a : c = \) 36:55.
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