If a/b = 2/3 and b/c = 4/5, find a:c.

Explanation

• Multiply the two fractions so that b cancels: a/c = (a/b) × (b/c) = (2/3) × (4/5) = 8/15.
• As a ratio this is written a : c = 8 : 15.
• Only the shared letter b can cancel, which is why the two ratios must be chained in this order.
• Second method: scale a:b = 2:3 to 8:12 and b:c = 4:5 to 12:15, which gives a:b:c = 8:12:15.
• Since 8/15 is about 0.53, a is a little more than half of c, and that makes a quick sanity check.