To combine ratios with a shared quantity, make the value representing that quantity identical before joining them. When quantities change, use actual amounts or a common multiplier; the old ratio need not remain true. Example If A:B=2:3 and B:C=4:5, write A:B=8:12 and B:C=12:15. Hence A:B:C=8:12:15. A mixture contains 10 litres of juice and 15 litres of water, ratio 2:3. Adding 5 litres of juice changes the ratio to 15:15=1:1. Equal additions to two amounts generally change their ratio; equal multiplication preserves it.

To combine ratios with a shared quantity, make the value representing that quantity identical before joining them. When quantities change, use actual amounts or a common multiplier; the old ratio need not remain true.

If \(A:B=2:3\) and \(B:C=4:5\), write \(A:B=8:12\) and \(B:C=12:15\). Hence \(A:B:C=8:12:15\).

A mixture contains \(10\) litres of juice and \(15\) litres of water, ratio \(2:3\). Adding \(5\) litres of juice changes the ratio to \(15:15=1:1\).

Equal additions to two amounts generally change their ratio; equal multiplication preserves it.

Combining and changing ratios

Combining and changing ratios