A worked example: 2:3 = 10:D
Solving 2:3 = 10:D for D gives 15 — the ratio 2:3 scaled up so that the first number becomes 10 scales the second number to 15 in the same proportion.
The formula: D = (B × C) ÷ A
Cross-multiplication turns A:B = C:D into A × D = B × C, which rearranges to solve for D: (3 × 10) ÷ 2 = 15. The same cross-multiplication move works for any proportion, not just this specific example.
A different scale factor: 4:6 = 20:D
Solving 4:6 = 20:D gives D = 30 — (6 × 20) ÷ 4 = 30. Notice 4:6 is the same underlying ratio as 2:3 (just not simplified), and scaling it to a first value of 20 instead of 10 produces double the second value too, exactly as the proportional relationship requires.
What real-world problems use this structure
Scaling a recipe, converting between map distance and real distance, and comparing rates (like speed or price-per-unit) all reduce to solving a proportion — three known values and one unknown, connected by a fixed ratio.
Solving for a different position in the proportion
This formula is set up to solve specifically for D. To solve for A, B, or C instead, rearrange which known and unknown values go where — for example, solving for A given B, C, D means treating it as B:A = D:C and entering the values in that rearranged order.