Two starting ratios, one identical answer
Simplifying 8:12 gives 2:3, from the real ratio calculator. Using that simplified 2:3 in the proportion 2:3 = 10:D solves to D = 15. Using the original, unsimplified 8:12 in the same proportion — 8:12 = 10:D — also solves to exactly D = 15, with no difference in the final answer at all.
Why this has to be true
Cross-multiplication (D = (B × C) ÷ A) works with whatever numbers represent the ratio, whether reduced or not — since 8:12 and 2:3 describe the identical proportional relationship, plugging either pair into the same formula alongside the same C value produces the same D. Simplifying doesn't change the ratio's meaning, only how compactly it's written.
So why simplify at all?
Working with smaller numbers is easier to reason about and less error-prone by hand — 2:3 is simpler to scale mentally than 8:12, even though both give the same result through a calculator. Simplifying is a readability and convenience step, not a mathematical requirement for correctness.
When simplifying first genuinely helps
For a proportion with much larger or messier starting numbers, simplifying first can make intermediate cross-multiplication values smaller and easier to verify by hand — a practical benefit even though a calculator handles either form identically.