Recipe Scaling Factor
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Most ingredients do scale linearly, but leavening agents (baking soda, baking powder, yeast), spices, and salt often don't need to scale at exactly the same rate, since their effect isn't strictly proportional to batch size; the scaling factor is the right starting point, but taste and texture should guide fine adjustments for these.

It's simply your target yield divided by the original recipe's yield, expressed as a decimal multiplier; a recipe for 4 servings scaled to 10 servings uses a factor of 2.5, and every linearly-scaling ingredient is multiplied by that factor.

Yes, and this is often overlooked: doubling a cake recipe but keeping the same pan size means a much taller cake with a longer, less even bake, so pan area should scale roughly with the recipe, which usually means a bigger pan or multiple pans, not the same pan filled higher.

Cooking time depends more on the dimensions of the food (thickness, depth in the pan) than on total ingredient quantity, so doubling a recipe rarely doubles cooking time; expect a modest increase and rely on a doneness test rather than a scaled time.

Yes, the same multiplier logic applies below 1 (a factor of 0.5 halves the recipe), but very small scaled quantities become hard to measure precisely with standard kitchen tools, so scaling down by more than half often needs a kitchen scale for accuracy.