Thirty Guests and a Pancake Recipe for Six
Imagine you want to make pancakes for thirty guests, but your recipe serves only six. You cannot just guess. You need a ratio, which is a way to compare two amounts. Here the ratio is thirty guests to six servings. If you divide 30 by 6, you get 5. That means you need to make the recipe five times.
Now look at the ingredients list. The recipe for six calls for 2 cups of flour, 3 eggs, 1 teaspoon of salt, and half a cup of milk for each cup of flour. To scale it up, multiply every amount by 5. You will need 10 cups of flour, 15 eggs, and 5 teaspoons of salt. The ratio between the ingredients stays the same, so the pancakes should taste the same, too.
A cook must multiply every ingredient. If you change only the flour, the batter will come out too thick or too thin. Math keeps the whole recipe in balance.
Some things do not simply multiply, however. A huge batch will not fit in one small pan. You would cook it in several rounds or use more pans. The cooking time for each pancake stays about the same, too, because a pancake is still the same size. A smart cook uses math for the amounts and common sense for the rest.