Map scale, sugar-water concentration, photo enlargement — all three follow the same idea: "the ratio between two quantities stays constant." Click a tab to see how ratios show up in three different situations.
Ratios are hidden all around us. A map's scale is the ratio between real-world distance and distance on the map, and enlarging or shrinking a photo has to keep the width-to-height ratio the same or the shape gets distorted. Getting the sugar-water concentration right in cooking is also about keeping the ratio of sugar to water.
A ratio compares two quantities by division (e.g. sugar:water = 1:4). Thanks to the property that multiplying or dividing both numbers by the same number doesn't change the ratio, a map keeps its real-world shape no matter how much you shrink it, and adding more water lets you make a bigger batch while keeping "the same concentration."
An equation stating that two ratios are equal is called a proportion (a:b = c:d). The product of the two outer numbers (the extremes) always equals the product of the two inner numbers (the means) — a×d = b×c. This property makes it easy to find an unknown value.