a ratio
A ratio is a way of saying how big one quantity is compared with another. If a recipe uses 2 cups of flour for every 1 cup of sugar, the ratio of flour to sugar is 2 to 1. It is not a count of how much there is in total; it is a comparison — a 'for every' statement that stays the same whether you make a small batch or a large one.
We write a ratio of a to b as a : b, or as the fraction a/b (with b not zero). The order matters: the ratio of flour to sugar 2 : 1 is not the same as sugar to flour 1 : 2. A ratio is usually reduced to lowest terms, so 6 : 4, 3 : 2, and 1.5 : 1 are all the same ratio. The two quantities being compared should be measured in the same unit before you form the ratio — comparing 30 cm to 2 m means first writing both as 30 cm to 200 cm, giving 3 : 20.
Ratio is the seed of this whole field. Once you can say 'this side is twice that one', you can ask when two whole figures have all their sides in the same ratio — and that is similarity. A ratio of two quantities with different units (like distance over time) is usually called a rate; the arithmetic is identical, but the name signals that the answer carries a unit such as kilometres per hour.
In a class of 18 girls and 12 boys, the ratio of girls to boys is 18 : 12, which reduces to 3 : 2. The ratio of girls to the whole class is 18 : 30 = 3 : 5.
A part-to-part ratio (3 : 2) and a part-to-whole ratio (3 : 5) describe the same class differently.
A common slip is to treat a part-to-part ratio as if it were a fraction of the whole: 3 : 2 girls to boys does not mean three-fifths of the girls — it means girls are three-fifths of the whole class only after you add the parts to get the total of 5.