ratio
A ratio compares two quantities by asking how many times one is, relative to the other. 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 captures the relationship, not the actual amounts: 4 cups to 2 cups is the same ratio scaled up.
A ratio of a to b is written in several equivalent ways: a to b, a : b, or the fraction a/b. Because it is essentially a division, a ratio can be simplified by dividing both quantities by a common factor, just as a fraction is reduced to lowest terms. The ratio 6 : 9 simplifies to 2 : 3.
Order matters and units matter. The ratio of boys to girls is not the same as girls to boys. And when comparing two measurements they should be in the same unit before forming the ratio — 50 cm to 2 m means 50 : 200, which is 1 : 4, not 50 : 2. A second quantity of zero is not allowed, since dividing by zero is undefined.
A class has 12 boys and 18 girls. The ratio of boys to girls is 12 : 18, which simplifies (dividing both by 6) to 2 : 3.
Simplify a ratio the same way you reduce a fraction — divide both parts by a common factor.
A ratio and a fraction look alike but answer different questions. The fraction 2/3 can be a part of a whole; the ratio 2 : 3 compares two separate parts, where the whole is 2 + 3 = 5 parts.