# 15 Ratio and proportionality

A ratio is a constant number by which one set of data (measurements on an architect’s drawings, a map, the distance of a mass from a fulcrum) may be multiplied to give a second set of data (scale, balance distance from fulcrum). Ratios describe constant multiplicative relationships between two variables. The mathematical form is y=mx. As y increases, so does x to keep m constant. Proportionality requires the comparison of two ratios, as in looking at gear sets or the relative concentrations of solute to solvent in solutions. To use proportional thinking to compare two different solutions to see if they have the same concentration requires the mental manipulation of at least four independent variables.