Ratio and proportion. Proportionality
The main property of a proportion.
Proportional values. Factor of a proportionality.
Ratio is a quotient of dividing one number by another.
Proportion – an equality of two ratios. For instance:
12 : 20 = 3 : 5; a : b = c : d .
Border terms of the proportion: 12 and 5 in the first proportion;
a and d in the second proportion.
Middle terms of the proportion: 20 and 3 in the first proportion;
b and c in the second proportion.
The main property of a proportion: A product of border terms of a proportion is equal to a product of its middle terms.
Two mutually dependent values are called proportional ones, if a ratio of their values is saved as invariable. This invariable ratio of proportional
values is called a factor of a proportionality.
|E x a m p l e .|| A mass of any substance is proportional to its volume. For instance,
2 liters of mercury weigh 27.2 kg, 5 liters weigh 68 kg, 7 liters weigh 95.2 kg.
A ratio of mercury mass to its volume ( factor of a proportionality ) will be
Thus, a factor of a proportionality in this example is density.