proportional

/proportional/
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proportional

The punishment should be proportional to the crime.

Definition
  1. Adjective:

    • Having a constant ratio: Describes a relationship between two quantities where their ratio remains constant. If one quantity changes, the other changes by a consistent multiplicative factor.
    • Properly related in size or degree: Describes something that is appropriate in scale or severity relative to something else, often followed by 'to'.
  2. Noun:

    • One of the quantities in a mathematical proportion: Refers to any one of the numbers or variables that are related in a proportional equation (e.g., in the proportion a/b = c/d, a, b, c, and d are the proportionals).
Usage Examples
  • Adjective:

    • The map is drawn to a proportional scale, so one inch represents ten miles.
    • A good leader ensures that responsibility is proportional to authority.
    • The increase in salary was proportional to the rise in the cost of living.
  • Noun (less common in everyday use):

    • In the equation 2/4 = 3/6, the numbers 2, 4, 3, and 6 are the proportionals.
Advanced Usage
  • Directly proportional: A relationship where an increase in one quantity causes a corresponding increase in the other. The formula is typically y = kx, where k is the constant of proportionality.

    • The force applied is directly proportional to the acceleration produced.
  • Inversely proportional: A relationship where an increase in one quantity causes a decrease in the other. The product of the two quantities is constant (xy = k).

    • At a constant temperature, the pressure of a gas is inversely proportional to its volume.
  • Proportional to: The standard phrase used to link the two related items.

    • The amount of tax you pay is proportional to your income.
Variants and Related Words
  • Proportionally (adverb): In a proportional manner; correspondingly.

    • Resources were allocated proportionally based on need.
  • Proportionality (noun): The quality or state of being proportional.

    • The principle of proportionality is key in international law.
  • Proportion (noun): A part, share, or number considered in comparative relation to a whole; the relationship of one thing to another in terms of size, quantity, or degree.

    • A large proportion of the budget is spent on healthcare.
Synonyms
  • Adjective: Corresponding, commensurate, equivalent, relative, symmetrical.
  • Noun: Term, element, component (of a proportion).
Antonyms
  • Adjective: Disproportionate, incommensurate, unequal, unbalanced.
Related Phrases and Concepts
  • Proportional representation: An electoral system in which parties gain seats in proportion to the number of votes cast for them.

    • The country adopted a system of proportional representation to ensure all voices are heard.
  • Constant of proportionality: The constant value (k) of the ratio of two proportional quantities.

    • In the equation for Hooke's Law, F = kx, 'k' is the constant of proportionality.
proportional

The punishment should be proportional to the crime.

Adjective
  1. having a constant ratio
  2. properly related in size or degree or other measurable characteristics; usually followed by `to'
    • the punishment ought to be proportional to the crime
    • earnings relative to production
Noun
  1. one of the quantities in a mathematical proportion