ratio

ratio — noun

1. A relationship between two numbers or amounts that shows how many times one is l

1.nounB1
Definition

A relationship between two numbers or amounts that shows how many times one is larger or smaller than the other.

Example

The ratio of boys to girls in Jin's class is three to two.

ratio of X to Y pattern

To make the perfect lemonade, mix water and lemon juice in a 4:1 ratio.

ratio expressed as X:Y

Common collocations
  • high ratio
  • low ratio
  • student-to-teacher ratio
  • sex ratio
  • ratio of A to B
Synonyms
  • proportion

    Focuses on the share of a part relative to the whole, often expressed as a percentage

  • rate

    Compares two quantities with different units, such as speed or cost per item

Grammar Patterns

ratio of [amount] to [amount]

ratio between [two things]

Usage Note

Typically expressed with a colon (3:1) or the word 'to' (three to one). The preposition pattern 'ratio of A to B' is more common than 'ratio between A and B.'

Common Mistakes

The ratio of boys to girls is five.
The ratio of boys to girls is 5:1.
A ratio keeps two numbers separated by a colon; it is not reduced to a single number.

2. In mathematics, the value obtained by dividing one number by another, often writ

2.nounB2
Definition

In mathematics, the value obtained by dividing one number by another, often written as two numbers with a colon between them or as a fraction.

Example

The ratio of a circle's circumference to its diameter is always about 3.14 to 1.

ratio of ... to ... in math contexts

Shanti simplified the ratio 12:16 to its lowest terms and got 3:4.

simplify a ratio to lowest terms

Common collocations
  • common ratio
  • gear ratio
  • aspect ratio
  • trigonometric ratio
  • simplify a ratio
Synonyms
  • quotient

    The result of division; a closer synonym in strict mathematical use but less common in everyday speech

  • fraction

    A way of writing a ratio; fraction emphasizes a part of a whole, while ratio emphasizes comparison

Grammar Patterns

ratio of [number] to [number]

simplify a ratio

express as a ratio

Usage Note

Common in geometry and trigonometry (sine, cosine, tangent as ratios of side lengths). In a fraction form like 3/4, the ratio is read as 'three to four.'

Common Mistakes

Simplify the ratio 12:16 and you get 4.
The ratio 12:16 in simplest form is 3:4.
Simplifying a ratio keeps two numbers; do not reduce to a single number.

Word family

Synonym discussion

Sense: noun/1

Ratio, proportion, and rate all describe relationships between quantities, but serve different purposes. A ratio compares two numbers of the same unit directly, often written with a colon (2:1) — for example, 'the ratio of sugar to flour is 1:3.' A proportion refers to a part of the whole, frequently expressed as a percentage or fraction: 'a large proportion of the students passed the exam.' A rate compares quantities with different units, such as speed (kilometres per hour) or cost (dollars per kilogram). In short, think of ratio for direct comparisons between same-unit amounts, proportion for how much a part makes of the whole, and rate for change or exchange across units. Try saying: 'The nurse measured the ratio of staff to patients, noted the proportion of elderly patients, and checked the heart rate of each patient.'

ratio ↗proportion ↗rate ↗

Common collocations

Nouns

Adverbs

Phrases

  • in the ratio of X to Y
  • at a ratio of

Prepositions

Etymology

LatinEnglish

Ratio comes from Latin 'ratio,' which meant 'reason, calculation, or reckoning.' It traces back to 'ratus,' the past participle of 'reri' (to think or consider). The word entered English in the 1400s with the meaning 'reason' or 'rationality,' and by the mid-1600s it had taken on the mathematical sense of comparing numbers — reflecting how early scholars saw numerical comparisons as a form of logical reasoning.