quotient

mathematics

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July 13, 2026

Quick Summary

In mathematics, a quotient is the result obtained when one number is divided by another. For example, when 10 is divided by 2, the quotient is 5.1

The term "quotient" can also refer to the numerical ratio between a test score and a standard value, often multiplied by 100. Additionally, it can describe a share or quota, or the magnitude of a specific characteristic, such as a high "likability quotient".1

In calculus, the quotient rule is used to find the derivative of a quotient of two functions. If you have two differentiable functions, f and g, their quotient f(x)/ g(x) is also differentiable, and its derivative is calculated as (gf\u2032 \u2212 fg\u2032)/g².2

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$A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”$
arithmetic
Theory of divisors
…by”) leads to results, called quotients or fractions, which surprisingly include numbers of a new kind—namely, rationals—that are not integers. These, though arising from the combination of integers, patently constitute a distinct extension of the natural-number and integer concepts as defined above. By means of the application of the division…
Read More
…by”) leads to results, called quotients or fractions, which surprisingly include numbers of a new kind—namely, rationals—that are not integers. These, though arising from the combination of integers, patently constitute a distinct extension of the natural-number and integer concepts as defined above. By means of the application of the division…
Read More