Remainder

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the remainder is the amount "left over" after performing some computation. In <a href="/facts/Arithmetic/hvHwkbMV">arithmetic</a>, the remainder is the integer "left over" after <a href="/facts/Division_(mathematics)/FqLKNkmq">dividing</a> one <a href="/facts/Integer/PUwwrawx">integer</a> by another to produce an integer <a href="/facts/Quotient/JekSq1Ko">quotient</a> (<a href="/facts/Euclidean_division/hgNk37et">integer division</a>). In <a href="/facts/Algebra/nMdqczjo">algebra</a> of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. The <a href="/facts/Modulo_operation/V5xPUluD">modulo operation</a> is the operation that produces such a remainder when given a dividend and divisor.
Alternatively, a remainder is also what is left after <a href="/facts/Subtraction/dEUrp6k0">subtracting</a> one number from another, although this is more precisely called the <a href="/facts/Difference_(mathematics)/dEUrp6k0">difference</a>. This usage can be found in some elementary textbooks; colloquially it is replaced by the expression "the rest" as in "Give me two dollars back and keep the rest." However, the term "remainder" is still used in this sense when a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> is approximated by a <a href="/facts/Series_expansion/ElmJVK7Q">series expansion</a>, where the error expression ("the rest") is referred to as the <a href="/facts/Remainder_term/yDnlsgIe">remainder term</a>.

Remainder open-in-new

Remainder