REMAINDERS Meaning and
Definition
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Remainders are the quantities left over after a division or subtraction process has been completed. In mathematics, a remainder refers to the numerical value that remains when one number is divided by another and does not evenly divide it. It represents the amount that is left over or "left behind" after a specific calculation or operation.
When performing division, the remainder is the amount that cannot be evenly distributed or divided into equal parts. For instance, when dividing 10 by 3, the quotient is 3, but there is a remainder of 1. The remainder can range from zero to a value of one less than the divisor.
Remainders are often represented using the symbol "%", known as the modulo operator or modulus. Using this operator in mathematical notation, the remainder of dividing a number, a, by another number, b, can be expressed as a % b. For instance, 10 % 3 equals 1, indicating that the remainder of dividing 10 by 3 is 1.
Remainders are frequently encountered in number theory, modular arithmetic, and applications involving cyclic patterns or repetitions. They have various practical uses, such as determining divisibility, solving congruences, or finding patterns in arithmetic sequences. Additionally, remainders can be used to simplify fractions and perform long division. Understanding and manipulating remainders is essential for many mathematical computations and problem-solving techniques.
Common Misspellings for REMAINDERS
Etymology of REMAINDERS
The word "remainders" originated from the combination of two words: "remain" and "der".
The word "remain" has its roots in the Latin word "remanere", which is formed by combining "re-" (meaning "again" or "back") and "manere" (meaning "to stay" or "to remain"). Over time, this term evolved into "remain" in English, and it refers to what is left or stays after a part has been taken away.
The word "der" does not have a clear etymology on its own. However, in the context of "remainders", it is used as a suffix to denote plural or collective nouns. This suffix is derived from the Old English word "-eras", which evolved into "-er" or "-ers" in Middle English and is still used in contemporary English.
Similar spelling words for REMAINDERS
Conjugate verb Remainders
CONDITIONAL
I
would remainder
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would remainder
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would remainder
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would remainder
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would remainder
FUTURE
I
will remainder
we
will remainder
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will remainder
he/she/it
will remainder
they
will remainder
FUTURE PERFECT
I
will have remaindered
we
will have remaindered
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will have remaindered
he/she/it
will have remaindered
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will have remaindered
PAST
I
remaindered
we
remaindered
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remaindered
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remaindered
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remaindered
PAST PERFECT
I
had remaindered
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had remaindered
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had remaindered
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had remaindered
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had remaindered
PRESENT
I
remainder
we
remainder
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remainder
he/she/it
remainders
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remainder
PRESENT PERFECT
I
have remaindered
we
have remaindered
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have remaindered
he/she/it
has remaindered
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have remaindered
I
am remaindering
we
are remaindering
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are remaindering
he/she/it
is remaindering
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are remaindering
I
was remaindering
we
were remaindering
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were remaindering
he/she/it
was remaindering
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were remaindering
I
will be remaindering
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will be remaindering
you
will be remaindering
he/she/it
will be remaindering
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will be remaindering
I
have been remaindering
we
have been remaindering
you
have been remaindering
he/she/it
has been remaindering
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have been remaindering
I
had been remaindering
we
had been remaindering
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had been remaindering
he/she/it
had been remaindering
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had been remaindering
I
will have been remaindering
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will have been remaindering
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will have been remaindering
he/she/it
will have been remaindering
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will have been remaindering
I
would have remaindered
we
would have remaindered
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would have remaindered
he/she/it
would have remaindered
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would have remaindered
I
would be remaindering
we
would be remaindering
you
would be remaindering
he/she/it
would be remaindering
they
would be remaindering
I
would have been remaindering
we
would have been remaindering
you
would have been remaindering
he/she/it
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they
would have been remaindering
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