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Remainder Calculator

Written by:
PK

Below is a remainder calculator, which will only return a whole number quotient plus the remainder, or anything left over.

Remainder Calculator

What is a Remainder?

A remainder is the amount left over when you do division and the divisor doesn't divide the divisor equally. These terms are related in this form:

\frac{x}{y}=q+r

Where:

  • x: the divisor or number we will divide by y
  • y: the dividend, the number of times to divide x
  • q: the quotient, or the whole number times y could divide b
  • r: the remainder or left over number from dividing x by y

It's often used in long division, where the remainder is labeled as remainder or just r.

As a more practical example, the remainder is used in modular arithmetic or "module" or "mod" math (see the modulo calculator). For example, on a 12 hour clock, 3 hours after 11 AM is 2 PM.

Remainder Math Example

For example, let's say you want to divide 12 by 5. If you were to do this division without remainders, you would get 2.4.

However, doing the math with a remainder looks like this:

\frac{12}{5}=2\ remainder\ 2

Conceptually, if you divide 12 into groups of 5 what you get is 2 full sized groups, plus 2 left over. Here's how it looks:

🦆🦆🦆🦆🦆🦆🦆🦆🦆🦆🦆🦆/5=\\~\\🦆🦆🦆🦆🦆\\~\\🦆🦆🦆🦆🦆\\~\\remainder:\ 🦆🦆

Using the Remainder Calculator

To use the remainder calculator, enter in both a Dividend (top number in division) and a Divisor (bottom number). Next, hit the Compute Remainder button.

Immediately, you'll see the Quotient and Remainder box fill with the results of the division.

Afterwards, see our other tools.

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