How to Get a Remainder in Your Calculator

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When you work out a long division problem on your calculator, by default, it gives you the result as a whole number followed by a decimal with numbers after the decimal. But depending on the context for the division problem, you might require the answer as a whole number with a remainder instead. While most scientific calculators have a remainder function that you can locate either on the keyboard or by scrolling through their menus, this quick trick lets you calculate remainders with any calculator at all.

TL;DR (Too Long; Didn't Read)

Work the division in your calculator as normal. Once you have the answer in decimal form, subtract the whole number, then multiply the decimal value that's left by the divisor of your original problem. The result is your remainder.

For example, divide 346 by 7 to arrive at 49.428571. Round this to a whole number of 49. Multiply 49 by 7 to achieve 343 expressed as 49 x 7 = 343. Subtract this from the original number of 346 to arrive at a remainder of 3.

Setting Up the Problem

Before you figure out a division problem with a calculator, it helps to have some basic terms straight. The number divided into is the dividend, the number you're dividing it by is the divisor and the answer is the quotient. Often, you'll see division problems written like this: Dividend ÷ divisor = quotient. If you were to write your division problem out as a fraction, the number on top (also called the numerator) is the dividend, and the number on bottom (also called the denominator) is the divisor.

  1. Find the Decimal Answer

  2. Find the remainder of a division problem with your calculator, by working the division as usual. You'll get a decimal answer – that's fine.

  3. Subtract the Integer

  4. Subtract the integer from the answer you received. (That's whatever amount is to the left of the decimal point.) You're left with only the part of the answer that was to the right of the decimal point.

  5. Multiply by the Divisor

  6. Multiply what's left of your answer by the initial divisor. The result is your remainder. For example, if the initial problem was 11 ÷ 8, the calculator returns an answer of 1.375. After subtracting the integer, 1, you’re left with .375. Multiply that by 8 and you have the remainder: 3.

    Tips

    • Remember, the divisor is the number to the right of the ÷ sign or, if you wrote the division problem out as a fraction, it's the number on the bottom of the fraction. If you're writing out long division, the divisor is the number to the left (outside) of the long division sign.

References

About the Author

Lisa studied mathematics at the University of Alaska, Anchorage, and spent several years tutoring high school and university students through scary -- but fun! -- math subjects like algebra and calculus.

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