How do I Calculate the Quotient?

By Teresa J. Siskin
Calculating the quotient begins with a dividend, or number being divided, and a divisor, the number by which the dividend will be divided.
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When you divide one number, or integer, by another, the resulting number from that division is known as the quotient. Evenly divisible numbers produce quotients of a round number. Other numbers, however, will yield a quotient followed by a remainder.

Whole Quotients and Simple Remainders

You can distinguish between evenly divisible numbers and numbers that produce quotients with remainders through some examples. If you divide the number 24 by 8, for example, your quotient is 3 because the number 8 goes into 24 three times exactly. When dividing 20 by 8, however, your quotient will have a remainder. The number 8 goes into 20 two times, leaving a remainder of 20 minus 16, or 4. You would report your quotient as "2 R 4."

Remainders as Fractions or Decimals

You can also express the quotient remainder as a fraction or decimal. You can calculate the decimal by first placing a decimal point following your quotient of 2 and then continuing long division by adding a zero to your remainder, transforming it from 4 to 40. The number 8 goes into 40 five times, resulting in a final quotient of 2.5. So, if, for example, this was a monetary transaction in which you had to divide $20 between eight people, this quotient with the decimal remainder determines that each person receives $2.50. To convert this decimal to a fraction, you would translate .5 to 5/10, then reduce it to its lowest terms, which would be 1/2.

About the Author

Teresa J. Siskin has been a researcher, writer and editor since 2009. She holds a doctorate in art history.