How do I Calculate the Quotient?

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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.

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