Key takeaway: The quotient is the result you get when one number, the dividend, is divided by another, the divisor, and it tells how many times the divisor fits into the dividend.
Grade 66.NS.B.2Numbers and Operations
Definition of Quotient
A quotient is the answer to a division problem. In \(91.2 : 3.8 = 24\), the number 91.2 is the dividend, 3.8 is the divisor, and 24 is the quotient.
It answers two kinds of questions: how many equal groups of the divisor fit into the dividend, or how large each share is when the dividend is split evenly. When the division is not exact, the answer can be written with a remainder, as a mixed number or as a decimal.
Formula and notation
Division can be written three ways, and each gives the same result:
\[\text{dividend} : \text{divisor} = \text{quotient} \qquad \frac{\text{dividend}}{\text{divisor}} \qquad \text{divisor}\overline{)\text{dividend}}\]
The divisor can never be 0. Multiplying the result by the divisor returns the dividend.
Key facts
- Dividend equals divisor times quotient, so multiplication checks any division.
- Multiplying dividend and divisor by the same power of 10 leaves the answer unchanged.
- The result can be smaller than the dividend, equal to it, or larger when dividing by a fraction less than 1.
- Dividing by 0 has no answer, because no number times 0 gives a nonzero dividend.
Quotient example
A 91.2-foot rope is cut into pieces that are each 3.8 feet long. How many pieces are there?
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Multiply both numbers by 10 so the divisor is whole: \(91.2 : 3.8 = 912 : 38\).
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Divide: \(38 \times 24 = 912\), so \(912 : 38 = 24\).
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Check with the original numbers: \(3.8 \times 24 = 91.2\).
The quotient is 24, so the rope makes 24 pieces.
Common mistake
Watch out
Kai computes \(100 : 7\) and writes the quotient as \(14.2\), because the remainder is 2.
Why it is wrong
The remainder 2 is leftover units, not the digits after a decimal point. As a remainder form, \(100 : 7 = 14\text{ R }2\). As a decimal, \(100 : 7 \approx 14.29\), since \(\frac{2}{7} \approx 0.29\).
Related terms and lessons
- Grade 6 · Multi-Digit DivisionLessonWorksheetQuiz
- Grade 6 · Adding, Subtracting, Multiplying and Dividing DecimalsLessonWorksheetQuiz
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