Use partial quotients

Partial-quotient division represents a whole-number dividend as a sum of convenient multiples of the divisor, subtracting those products and adding their corresponding quotient parts to determine the total quotient. The relationship $\text{dividend}=\text{divisor}\times\text{quotient}+\text{remainder}$ must hold, with any remainder smaller than the divisor; the method applies to multi-digit whole-number dividends and one- or two-digit divisors, not to more advanced polynomial, fractional, or generalized division.

Detailed Explanation: Use partial quotients

To divide using partial quotients, break the dividend into convenient multiples of the divisor. Subtract each multiple, and add the matching quotient parts.

Example: Find $(874 \div 23)$ .

Choose a convenient multiple of $(23)$ .
Since $(20 \times 23=460)$ , subtract $(460)$ from $(874)$ :

874-460=414

Record the partial quotient $(20)$ .

Subtract another convenient multiple.
Since $(10 \times 23=230)$ :

414-230=184

Record the partial quotient $(10)$ .

Use the remaining amount.
Since $(8 \times 23=184)$ :

184-184=0

Record the partial quotient $8$ .

Add the partial quotients:

20+10+8=38

Therefore,

874\div 23=38.

Check the answer:

23\times 38=874,

874=23\times 38+0.

The remainder is $0$ , which is smaller than $(23)$ , so the answer is correct.

Learn by doing: Use partial quotients

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Division as Fraction - With Remainder 3 x 2

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Use partial quotients

Detailed Explanation: Use partial quotients

Learn by doing: Use partial quotients

Practice with unlimited practice problems

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Division as Fraction - With Remainder 3 x 2