Use partial quotients

Partial quotients represents division of a whole-number dividend of up to four digits by a one-digit divisor as the subtraction of convenient, place-value-based multiples of the divisor; the recorded partial quotients are added to form the quotient, with any remainder smaller than the divisor. The method connects multiplication, place value, and the equation dividend = divisor × quotient + remainder, without extending to decimal quotients, fractions, or multi-digit divisors.

Detailed Explanation: Use partial quotients

Partial quotients break a division problem into easier groups. Each group is a convenient multiple of the divisor.

Example: Find $947 \div 4$ .

Start with the dividend, $947$ . Take away a large, easy multiple of $4$ :

200 \times 4=800

Subtract:

947-800=147

Record the partial quotient $200$ .

Take away another convenient multiple of $4$ :

30 \times 4=120

Subtract:

147-120=27

Record the partial quotient $30$ .

Take away another multiple of $4$ :

6 \times 4=24

Subtract:

27-24=3

Record the partial quotient $6$ .

The remainder is $3$ . It is smaller than the divisor, $4$ , so we stop.
Add the partial quotients:

200+30+6=236

Therefore,

947\div4=236\text{ remainder }3.

Check the answer using multiplication:

4\times236+3=944+3=947.

So the division is correct.

Learn by doing: Use partial quotients

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Long Division - No Remainder 4 x 1

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Use partial quotients

Detailed Explanation: Use partial quotients

Learn by doing: Use partial quotients

Practice with unlimited practice problems

Practice:

Long Division - No Remainder 4 x 1