Division: Partial Quotients Method

The partial quotients method (also called stacking or chunking method) is an elementary approach for solving simple division questions by repeated subtraction. It is also known as the hangman method with the addition of a line separating the divisor, dividend, and partial quotients.

To calculate the whole number quotient of dividing a large number by a small number, the student repeatedly takes away "chunks" of the large number, where each "chunk" is an easy multiple (for example 100×, 10×, 5× 2×, etc.) of the small number, until the large number has been reduced to zero – or the remainder is less than the small number itself.

Understanding Partial Quotients as a Division Strategy
The division operation is defined as the process of repeated subtraction. It is exactly the opposite of multiplication. In the standard form of division, the divisor is used to determine how many times it can be subtracted from the dividend.

Example:

20 ÷ 5

20 - 5 = 15

15 - 5 = 10

10 - 5 = 5

5 - 5 = 0

5 is subtracted 4 times to get the remainder of 0.

so 

20 ÷ 5 = 4

In the partial quotient division, we break the dividend into smaller parts by subtracting multiples of the divisor until the remainder is 0 or less than the divisor. The multipliers (numbers used to multiply the divisor to find these multiples) are the partial quotients, which are then summed to find the final quotient.

Steps with Example

https://mrsrenz.com/division-strategies-made-easier-partial-quotients-method-and-more/

https://www.splashlearn.com/math-vocabulary/division/partial-quotient

https://en.wikipedia.org/wiki/Chunking_(division)