Partial -Quotients Division is an alternative method for solving division problems.
Even students whose basic-facts knowledge and estimation skills are limited can find correct answers using this common sense approach. In this process, students quickly discover that the better their estimates, the fewer steps they will need to take.
Information from the Algorithms Handbook of the Everyday Math Program
Created by: Chris Cheatham and Maria Farmer WB 2010

Solving a problem
The first step to solving a partial-quotients division problem is to estimate how many times the divisor goes into the dividend.
Students are encouraged to use multiples of
10 when making their first estimate, because multiples of ten are easy numbers to work with.
You will need to record your estimates or partial quotients in a separate column to the right of the problem. In our first example our partial quotient is 20.
Example from the Algorithms Handbook of the Everyday Math Program
Created by: Chris Cheatham and Maria Farmer WB 2010

Solving a problem
Next take your partial quotient and multiply it by your divisor. This will give you the first number that you will need to subtract from the dividend. In our example that number is 540.
After you subtract you will get a difference.
You will then need to ask yourself how many times the divisor goes into that difference. In our example the difference is
81. We need to ask ourselves how many times 27 goes into 81.
You need to be as accurate as possible with this second estimate, because the more accurate you are the less steps you will have to take.
In our example 27 goes into 81 three times.
Your second partial quotient will be 3.
Example from the Algorithms Handbook of the Everyday Math Program
Created by: Chris Cheatham and Maria Farmer WB 2010

Solving a problem
Again take your partial quotient and multiply it by your divisor. This will give you the number that you will need to subtract from the difference.
In our example that number is 81.
In this example when we subtract we are left with a zero. In many problems you will be left with a number that is smaller than your divisor. If this happens that number will have a remainder.
Finally you need to add your partial quotients together to give you your final quotient (answer).
In our example 20+3=23. Our final quotient would be 23. This quotient does not have a remainder because after subtracting we were left with the answer 0. If your answer does have a remainder, remember to record that in your quotient.
Example from the Algorithms Handbook of the Everyday Math Program
Created by: Chris Cheatham and Maria Farmer WB 2010