Partial-Quotients Division
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
In our example 27 goes into 81 three times.
it by your divisor. This will give you the
Your second partial quotient will be 3.
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.
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