Your Ad Here

Division through Fun Games
before Long Division

For details, see near
the bottom of this page.

Please study
if you have not already done so.

There we have covered division
as repeated subtraction.

We have also seen the concept of
division as sharing equally every
time and as making sets.

We have also seen the relation
between multiplication and division.

We also emphasized the need of
Multiplication Tables in division.

Here, we will proceed to explain the
standard procedure suitable for dividing
simple or complex multi-digit numbers.

It breaks down a division problem into
a series of easier steps. It enables
divisions involving arbitrarily large
numbers to be performed by following
this series of simple steps.

It is one of the most essential skills
to be learnt in elementary math.

This standard procedure
is called Long Division.

Terms involoved in Long Division :
Dividend, Divisor, Quotient and Remainder

Example 1

Suppose I ask you to find 21 ÷ 4.

You recall 4 times table and
realise that there is no number
which when multiplied by 4 gives 21.

Then, how to find 21 ÷ 4 ?

We will try to find a number
which when multiplied
gives a value near to 21.

From 4 times table, we know
4 x 5 = 20 and 20 is near 21.

The difference of 21 and 20 = 1
is called the Remainder
when 21 is divided by 4.

21 is called Dividend and
4 is called Divisor
and 5 is called the Quotient.

The Remainder (= 1) is less
than the Divisor ( = 4).

The number being divided
is called the Dividend.
The number that divides
is called the Divisor.
The number got after division
is called the Quotient.
The number that remains undivided
is called the Remainder.
The Remainder should always
be less than the Divisor.

Vertical Presentation

The process is shown below in vertical

Finding 21 ÷ 4 :

 Divisor   4 )   21   ( 5   Quotient    
                  1   Remainder 

The vertical presentation
shown above is what we
follow in future division sums.

It is explained below.

First the Dividend (21 here) is
written. Then the Divisor (4 here)
with a bracket ')' is written
to the left of 21. and a bracket
'(' is written to the right of 21.

Now we recall 4 times table and find
a number such that the number x 4 is
near to 21. The number we know is 5.

This 5 (Quotient) is written
to the right side of 21 after
the bracket '(' already provided.

The value of 5 times 4 which is 20,
is written below the Dividend (21 here).

20 is subtracted from 21 to
get 1 (Remainder), which is
written below, between two lines.

Thus, we got the Quotient ( 5 here )
and the Remainder (1 here )
in the Division process.

The Remainder should always
be less than the Divisor.

In Division, either at the end or
at any stage, the Remainder should
always be less than the Divisor.

Get The Best Grades With the Least Amount of Effort

Here is a collection of proven tips,
tools and techniques to turn you into
a super-achiever - even if you've never
thought of yourself as a "gifted" student.

The secrets will help you absorb, digest
and remember large chunks of information
quickly and easily so you get the best grades
with the least amount of effort.

If you apply what you read from the above
collection, you can achieve best grades without
giving up your fun, such as TV, surfing the net,
playing video games or going out with friends!

Know more about the

Speed Study System.

Example 2

Find the quoitient and the remainder
when 89 is divided by 9.

Solution :
We know 9 x 9 = 81 which is near 89.

 Divisor   9 )   89   ( 9   Quotient    
                  8   Remainder 

Thus, the quotient = 9 and
the remainder = 8. Ans.

Great deals on School & Homeschool Curriculum Books and Software

The relation among Dividend,
Divisor, Quotient and Remainder

We can see from Example 1
that 21 = 4 x 5 + 1.

Also, we can see from Example 2
that 89 = 9 x 9 + 8.

From these observations, we can say,

Dividend = Divisor x Quotient + Remainder.

If remainder is zero,
Dividend = Divisor x Quotient.

This is what we saw, (remainder = 0),
in examples and exercises of

Division as repeated addition


Division using Multiplication tables.

Great Deals on School & Homeschool Curriculum Books

Long Division Problems

For problems on long division
by a single digit number, go to

Division Problems.

For more problems and
introduction of long division
by two digit numbers, go to

More Division Problems.

For long division by two or
more digit numbers, go to

Division by Two
or more digit numbers.

Progressive Learning of Math : Long Division

Recently, I have found a series of math curricula
(Both Hard Copy and Digital Copy) developed by a Lady Teacher
who taught everyone from Pre-K students to doctoral students
and who is a Ph.D. in Mathematics Education.

This series is very different and advantageous
over many of the traditional books available.
These give students tools that other books do not.
Other books just give practice.
These teach students “tricks” and new ways to think.

These build a student’s new knowledge of concepts
from their existing knowledge.
These provide many pages of practice that gradually
increases in difficulty and provide constant review.

These also provide teachers and parents with lessons
on how to work with the child on the concepts.

The series is low to reasonably priced and include

Elementary Math curriculum


Algebra Curriculum.

Learning/Teaching Math Can Be Fun

Here is a collection of kids math
games and fun math activities for
the class room or for the home, to
make math exciting and easy to learn.

They help you

* To save you time and money to be
spent on resources, games and books.

* To become a wonderful, fun teacher
or parent who knows how to make math
fun, interesting and effective.

* To cater for all different ability
levels and cater for different
learning styles.

* To see your kids math skills soar
and their grades in math going
up and up.

This Collection of Fun Math Games
are electronic books (e-books)
that are downloaded to your computer
in a flash. You can start printing
games right away. You get to print
only what you want and as many
copies as you need.

For more information or to have
some FREE samples or to order
click HERE.