# DIVISION PROBLEMS - LONG DIVISION MADE EASY, SOLVED EXAMPLES, EXERCISES

Learn/Teach
Division Problems
through Fun Games

For details, see near

Long Division,
if you have not already done so.

There we explained the terms involved
in division namely Dividend, Divisor,
Quotient and Remainder
and the relation among them.

We also explained the process of
Long Division by Vertical Presentation.

That knowledge is a prerequisite here.

Here we see division of two or three
or four or more digit numbers
divided by single digit numbers.

As usual, Multiplication Tables
upto 9 times 9 is a prerequisite here.

### Example 1 of Division Problems

Find the quotient and the remainder
when 97 is divided by 7.

Solution to the division Problem:

Step1 :
Here, we first find a number which
when multiplied by 7 is near to 9
(not 97 because 9 is bigger than 7. ).
We know 1 x 7 = 7 is near 9. we write 1
in the right bracket and 7 below 9.
7 subtracted from 9 gives 2.

```
Dividend
Divisor   7 )   97   ( 1
7
---
2

```

You may note that
In division either at the end or
at any stage the remainder should
always be less than the divisor.

Step2 :
To the right of this 2, we descend
the next (last) digit 7 in the
dividend to make it 27.

Now we try to find a number which
when multiplied by 7 is near to 27.

We know 3 x 7 = 21 is near 27.
We write 3 in the right bracket to
the right of 1 and 21 below 27.
21 subtracted from 27 gives 6.

As there is no other digit left
in the dividend to descend,
6 is the remainder.

The long division process
is shown below.

```
Dividend
Divisor   7 )   97   ( 13   Quotient
7
---
27
21
---
6   Remainder
---

```

You may note that
In division either at the end or
at any stage the remainder should
always be less than the divisor.

Thus, quotient = 13 and remainder = 6
when 97 is divided by 7.

Check :
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.

R.H.S. = Divisor x Quotient + Remainder
= 7 x 13 + 6 = 13 x 7 + 6

To Find 13 x 7 :

```      13
7
----           2
91
----
```

R.H.S. = Divisor x Quotient + Remainder
= 7 x 13 + 6 = 91 + 6 = 97
= Dividend = L.H.S. (Verified. )

### Example 2 of Division Problems

Divide 124 by 3.

Solution to the division Problem:

Step1 :
Here, first digit of dividend is 1
which is less than the divisor 3.
So we see the first two digits
of the dividend which is 12.
We find how many times 3 divides 12.
We know 4 x 3 = 12. We put 4 in the
right bracket and 12 below 12 of the
dividend. 12 subtracted from 12 gives 0.

```
Dividend
Divisor   3 )   124   ( 4
12
---
0
```

Step2 :
We descend the next (last) digit
of the dividend, 4 to the right of 0
to make it 04. We know 3 divides 4,
one time. 1 x 3 = 3. We write 1 in the
right bracket after 4 and 3 below 04.
3 subtracted from 4 gives 1
which is the remainder.

```
Dividend
Divisor 3 )   124   ( 41 Quotient
12
---
04
3
---
1   Remainder
---

```

Thus 124 ÷ 3 gives quotient = 41
and remainder = 1. Ans.

Check :
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.

R.H.S. = Divisor x Quotient + Remainder
= 3 x 41 + 1 = 41 x 3 + 1

To Find 41 x 3 :

```      41
3
----
123
----
```

R.H.S. = Divisor x Quotient + Remainder
= 3 x 41 + 1 = 123 + 1 = 124
= Dividend = L.H.S. (Verified. )

### Example 3 of Division Problems

Divide 2479 by 9.

Solution to the division Problem:

```
Dividend
Divisor 9 )   2479   ( 275 Quotient
18
-----
67
63
-----
49
45
-----
4   Remainder
-----

```

Step1 :
Here first digit of dividend is 2
which is less than the divisor 9.
So we see the first two digits
of the dividend which is 24.
We find how many times 9 divides 24.
We know 2 x 9 = 18.
(Note that 3 x 9 = 27 exceeds 24.)
We put 2 in the right bracket and
18 below 24 of the dividend.
18 subtracted from 24 gives 6.

```
Dividend
Divisor   9 )   2479   ( 2
18
-----
6
```

Step2 :
We descend the next digit of the
dividend, 7 to the right of 6 to
make it 67. We know 9 divides 67,
seven times. 7 x 9 = 63.
(Note that 8 x 9 = 72 exceeds 67.)
We write 7 in the right bracket
after 2 and 63 below 67.
63 subtracted from 67gives 4.

```
Dividend
Divisor   9 )   2479   ( 27
18
-----
67
63
-----
4

```

Step3 :
We descend the next (last) digit of
the dividend, 9 to the right of 4
to make it 49. We know 9 divides 49,
five times. 5 x 9 = 45.
(Note that 6 x 9 = 54 exceeds 49.)
We write 5 in the right bracket
after 27 and 45 below 49. 45 subtracted
from 49 gives 4 which is the remainder.

```
Dividend
Divisor   9 )   2479   ( 275   Quotient
18
-----
67
63
-----
49
45
-----
4   Remainder
-----

```

Thus 2479 ÷ 9 gives quotient = 275
and remainder = 4. Ans.

Check :
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.

R.H.S. = Divisor x Quotient + Remainder
= 9 x 275 + 4 = 275 x 9 + 4

To Find 275 x 9 :

```      275
9
----           4 6
2475
----
```
R.H.S. = Divisor x Quotient + Remainder
= 9 x 275 + 4 = 2475 + 4 = 2479
= Dividend = L.H.S. (Verified. )

### Exercise on Division Problems

Find the quotient and the remainder
in the following Division Problems.

1. 97 ÷ 2
2. 138 ÷ 5
3. 3791 ÷ 6
4. 87341 ÷ 7
5. 102109 ÷ 9
6. 101 ÷ 3
7. 3751 ÷ 4
8. 30869 ÷ 8
9. 98765 ÷ 9
10. 4895 ÷ 8
bottom of the page.

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.

and remember large chunks of information
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.

### More Long Division Problems

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

More Long Division Problems.

Great Deals on School & Homeschool Curriculum Books

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

Long Division by Two
or more digit numbers.

## Progressive Learning of Math : Division Problems

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

and

Algebra Curriculum.

## Learning/Teaching Math Can Be Fun : Division Problems

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.

* 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)
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.

some FREE samples or to order

### Answers to Exercise on Division Problems

1. quotient = 48, remainder = 1;
2. quotient = 27, remainder = 3
3. quotient = 631, remainder = 5;
4. quotient = 12477, remainder = 2
5. quotient = 11345, remainder = 4;
6. quotient = 33, remainder = 2
7. quotient = 937, remainder = 3;
8. quotient = 3858, remainder = 5
9. quotient = 10973, remainder = 8;
10. quotient = 611, remainder = 7

## Research-based personalized Math Help tutoring program : Division Problems

Here is a resource for Solid Foundation in
Math Fundamentals from Middle thru High School.
You can check your self by the

### FREE TRIAL.

Are you spending lot of money for math tutors to your
child and still not satisfied with his/her grades ?

Do you feel that more time from the tutor and
more personalized Math Help to identify and fix
the problems faced by your child will help ?

Here is a fool proof solution I strongly recommend
and that too With a minuscule fraction of the amount
you spent on tutors with unconditional 100% money
back Guarantee, if you are not satisfied.

### SUBSCRIBE, TEST, IF NOT SATISFIED, RETURN FOR FULL REFUND

It is like having an unlimited time from an excellent Tutor.

It is an Internet-based math tutoring software program
that identifies exactly where your child needs help and
then creates a personal instruction plan tailored to your
child’s specific needs.

If your child can use a computer and access
the Internet, he or she can use the program.
And your child can access the program anytime
from any computer with Internet access.

### Unique program to help improve math skills quickly and painlessly.

There is an exclusive, Parent Information Page provides YOU
with detailed reports of your child’s progress so you can
monitor your child’s success and give them encouragement.
These Reports include

• Time spent using the program
• Assessment results
• Personalized remediation curriculum designed for your child
• Details the areas of weakness where your child needs additional help
• Provides the REASONS WHY your child missed a concept
• List of modules accessed and amount of time spent in each module
• Quiz results
• Creates reports that can be printed and used to discuss issues with your child’s teachers
These reports are created and stored in a secure section
of the program, available exclusively to you, the parent.
The section is accessed by a password that YOU create and use.
No unauthorized users can access this information.

### Personalized remediation curriculum designed for your child

Thus The features of this excellent Tutoring program are

• Using detailed testing techniques
• Identifing exactly where a student needs help.
• Its unique, smart system pinpointing precise problem areas -
• slowly and methodically guiding the student
• raising to the necessary levels to fix the problem.

### Not a “one-size-fits-all” approach!

Its research-based results have proven that
it really works for all students! in improving
math skills and a TWO LETTER GRADE INCREASE in
math test scores!,if they invest time in using
the program.

Proven for More than 10,000 U.S. public school
students who increased their math scores.