DIVISION - DIVISION OF NUMBERS MADE EASY, WORD PROBLEMS, EXAMPLES, EXERCISES

Learn/Teach
Division through Fun Games.
For details, see near
the bottom of this page.

Please study
the decimal number system,
Subtraction and
Multiplication,
if you have not already done so.

They are prerequisites here.

Example 1 :
Repeated Subtraction

Suppose you have 21 chocolates
with you. You have six friends. You
want to distribute the chocolates
equally amongst yourselves.
How do you do that ?

First, you give a chocolate to
each of your friends and keep
one for your self. How many
chocolates are distributed ?
6 + 1 = 7.
Out of 21, 7 chocolates
are distributed.
How many are remaining ?
21 - 7 = 14.

Now you give one more chocolate
to each of your friends and
again keep one for your self.
This time how many are given ?
again 6 + 1 = 7.
How many remain ? 14 - 7 = 7.

For the third time you
distribute one chocolate
to each of your friends
and keep one for your self.
This time also you distributed
6 + 1 = 7.
How many remain ? 7 - 7 = 0.

We can subtract 7 from 21
three times.
or 7 goes three times in 21.

How many chocolates does
each one of you get ?
Since you have distributed
three times, each one of
you gets 3 chocolates.

Now, we can say, when 21
chocolates are distributed
equally among 7 friends,
each one gets 3 chocolates.

That means, when 21 is divided
by 7, 3 is obtained.
We write this as
21 ÷ 7 = 3.

The above example is an example
of Division as repeated subtraction.

Instead of distributing three times,
you want to give at a time,
the equal share of chocolates to
each one of you by packing the chocolates.

i.e. you want to make 7 packs
from the 21 chocolates.
How many chocolates are
to be put in each pack ?

You need to know before hand,
that 3 chocolates are to be
put in each pack. That means
you need to know 21 ÷ 7 = 3.

Let us see one more example.

Example 2 : Division
as repeated subtraction

Suppose you have 20 pencils.
You have to make packs of
five pencils each.
How many packets can you make ?

See the difference between this
problem and the previous one.
There we know the number of packs
and the number of items in
each pack are to be known.
Here, we know the number of
items in each pack and the number
of packs are to be known.

How do you solve this problem ?

First you seperate a set of
5 pencils from the 20 pencils
and make that set of 5 as a pack.
Then how many pencils remain ?
20 - 5 = 15.

Then, you seperate another set of
5 pencils from this 15 and
make it as another pack.Then
how many pencils remain ?
15 - 5 = 10.

For the third time, you seperate
another set of 5 pencils from this
10 and make it as a pack.Then
how many pencils remain ?
10 - 5 = 5.

You make this remaining
5 as a fourth pack.

Thus, you make 4 packs of 5 pencils
each from the given 20 pencils.

We can say this as : we can
subtract 5 from 20 four times.
Or 5 goes four times in 20.
That means we get 4 when
20 is divided by 5.
We write this operation
as 20 ÷ 5 = 4.

If you know, 20 ÷ 5 = 4,
you can answer that you can
make 4 packs of 5 pencils each
from the given 20 pencils without
actually making the sets.

You have seen the concept of
division as sharing equally
every time in Example 1
and as making sets in Example 2.

Exercise on Division
Word problems

1. How many packs of 2 biscuits
   can we make from 10 biscuits ?
2. How many times can
   we subtract 5 from 15 ?
3. How many times does
   4 go in 16 ?
4. 12 apples are distributed
   among 4 persons. How many apples
   does each person get ?
5. How many pairs can we
   make out of 12 socks ?
6. Each shelf can accomodate
   5 books. How many shelves
   are required to put 25 books.
7. 6 students can sit on a bench.
   How many benches are required
   for 30 students ?
8. 24 students have to stand in 8 rows.
   How many students have to stand
   in each row.
9. We have to make 6 parcels out
   of 18 items. How many items are
   to be put in each parcel ?
10. To how many students can you
    distribute 18 chocolates, if each
    student has to get 2 chocolates ?

For Answers see at the
bottom of the page.

Relation between
multiplication and division

In both examples 1 and 2,
we have seen the concept of
division as repeated subtraction.

We have already seen the concept
of Multiplication
as repeated addition.

Look at the example 1, above. How many
chocolates are there with all the seven
friends ? Each one has 3 chocolates.
So all of them have 3 + 3 + 3 + .....7 times
= 7 times 3 = 7 x 3 = 21.

We already have 21 ÷ 7 = 3.

See the link between the two statements.
If 21 ÷ 7 = 3, then 7 x 3 = 21.
Or if 7 x 3 = 21, then 21 ÷ 7 = 3.

So finding 21 ÷ 7 is nothing
but finding a number which when
multiplied by 7 gives 21.
Or how many times 7 gives 21.

To answer, how many times 7 gives 21, you
need to know the 7 times table from the
Multiplication Tables.

Similarly, in example 2 above, how many
pencils are there in all the four sets.
There are 5 + 5 + ... 4 times
= 4 times 5 = 4 x 5 = 5 x 4 = 20.

But, 20 ÷ 5 = 4.

Thus finding 20 ÷ 5 is
nothing but finding a number
which when multiplied by 5 gives 20.
Or how many times 5 gives 20.

To answer, how many times
5 gives 20, you need to know
the 5 times table from the
Multiplication Tables.

Thus, to solve the division problems,
you need to know the Multiplication Tables.

So study the
Multiplication Tables,
if you have not already done so,
and then go to
Solving Division problems
using Multiplication Tables.

Other Topics of Division

We study Long Division in
the following four Links.

Introduction.

Problems.

More Problems.

by Two or more digit numbers.

Dividing Fractions.

Dividing Decimals.

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Answers to Exercise
on Word Problems

1. 5
2. 3
3. 4
4. 3
5. 6
6. 5
7. 5
8. 3
9. 3
10. 9