LEARN MULTIPLICATION - STARTING WITH MULTIPLICATION BY SINGLE DIGIT, EXAMPLES

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Learn Multiplication
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Please study
learning multiplication table,
if you have not already done so.

There, We explained the need of
remembering the products of
single digit numbers and guide
you to the tricks of how to
remember.

Multiplication of a two digit
number by a single digit

Knowledge of Multiplication Tables
upto 9 times 9 is a prerequisite
here. Learn them thouroughly,
if you have not already done so.

Now Look at the problems 4, 5,
9 and 10 of Exercise 1A of
Multiplication as repeated addition
where we have to find 4 x 12,
6 x 20, 2 x 30, 4 x 15.

Also look at the problems 9 and
10 of Exercise 1B of
Multiplication as repeated addition
where we have to find
4 x 11 and 5 x 13.

In all these problems, we have to
find the multiplication of two digit
number with a single digit number.





Example 1 :
Learn Multiplication

Let us find 4 x 12.

From the knowledge of
decimal number system ,
we know, 12 has 1 ten and 2 ones.
i.e. 12 = 2 x 1 + 1 x 10 = 2 + 10.

So, 4 x 12 = 4(12) = 4(2 + 10)
= 4 x 2 + 4 x 10 = 8 + 40 = 48.

We will show it in vertical
presentation as follows.

          12
           4
          ---
           8
          40
          ---
          48
          ---

Or more simply

          12
           4
          ---
           8
          4
          ---
          48
          ---

The second vertical presentation
above is simple way of presenting
process of multiplication.

Note that when tens' place digit
is multiplied, we presented the
result in tens' place.

If the result has more than
one digit, we place the result
starting from tens' place
and proceeding to the left,
as seen in the next example.

While adding, 8 in units' place
is descended down in units'
place and 4 in tens' place is
descended down in tens' place.

Thus the result is 48.

Example 2 :
Learn Multiplication

Now, we find 6 x 20 by presenting
the process directly in the simple
vertical presentation explained above.

           20
            6
          ---
            0
           12
          ---
          120
          ---

Here 0 x 6 gave 0 and we placed it
in ones' place. 2 x 6 gave 12 and
we placed it starting from tens'
place and proceeding to the left.

While adding, we descend the 0 in
units' place, 2 in tens' place and
1 in hundreds' place.

Thus the result is 120.

In fact, to find 20 x 6, it is
enough to find 2 x 6 and then put
0 to the right of the result.
2 x 6 = 12. Putting 0 to the right,
the answer is 120 same as above.

Example 3 :
Learn Multiplication

2 x 30 is simple to understand
and we present it below.

          30
           2
          ---
           0
           6
          ---
          60
          ---

So 2 x 30 = 60. Ans.

In fact, to find 2 x 30, it is
enough to find 2 x 3 and then
put 0 to the right of the result.
2 x 3 = 6. Putting 0 to the right,
the answer is 60, same as above.

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Example 4 : To Learn Multiplication

Now let us find 4 x 15.

          15
           4
          ---
          2
           0
          4
          ---
          60
          ---

Here, multiplication of units' place
digits (5 x 4) gave a two digit
number (20). We wrote 0 in units
place and 2 ( small 2 indicating
that it is carried over from the
result of units' place) in tens' place.

1 x 4 gave 4 and we wrote
it in tens' place.

While adding, we descend 0 in units'
place and add small 2 and 4 in tens'
place to get 6 in tens' place.

Thus 15 x 4 = 60.

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Example 5 : To Learn Multiplication

4 x 11 is simple to understand
and we present it below.

          11
           4
          ---
           4
          4
          ---
          44
          ---

So 4 x 11 = 44. Ans.

Example 6 : To Learn Multiplication

Now let us find 5 x 13.

          13
           5
          ---
          1
           5
          5
          ---
          65
          ---

The explanation is similar
to the one 4 x 15 above.

Thus 5 x 13 = 65.

Thus, we can multiply any two digit
number with a single digit number.

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Further Topics to
Learn Multiplication

The following Links take you to
different topics to learn Multiplication.

Additional problems on
multiplying by single digit number

multiplying by Two digit numbers,

Multiplying Two Digit Numbers
easily using Vedic math

multiplying by Three
or more digit numbers,

Multiplying Three Digit Numbers
easily using Vedic math

Multiplying Four Digit Numbers
easily using Vedic math

multiplication word problems.

multiplying fractions,

multiplying decimals.

Learn Multiplication from the above Links.

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