We can inculcate a sense of humor and curiosity
in the young miinds by showing novel ideas and concepts. Incidentally
even at an early age the student will develop a sort of fascination
for numbers and he will find enjoyment, amusement and recreation
in solving problems. Is not what every parent's dream? The student
will develop positive initerest in mathematics which will stay with
him for the rest of his life. Instead of coming out of the class
with tears in their eyes, there will be all smiles. Mathematics
will be a fun class. This goal can be achieved through recreational
methods of teaching mathematics.
Nepier Multiplications |
Any number of digits multiplications
can be done by using this system While taking the products
corresponding to the first row and the last column, we write
tens value on the upper side of the diagonal and write the
units place in the lower side of the diagonal. Without using
the logarithms we can do bigger mutiliplications also with
this system. |
 |
| Step 1: |
From the first row and the last column choose
the corresponding squares and write them side by side |
| Step 2: |
Add the digits diagonally from right to left from bottom. |
| Example 1: For 23 x 45 |
 |
Units = 5 |
| Tens = 0 + 1 + 2 =3 |
| Hundreds = 1 + 8 + 1 = 10, carry 1. |
| Thousands = 1 + 0 = 1 |
| Hence 23 x 45 = 1035 |
| |
|
|
| Example 2: For 698 x 47 |
 |
Units = 6 |
| Tens = 3 + 5 + 2 = 10, carry 1 |
| Hundreds = 1 + 2 + 6 + 6 = 18, carry 1 |
| Thousands = 1 + 4 + 4 + 3 = 12 |
| Hence 698 x 47 = 32806 |
| |
|
|
| Example 3: For 786 x 594 |
 |
Units = 4 |
| Tens = 2 + 2 + 4 = 8 |
| Hundreds = 8 + 3 + 2 + 5 + 0 = 18, carry 1 |
| Thousands = 1 + 2 + 3 + 7 + 3 = 16, carry 1 |
| Hundred Thousands = 1 + 3 = 4 |
| Hence 786 x 594 = 466,884 |
| |
|
|
| ^ top |
Multiplications with twice of the numbers
If we know how to twice the numbers, we can find the products
without doing multiplications |
| Step 1: |
Write the twice of the numbers starting from 1 on the left
side |
| Step 2: |
Write the twice of the multiplier on the right side |
| |
Example 1: For 16 x 48 |
| |
| 1 |
|
48 |
| 2 |
|
96 |
| 4 |
|
192 |
| 8 |
|
384 |
| 16 |
 |
768 |
Hence 16 x 48 = 768 |
| |
Example 2: For 35 x 56 |
| |
| 1 |
|
56 |
| 2 |
|
112 |
| 4 |
|
224 |
| 8 |
|
448 |
| 16 |
|
896 |
| 32 |
|
1792 |
Since 35 = 32 + 2 + 1, add the numbers opposite to 32, 2 and
1 and take it as the number.
Hence 35 x 56 = 1792 + 112 + 56 = 1960 |
| |
^ top |
Multiplications with half and twice of the numbers
If we know how to write half of the numbers and how to write
twice of the numbers we can do all multiplications. |
| Step 1: |
Write the multiplicand on the left side and the multiplier
on the right side |
| Step 2: |
Take half of the left hand numbers till you arrive at 1, leaving
the remainders if any |
| Step 3: |
Take the twice of the right hand numbers and write them opposite
to the left hand numbers |
| Step 4: |
Add the numbers opposite to the odd numbers of the left hand
side and take it as the answer |
| |
Example 1: For 16 x 18 |
| |
| 16 |
|
18 |
| 8 |
|
36 |
| 4 |
|
72 |
| 2 |
|
144 |
| 1 |
|
288 |
On the left side odd number is 1.
Hence 16 x 18 = 288 |
| |
Example 2: For 24 x 52 |
| |
| 24 |
|
52 |
| 12 |
|
104 |
| 6 |
|
208 |
| 3 |
|
416 |
| 1 |
|
832 |
On the left side odd number are 1 and 3.
Hence 24 x 52 = 416 + 832 = 1248 |
| |
^ top |
|
Multiplications with the reverse of the second number
|
| |
Product of two digit numbers |
| Step 1: |
Write the multiplicand at three different places as shown
below |
| Step 2: |
Write the multiplier in the reverse order on a pience of paper
and place it below the first number as shown below at three
stages |
| Step 3: |
Find the products of the opposite numbers and find the sum |
| |
Example 1: For 21 x
32 |
|
Write 32 as 23 on a piece of paper and
place it below the first number as shown below. |
| |
2 |
1 |
| |
x |
|
| 2 |
3 |
|
|
| |
6 |
|
|
| 2 |
1 |
| x |
x |
| 2 |
3 |
|
| 4 + 3 = 11 |
|
| 2 |
1 |
|
| |
x |
|
| |
2 |
3 |
|
| |
2 |
|
|
| Hence 21 x 32 = 672 |
| |
EXAMPLE 2: For 321 x 321 |
|
| |
4 |
1 |
| |
x |
|
| 1 |
4 |
|
|
| |
16 |
|
|
| 4 |
1 |
| x |
x |
| 1 |
4 |
|
| 4 + 4 = 8 |
|
| 4 |
1 |
|
| |
x |
|
| |
1 |
4 |
|
| |
1 |
|
|
| Hence 41 x 41 = 1681 |
|
| |
^ top |
|
Product of three digit numbers
|
| Step 1: |
Write the multiplicand at five different places as shown below |
| Step 2: |
Write the multiplier in the reverse order on a piece of paper
and place it below the first number as shown below at five stages |
| Step 3: |
Find the products of the opposite numbers and find the sum |
|
| ^ top |
play for yourself
