Here in
this post I am going to show you some tricks to practice to fasten you
calculation mainly based on multiplications. This will help you to face any
problems with full confidence and solve calculation process mentally or with a
little calculations. The work of shortening the procedure is to be done by the
student with the help of practice and also depending on his calibre and speed as,
in this
post I am going to elaborate each and every concept in very detail manner with
the help of you will be able to understand and solve the problems of this type
self without any help.
Let’s
continue with this chapter............
Type 1st :- Multiplication
of Any natural number by 10 and Powers of 10.
Ø
To
multiply a natural number by 10 suffix it by a zero.
Ø
To multiply a natural number by 100 suffix it
by two zeros.
Ø
To
multiply a natural number by 1000 suffix it by three zeros.
General
Rule :- To multiply a natural number by 10n suffix it by n- zeros.
Examples :-
754 × 10 = 7540.
754 × 100 = 75400.
754 × 1000 = 754000.
Type 2nd :-
Multiplication of Decimal number by 10 and Powers of 10.
Ø
To
multiply a decimal by 10 shift the decimal by 1 place to right.
Ø
To
multiply a decimal by 100 shift the decimal by 2 places to right.
Ø
To
multiply a decimal by 1000 shift the decimal by 3 places to right.
General
Rule :- To multiply a decimal number by 10n shift the decimal by n- places
to right.
Examples :-
3.5482 × 10 = 35.482.
3.5482 × 100 = 354.82.
3.5482 × 1000 = 3548.2.
Type 3rd :-
Multiplication by 5 and Powers of 5.
We know
that 5 × 2 = 10, 25 × 4 = 100, 125 × 8 =
1000, 625 × 16 = 10000
Ø
To
multiply a number by 5 suffix 0 to the number and divide the product by 2.
Ø
To
multiply a number by 25 suffix 2 zeros to the number and divide product by 4.
Ø
To
multiply a number by 125 suffix 3 zeros to the number and divide product by 8.
Ø
To
multiply a number by 625 suffix 4 zeros to the number and divide product by 16.
General
Rule :- To multiply a number by 5n suffix n zeros to the number and
divide by 2n.
Examples :-
240 × 5 = 2400 ÷ 2 =
1200.
240 × 25 = 24000 ÷ 4 =
6000.
256
× 125 = 256000 ÷ 8 = 32000.
128 × 625 = 1280000 ÷ 16
= 80000.
Type 4th :- Multiplication by 9, 99, 999, 9999 etc.
We know
that 9 = (10 – 1), 99 = (100 - 1), 999 = (1000 - 1), 9999 = (10000 - 1) etc.
Let a
number be x.
So, x × 9 = x × (10 - 1) = x × 10 – x
x × 99 = x × (100 - 1) = x × 100 – x
x × 999 = x × (1000 - 1) = x × 1000 – x
x × 9999 = x × (10000 - 1) = x × 10000
– x.
General
Rule :- x × 99.......(n - times)9 = x × {100....(n - times)0 – 1} = x ×
100....(n - times)0 – x.
Examples :-
73 × 9 = 73 × 10 – 73 = 730 – 73 = 657.
56 × 99 = 56 × 100 – 56 =
5600 – 56 = 5544.
94 × 999 = 94 × 1000 – 94
= 94000 – 94 = 93906
513 × 9999 = 513 × 10000
– 513 = 5130000 – 513 = 5129487.
Type 5th :- Single Line
Multiplication (2 – digit Numbers) {a b × c d}
a(tenth place digit) b (unit place digit) × c(tenth
place digit) d(unit place digit).
Box no. 3rd
|
Box no. 2nd
|
Box no. 1st
|
= (Product)
Step 1st :- Find b × d. If it is a one- digit
number write it in box no. 1st. If it is a two – digit number write
its unit digit in box no. 1st and carry over the tenth place digit.
Step 2nd :- Find { a × d + b × c + carried over
if any.}. If it is a one – digit number write it in box no. 2nd. If
it is a two – digit number then write its units digit in box no. 2nd
and carry over the rest.
Step 3rd :- Find {a × c + carried over if
any.}. Write this result in box no. 3rd.
Step 4th :- Read the number so obtained from
left to right. This number is the required product.
Example :-
Find the product of 56 and
23.
Solution
:- 56 × 23
Box no. 3rd
12
|
Box no. 2nd
8
|
Box no. 1st
8
|
= (Product)
Step 1st :- 6 × 3 = 18, we write 8 in box no.
1st and carry over 1.
Step 2nd :- {5 × 3 + 6 × 2 + 1 = 28.}. We
write 8 in box no. 2nd and carry over 2.
Step 3rd :- {5 × 2 + 2 = 12.}. We write 12 in
box no. 3rd.
Step 4th :- The required product 1288.
Example :-
Find the product of 64 and
38.
Solution
:- 64 × 38
Box no. 3rd
24
|
Box no. 2nd
3
|
Box no. 1st
2
|
= (IProduct)
Step 1st :- 4 × 8 = 32, we write 2 in box no.
1st and carry over 3.
Step 2nd :- {6 × 8 + 3 × 4 + 3 = 63.}. We
write 3 in box no. 2nd and carry over 6.
Step 3rd :- {6 × 3 + 6 = 24.}. We write 24 in
box no. 3rd.
Step 4th :- The required product 2432.
Note you may say that this is so
long but dear this is the only way to explain the whole concept of the question
to you now its upto you that how fast and short handedly you can solve these
type of questions)
More types
of questions will be followed soon on this blog........................
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