The following are the operations performed on numbers. Different types of operations are used to deal with different situations hence each operation has it own importance.
When two or more numbers are combined together then it is called addition. Addition is denoted by ‘+’ symbol
Example: 20 + 25 + 30=75
When one or more numbers are taken out from a larger number then it is called subtraction. Subtraction is denoted by ‘-’ symbol.
Example: 100-30-20=50
When ‘a’ is multiplied by ‘b’, then ‘a’ is added ‘b’ times or ‘b’ is added ‘a’ times. It is denoted by ‘×’.
Example: If a= 4, b=8, then
4 × 8 = 32 or (4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32)
Here, ’a’ is added ‘b’ times or in other words 4 is added 8 times.
When D and d are two numbers, then D/d is called the operation of division where D is the dividend and d is the divisor. A number which tells how many times a divisor (d) exists in dividend D is called quotient Q.
If dividend D is not a multiple of divisor d, then D is not exactly divisible by d and in this case remainder R is obtained. Let us see the following operation of division:
Let D=16, d=5
Then,
Here,
3 is Quotient (Q)
5 is Divisor (d)
1 is Remainder (R)
Hence, 16 = 5 × 3 + 1
In such cases, n zeros are put extreme right end of Y to make a new number X and then Y is subtracted from this new number to get the result. (X-Y) is the result of multiplication. (here, number of zeros equal to number of 9s in (10n -1))
Example: Multiply 1528 with 99.
Here,
Y = 1528
(10n -1) = (102 -1) = 99 so n=2
So 2 zeros are put at extreme right of Y to get X
X = 152800
According to the trick,
152800 - 1528
(X-Y) =151272
In such cases, n zeros are put at the extreme right end of Y to make a new number X and then Y is added to this new number to get the result. (X+Y) is the result of multiplication.
Example 2: Multiply 5362 with 101.
Here,
Y = 5362
(10n +1) = (102 +1) =101 so n=2
So 2 zeros are put at extreme right of Y to get X
According to the trick,
536200 + 5362
(X+Y) = 541562
In such cases, n zeros are put at the extreme right end of Y to get a new number X and then X is divided by 2n to find the required result of multiplication.
Example: Find the value of 8372 × 25
Here,
Y=8372,
5n = 25 = 52 so n = 2
According to the trick,
In such cases, number coming before 5, say n, is multiplied with n+1 and 25 is put at the right end of the result obtained from n (n+1).
Example: Find the square of 45
Here, n=4
According to the trick,
n (n+1) =4 (4+1) =20
Hence required square = 2025
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