LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

RULES FOR FUNDAMENTAL OPERATION

__RULES & EXAMPLES __

**Properties
Of Addition**** – ( If, x & y are whole numbers then x + y is a whole
number.)**

**Closure property –
The sum of any two whole number should be as a whole number **

__Example – __

**1) 12 + 25 =
37, whole number**

**2) 48 + 120 =
168, whole number**

**3) 124 + 237
= 361, whole number**

**4) 1248 + 3045
= 4293, whole number**

**Commutative
property**** – ( If, x & y are whole numbers then x + y = y + x
)**

**Sum of two whole
number remains the same irrespective of the order in which we add them and the result will be the same on each case -**

__Example –__

**1) 15 + 30 = 30
+ 15**

**2) 100 + 221 = 221 +
100**

**3) 222 + 111 =
111 + 222**

**Associative
property**** – [ If, x, y & z are whole numbers then ( x + y ) + z = x
+ ( y + z ) = x + y + z ]**

**If we would like to
find the sum of three whole numbers then, then first we would like to add any two
of the number then whatever the result will be obtained that will be added with the 3 ^{rd}
number.**

__Example – __

**1) 25 + 50 +75 = ( 25
+ 50 ) + 75 = 25 + (50 + 75 )**

** => 75 + 75 = 25 + 125 =
150 ( from both side obtained result are same )**

**2) 125 + 110 +
150 = ( 125 + 110 ) + 150 = 125 + ( 110 + 150 ) **

** => 235 +
150 = 125 + 260 = 385 ( from both side obtained result are same )**

**3) 200 + 1000 +
50 = ( 200 + 1000 ) + 50 = 200 + ( 1000 + 50 )**

** => 1200 + 50 = 200 + 1050 = 1250 ( from both side
obtained result are same )**

**4) 220 + 100 +
150 + 30 = ( 220 + 100 ) + ( 150 + 30 ) **

** = ( 220 + 30 ) + ( 100 + 150 )**

** => 320 + 180 = 250 + 250 =
500 ( from both side obtained result are same )**

**Properties
of Multiplication****
– [ If, a & b are whole numbers then the result of
a X b is also a whole number.]**

**The product of any
two whole number would be only a whole number**

__Example
– __

**1) 12 X 10 =
120**

**2) 1080 X 100 =
108000**

**3) 12 X 15 =
180**

**Commutative
property**** – [ If, a & b are whole numbers then a X b = b X a
]**

**The product of two
whole numbers remains the same irrespective of the order in which we multiply
them.**

__Examples
–__

**1) 12 X 15 = 15
X 12 ; 12 x 15 = 180 and 15 X 12 = 180 ; so, 12 X
15 = 15 X 12 = 180 ; **

**So, 12 X 15 =
15 X 12 (Proven)**

**2) 20 X 14 = 14
X 20 ; 20 X 14 = 280 and 14 X 20 = 280 ; So, 20 X 14 =
14 X 20 = 280 ;**

**So, 20 X 14 =
14 X 20 (Proven)**

**3) 30 X 17 = 17
X 30 ; 30 X 17 = 510 and 17 X 30 = 510 ;
So, 30 X 17 = 17 X 30 = 510 ;**

**So, 30 X 17 =
17 X 30 (Proven)**

**Associative
Property**** – [ If, a, b & c are whole numbers then a X ( b X c ) =
(a X b ) X c = a X b X c ]**

**To find the product
of three whole numbers we first multiply any of the two given number, and then
the obtained product will be multiplied by 3 ^{rd} number, result always
would be the same and not matters which first two numbers we have multiply 1^{st}
and which 3^{rd} number multiply with an obtained product of any of first
two numbers.**

__Example
– __

**1)
10 X 20 X 15 = ?**

**Ans.) 10 X 20 X
15 = ( 10 X 20 ) X 15 = 3000, by associative property**

**Changing arrangement,
10 X (20 X 15 ) = 3000 , by commutative property**

**( 10 X 20 ) X 15 = 10
X (20 X 15 ) = 3000**

**2)
30 X 20 X 45 = ?**

**Ans.) 30 X 20 X
45 = ( 30 X 20 ) X 45 = 27000, by associative property**

**Changing arrangement,
30 X (20 X 45 ) = 27000 , by commutative property**

**( 30 X 20 ) X 45 = 30
X (20 X 45 ) = 27000.**

**3)
25 X 20 X 10 = ?**

**25 X 20 X 10 = ( 25 X
20 ) X 10 = 5000, by associative property**

**Changing arrangement,
25 X (20 X 10 ) = 5000, by commutative property**

**( 25 X 20 ) X 10 = 25
X (20 X 10 ) = 5000.**

**Distributive
Property**** – [ If, a, b & c are whole numbers then a X ( b + c
) = ( a X b ) + ( a X c ) ]**

**For any whole number
a, a X 1 = 1 X a = a**

**Example
–**

**1) 10 X ( 20 +
15 ) = ( 10 X 20 ) + ( 10 X 15 ) = 200 + 150 = 350**

**In other way 10 X (
20 + 15 ) = 10 X 35 = 350 **

**Operation
Of Division**** – [ Dividend = Divisor X Quotient + Remainder ]**

** As we all know
that, if we divide any whole number as a ‘Dividend’ by another whole number as
a ‘Divisor’, then the obtained result is considered as ‘Quotient’ and as remaining
number would be considered as ‘Remainder’. **

**DIVISOR
) DIVIDEND (
QUOTIENT
**

** DIVIDEND**

**
------------------- = QUOTIENT **

**
DIVISOR**

** **

**If there are
remainder, then the equation should be **

**DIVIDEND
= DIVISOR X QUOTIENT + REMINDER**

** **

**DIVISOR
) DIVIDEND (
QUOTIENT
**

**
------------------
**

**
REMINDER
**

**If there 11 is
dividend, 3 is a divisor and 3 is a quotient then remainder would be 2**

**As per the
formula, Dividend = Divisor X Quotient +
Remainder **

**
= 3 X 3 + 2 = 11 (Dividend)**

**Example
– 1**

**1)
Divide 175 by 12 and verify the division algorithm**

**
Ans.)
As per the given condition,**

**As per the formula,**

**Dividend = Divisor X Quotient + Remainder
**

**= 12 X 14 + 7 = 168 + 7 = 175**

**Example – 2**

**2) Find the largest four-digit number which is exactly divisible by 25.**

**Ans.) The largest four-digit number is 9999.**

**Here we can find
that, 25 is divisor, 9999 is Dividend, 399 is Quotient, and 24 is
remainder.**

**So as per requirement
to find four-digit largest number we have to deduct remainder from 9999,**

**Hence the required
number is **

**= 9999 – 24 = 9975**

**Example– 3**

**Find the smallest five digit number which is exactly divisible by 15.**

**Ans.) Five digit smallest number is 10000**

**Here we can find
that, 15 is the divisor, 10000 is Dividend, 666 is Quotient, and 10 is
remainder.**

**Required number must
be greater than 10000, So as per requirement to find five-digit smallest number
first I have to deduct remainder 10 from divisor 15 ; 15 – 10 = 5**

**Thus the required
number = 10000 + 5 = 10005 **

**So, the five-digit
smallest number is 10005 which is divisible by 15.**