Understanding Number Systems - 1

 Number Systems is a very Important topic for most competitive exams. This post should help you prepare better for Number System questions.

Important Rules of Numbers

Addition:

1.  Positive Number + Positive number = Positive Number  ( 2 + 3 = 5)
2.  Negative Number + Negative Number = Negative Number  (-2 + -3 = -5)
3.  Positive Number + Negative Number= Positive Number if Positive Number is Larger ( 5 + -3 = 2)
4. Positive number + Negative Number = Negative Number if absolute value of the Negative Number is larger (5 + -7 = -2)

 Subtraction:

1. Positive Number - Positive Number = Positive Number if first number is larger than the second( 3 - 2 = 1)   
2. Positive Number - Positive Number = Negative Number if first number is smaller than the second ( 2 - 3 = -1)   
3. Negative Number - Negative Number = Negative Number if the absolute value of the first is larger than the second ( -5 - (-4) = -1)
4.  Negative Number - Negative Number = Positive Number if the absolute value of the first is smaller than the second  ( -4 - (-5) = 1)
5.  Positive Number - Negative number = Always Positive Number ( 4 - (-5) = 9)
6. Negative Number - Positive Number = Always Negative Number ( -5 - 4 = -9)

Multiplication:

1. Positive Number x Positive = Positive Number ( 2 x 3 = 6)
2. Negative Number x Negative Number = Positive Number(-2 x -3 = +6)
3. Positive Number x Negative Number = Negative Number(2 x -3 = -6)
4. Negative Number x Positive Number = Negative Number (-2 x 3 = -6)

DIvision:

1. Positive Number / Positive = Positive  (6/3 = 2)
2. Negative Number / Negative Number = Positive (-6 / -3 = +2)
3. Positive Number / Negative Number = Negative (6 / -3 = -2)
4. Negative Number / Positive Number = Negative Number (-6 / 3 = -2)

 Types of Numbers:

(A) Rational Numbers: Numbers which can be expressed in the form of p/q; where p and q are both integers and q≠ 0 are called Rational Numbers when expressed in decimal form are either terminating or recurring.
Rational Numbers include all Whole Numbers, Natural Numbers, Integers and Fractions.

(B) Irrational Numbers : An irrational number is that number which gives an approximate number in the form of a fraction or a decimal. That is, the numbers whose decimal forms are non-terminating and non-recurring e.g √3 , Π, etc.

(C)Complex Numbers : The system of real numbers is inadequate as it contains no number whose square is a negative number. So complex numbers or imaginary numbers were employed to find solutions to quadratic equations. The generalized complex number n is of the form n=a ± bi, where a and b are any real number and i= √-1 (i² =-1), is known as the imaginary unit, a is the real part of n and b is its imaginary number where as if b=0, then the number is purely a real number.

Odd Numbers : Numbers which are not divisible by 2( 1,3,5,7 etc.)
Even Numbers : Numbers which are  divisible by 2( 2,4,6,8 etc.)

Simple Rules on Odd and Even Numbers:

1. Odd number + Odd Number = Even Number ( 5 + 3 = 8)
2. Even Number + Even Number = Even Number ( 4 + 4 =8)
3. Odd Number + Even Number = Odd number ( 5 + 4 = 9)
4. Even Number + Odd Number = Odd number (4 + 5 = 9)
5. Even number - Even number = Even number ( 8 - 4 = 4)
6. Odd number - Odd number = Even number ( 5 - 3 = 2)
7. Odd number - Even number = Odd number  (5 - 4 = 1)
8. Even number - Odd number = Odd number  (4 - 3 = 1)
9. Odd number x Odd number = Odd number ( 7 x 3 = 21)
10. Even Number x Even number = Even Number (6 x 4 = 24)
11. Odd Number x even number = Even Number (5 x 4 = 20)

Note:  Division Properties cannot be predicted unless the numbers are known. For example, 20/2 = 10 (even/even = even), while 10/2 = 5 (even/even = odd).


Solve Yourself Now: (Post your answer as comments and we will verify if you are answers are correct! Answers will also be available on our next post.)

1. Simplify : 7691 - (58+374+1693+2085) [Easy]
2. What happens when you multiply 3 even numbers? 2 even numbers and an odd number? 2 odd numbers and an even number? and 3 odd numbers? [Medium]
3. What happens when you multiply 'N' even numbers? and 'N' odd numbers? [Hard]
4. Ram multiplied 4 consecutive natural numbers and said the product was odd. Is Ram telling the truth? [Medium]



In the next post Number Systems - 2, we will explore Divisibility of Numbers, Prime Numbers, Power Cycle and Remainder Theorem.