Current Affairs 6th Class

NUMBER SYSTEM   FUNDAMENTALS                     
  •                   Digits: for representing any number we use ten symbols
0, 1, 2, 3,4,5,6,7,8,9 All the other numbers are written using 10 symbols. Example: 2, 3, 4, 5 etc.
  •                  Numeral: A group of digits representing a number is called a numeral.
Example: 243, 67842, 546380, etc. are numerals.
  •                  Notation: The system of expressing a number in figure or digits is called notation.
  •                  Numeration: The logic of representing a number in words is called numeration.
                                                 \[\Rightarrow \]    Let us see the chart of Indian system and understand about Indian system.
Periods Crores Lakhs more...
FRACTIONS AND DECIMALS   FUNDAMENTALS Natural numbers: All counting numbers are called natural numbers.
  •                   It is denoted by N.
  •                  \[N=\left\{ 1,2,3,4,\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \right\}\]
Whole number: Natural numbers together with zero are called whole numbers.
  •                  It is denoted by W.
  •                  \[~W=\left\{ 0,1,2,3,\_\_\_\_\_\_\_\_\_\_ \right\}\]
  •                 Fraction: A part of whole is called fraction.
or A number written in the form \[\frac{x}{y},\] where \[x\] and \[y\] are whole numbers and \[y\ne 0\] is called fraction,
  •                  \[\frac{x\to \text{Numerator}}{y\to \text{Denominator}}\]
  Types of Fraction                                      
  •                  Decimal fraction: A fraction whose denominator is 10, 100, 1000 etc.......is called a decimal fraction.
Example: \[\frac{1}{10},\frac{2}{100},\frac{5}{1000}\]etc...
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FACTORS AND MULTIPLES       FACTOR:
  •             One Number is said to be a factor of another when it divides the other exactly.
  •       If a number 'x' divides another number 'y' exactly, then we say that 'x' is a factor of 'y'.
  Example:                16 = 1, 2, 4, 8, 16., so, 1, 2, 4, 8 and 16 are factors of 16. 25 = 1, 5, 25. so, 1,5 and 25 are factors of 25.   MULTIPLE:
  •            A multiple of a number is a number obtained by multiplying it by integers.
or
  •           If a number 'x' divides another number 'y' exactly, then we say that 'y' is a multiple of x.
  Example:                5=5, 10, 15, 20.........and so on \[5\times 1=5,\,\,\,5\times 2=10,5\times 3=15,5\times 4=20....................\]Thus,           5, 10, 15, 20.....................are multiple of 5.   Properties of factors and multiples
  •            Factors of a number is finite.
  •            Multiples of a number is infinite.
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ALGEBRA   ALGEBRA The part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.   Introduction to Algebra
  •                   Variable: A letter symbol which can take various numerical values is called variable or literal.
Example: \[x,\,\,y,\,\,z\]etc.  
  •                   Constant: A symbol which can take a fixed numerical value is called a constant.
Example: \[-1,\,\,\frac{1}{2},\,\,2,\,\,4,\,\,3,\,\,5\]etc.  
  •                   Term: Numericals or literals or their combinations by operation of multiplication are called terms.
Example: \[5{{x}^{2}},\,\,7x,\,\,\frac{x}{7},\,\,\frac{{{y}^{2}}}{9},\,\,\frac{5}{2}x\]etc.  
  •                   Constant Term:  A term of an expression having no literal is called a constant term.
Example: \[4,\,\,\frac{-1}{2},\,\,\frac{7}{4}\]etc.  
  •                Algebraic expression: A combination of constant and variable connected by mathematical operations \[(+,\,\,-,\,\,\times ,\,\,\div )\] is called an algebraic expression.
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ALGEBRAIC EXPRESSIONS   ALGEBRAIC EXPRESSION
\[2x\] Expression
\[2x+y\] Binomial
\[2x=14\] Equation
 
  •                  Variable: A symbol which takes various values is known as a variable. Normally it is denoted by x, y, z etc.
  •                   Algebraic expression: A combination of constants and variables connected by some or all of the four fundamental operations \[+,\] \[-,\]\[\times \]and \[\div \] is called an algebraic expression.
e.g., \[-5x+6\]is an algebraic expression.
  •                   Here \[-5\]is the coefficient of the variable 'x' and 6 is the constant.
  Various types of algebraic expression: (a) Monomial: An algebraic expression which contains only one term, is called as monomial. Thus, \[2x,\] \[3y,\] \[5xy,\] \[6a{{b}^{2}},\] \[-11\] etc. are called monomials. more...

RATIO, PROPORTION AND UNITARY METHOD   RATIO The comparison of two quantity of same kind by division is called ratio.   Example: Ratio between Rs. 30 and Rs. 50, but there can be no ratio between Rs. 30 and 50 apples, form of ratio \[=x:y\] \[x\to \]antecedent \[y\to \]consequent                                                              
  •           B The ratio of \[x\]to \[y\]
  •           B \[x\]is to \[y\]
  •           \[x:y\]
  •           B \[x\]and \[y\] are called terms of ratio.
  Types of Ratio:
  •                Compound Ratio: Ratio is compound when antecedents are multiplied by respective antecedents and consequents are multiplied by respective consequents.
Example: \[a:b,\,\,c:d,\,\,e:f,\]then compound ratio is,\[\frac{a\times c\times e}{b\times d\times f}\]  
  •                   Duplicate Ratio: If \[x:y\] is a ratio, then\[{{x}^{2}}:{{y}^{2}}\]is duplicate ratio.
Example: Find duplicate ratio of\[5:7.\] more...

EXPONENT AND POWERS   POWER \[\frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m}}-n\] \[{{5}^{3}}\div {{5}^{2}}={{5}^{3}}-2\]   FUNDAMENTALS
  •                   Exponential form is nothing but repeated multiplication.
There are two part of an exponent. Exponent\[\to \]base, Power/ Index                                                             Example:            
  •                   Base denotes the number to be multiplied and the power denotes the number of times the base is to be multiplied.
\[a\times a\times a={{a}^{3}}\](read as 'a' cubed or 'a' raised to the power 3) \[a\times a\times a\times a\times a\times a={{a}^{6}}\](read as 'a raised to the power 6 or 6th power of a)             ................................................................................... \[a\times a\times a\].......(n factors) \[={{a}^{n}}\] (read as 'a' raise to the power n or nth power of a)
  •                    (a) When a negative number is raised to an even power the value is always positive.
e.g., \[{{\left( -5 \right)}^{6}}=\left( -5 \right)\times \left( -5 \right)\times \left( -5 \right)\times \left( -5 \right)\times \left( -5 \right)\times \left( -5 \right)\]\[=15625\] (b) When a negative number is raised to an odd power, the value is always negative. e.g., \[{{\left( -3 \right)}^{5}}=\left( -3 \right)\times \left( -3 \right)\times \left( -3 \right)\times \left( -3 \right)\times \left( -3 \right)=\left( -243 \right)\] Note:    (a) \[{{(-1)}^{odd\,\,number}}=-1\] (b) \[{{(-1)}^{even\,\,number}}=+1\]   more...

GEOMETRY   GEOMETRY Geometry is derived from two greek words "Geo" means "Earth" metron means "Measurement". That means measurement of Earth is called geometry.               Basics terms of geometry
  •                  There are three basics undefined terms of geometry.
(i) Point       (ii) Line       (iii) Plane   Point: Point is a mark of position, it is made by sharp tip of pen, pencil and nail.
  •           It is denoted by capital letter.
  •           It is represented by
  •           A point has no length, no breadth and no thickness.
 
  •                   Line segment: The distance between two points in a same plane is called a line segment.
  •           It is denoted by\[\overline{AB}\]. It is measured in 'cm' or 'inch'.
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MENSURATION BASICS   MENSURATION
  •                    The branch of geometry that deals with the measurement of length, area, or volume.
  PERIMETER
  •                   The length of the sides enclosing the figure is called its perimeter.
  AREA
  •                   The amount of space in the boundary of plane figure.
  •                    Unit of area is square unit.
  Some important formula of Mensuration SQUARE:-                        
  •                     Perimeter of square\[=4\times side=4a\]
  •                    Area of square\[={{(side)}^{2}}={{(a)}^{2}}\]
  •                    Diagonal of square \[=\sqrt{2}\times \] side
  RECTANGLE                         more...

MENTAL ABILITY   FUNDAMENTALS Mental Ability: The power to learn or retain knowledge, in law, the ability to understand the fact and significance of your behavior.
  •                      Mental ability develop logical thinking among students.
  •                      Mental ability is based on some concepts.
  Series completion                                        
  •                      Number series
  •                     Alphabet series
 
  •                Number Series: The three or more numbers having a sequence of pattern is given. The numbers follow a certain rule which relates the consecutive terms. Students should be able to recognize the rule or pattern. This will be help them to find the next term or number.
  Look at the example given below 1.            Series of odd number 1, 3, 5, 7, 9, ___________ Ans.:    Next number is 11.   2.            Series of even number. more...


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