# Current Affairs 6th Class

#### Notes - Exponent and Powers

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...

#### Ratio, Proportion & Unitary Method

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...

#### Algebraic Expressions

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...

#### Algebra

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.
more...

#### Factors & Multiples

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.
• more...

#### Fractions and Decimals

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...
• more...

#### Number System

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...

#### Symmetry

SYMMETRY   SYMMETRY Symmetry is when something is made up of two parts that are exactly the same and they are facing each other. Line Symmetry
•                   A line of symmetry divides a figure into two mirror - image halves.
•                  The line of Symmetry is imaginary line where you could fold the image and have both halves match exactly.
Example: •                    Letters and line symmetry •                   There are some letters which do not have any line symmetry. •                   Rhombus:
•                  Two lines of symmetry AC and BD • more...

#### Data Handling

DATA HANDLING   SYMMETRY
•                   The word 'data' means information. Its exact dictionary meaning is given facts.
•                   Statistical data are of two types (i) primary (ii) secondary.
•                   The number of times an observation occurs in the given data is called the frequency of the observation.
•                   There are two types of frequency distribution.
•          Discrete frequency distribution.
•          Continuous frequency distribution.

•                     In a discrete frequency distribution the cumulative frequency of a particular value of the variable is the total of all the frequencies of the values of the variable which are less than or equal to the particular value.
•               A table which displays the manner in which cumulative frequencies are distributed over various classes is called a cumulative frequency distribution or cumulative frequency table.
•            Bar graphs
• more...

#### Practical Geometry

PRACTICAL GEOMETRY   FUNDAMENTALS
•                    A ruler protractor and compass are used for constructions.
•                 Given a line 1 and a point P not on it, a line parallel to 1 can be drawn through the point P, using the idea of 'equal alternate angles' or 'equal corresponding angles'.
•                   The sum of lengths of any two sides of a triangle is greater than its third side.
•                   The difference of lengths of any two sides of a triangle is lesser than its third side.
•                   The sum of angles in a triangle is $180{}^\circ .$
•                   The following cases of congruence of triangles, help us construct the triangle.
(a) S.S.S: A triangle can be drawn given the lengths of its three sides. (b) S.A.S: A triangle can be drawn given the lengths of any two sides and the measure of the angle between them. (c) A.S.A: A triangle can be drawn given the measures of two angles and the length of the side included between them. (d) R.H.S: A right angled triangle can be drawn given the length of hypotenuse and the length of one of its legs.   more...

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