Current Affairs 5th Class

  MENTAL ABILITY   FUNDAMENTALS This chapter is based on four distinct concepts:   (a) Mathematical Series: Ø     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 help them predict the next term or number. ­ Rule/Pattern may exist in the following ways: (i) Series of odd number: Example: 1, 3, 5, 7, ...... Ans.     Next number will be 9 (ii) Series of even numbers: Example: 2, 4, 6, ........ Ans.     Next number will be 8. (iii) Series of prime numbers: Example: 2, 3, 5, 7, 11, 13....... Ans.     Next number will be 17 (iv) Series of square of natural numbers: Example: 1,4,9, 16, ....... Ans.     Next number will be 25 (v) Series of squares of even natural numbers: Example: 4, 16, 36, 64 Ans.     Next numbers will be 100 (vi) Series of cubes of natural numbers Example: 1, 8, 27....... Ans.     Next number will be 64   Solved Examples 1.            Find the number to fill in the blank: 48, 31, 18, ____? Ans.     Sequence comprises subtraction of prime numbers: \[\therefore \]It is 7 2.            Find 86, 61, 45,......? \[\therefore \]It is 36 Ans.     Square comprises subtraction of squares of natural numbers as follows: Therefore, you should have the following at finger tips: 1.     Sequence of prime numbers from 1 to 100 i.e., 2, 3, 5, 7, 11, 13,........97 2.     Sequence of squares of natural numbers from 1 to 20 i.e., 1,4, 9................361,400 3.     Sequence of cubes of natural numbers from 1 to 20 i.e., 1, 8, 27......... ..6859, 8000   Alphabetic Series Ø     An arranged sequence of letters which follows a particular rule/pattern is called an alphabetical series. Here again, the pattern of alphabets or distance between alphabets needs to be recognized. Example: The three blanks in the sequence can be given by (if the last blank contains ?G') S, ____; M, ____; G, _____; A, ____ G ____ (a) TPV                         (b) YSM                        (c) YSR                         (d) None Sol.   Now let us understand the pattern Similarity the gaps can be filled up more...

DATA HANDLING   FUNDAMENTALS Data handling can be done in different ways and one such way is representation of raw data in pictorial form. Such as bar diagram, histogram, pie-chart and line graph.   Bar diagram Bar diagrams is one of the simplest and most common graph used to represent data. In bar diagram usually bars of uniform width are drawn with equal spacing between them on one axis (x-axis) depicting the variables. The value of the variables is shown on the other axis (y-axis) and the height of the bars depends on the value of the variables. This is a form of representation like the bar graph out is used tor continuous class interval. It consists of continuous bars drawn adjacent to each other.   Pie Chart: A pie-chart is a pictorial representation of the numerical data by sectors of the circle. The area of each sector is proportional to the magnitude of the data represented by the sector.   Line Graph: Line graph is another method of representation of the numerical data. In line graph the collected data are represented by specific points joined together by straight lines. The points are plotted on two dimensional plane one on the horizontal axis and the other on the vertical axis.    

  MEASUREMENT               FUNDAMENTALS ü     The standard unit of length is meter and it is denoted by m.  ü     The other units of length are Millimeter (mm). Centimeter (cm) and Decimeter (dcm) which are lower units of length. Whereas Decameter (dm), Hectometer (hm), Kilometer are higher units.                                                                    Measurement units of length from lower level to higher level
Lower Units Base Unit Higher Units
Unit Millimeter (mm) Centimeter (cm) Decimeter (dam) Meter (m) Decameter (dam) Hectometer (hm) Kilometer (km)
Value \[\frac{1}{1000}\] (0.001 m) \[\frac{1}{100}m\] (0.01 m) \[\frac{1}{10}m\] (0.1 m) \[1\] \[10\,\,m\] \[100\,\,m\] \[1000\,\,m\]
Thus, we have, 1 mm = 0.001m, 1 cm = 0.01m, 1 dm = 0.1 more...

  MENSURATION   FUNDAMENTALS                              ü     Perimeter, the length of the sides enclosing the figure is called its perimeter. Perimeter of square\[=4\times \,\,side=4a\]   Perimeter of rectangle = 2 (length + breadth)\[=2(l+b)\] Perimeter of triangle = sum of its sides\[=(AB+BC+CA)\]   ü     Area: The area of any figure is the plane space occupied by it or the amount of surface enclosed within its boundary lines. ü     It is measured in square units i.e. Square meter\[({{m}^{2}})\], Square centimeter \[(c{{m}^{2}})\]etc. Area of square\[={{(side)}^{2}}={{a}^{2}}\,\,sq.\,\,unit\] Area of rectangle= length \[\times \] breadth\[=l\times b\]Sq. unit.

  GEOMETRY   FUNDAMENTALS          ü     In geometry, there are three basic terms point, line and plane. ü     Point: A point does not have length, breadth and height. It is a mark of position and is represented by a dot. ü     Line: A line normally refers to a straight line which extends indefinitely in both the directions. Thus, it has length but no breadth and no height. Example: If you hold a thread taut between two hands, it represents part of a line. ü     Plane: A plane has two dimensions, length and breadth, but no height. Example: A piece of paper represents a plane, Top of a table represents plane, etc. Passing through a point, an infinite number of lines can be drawn. \[{{l}_{1,}}{{l}_{2.................}}{{l}_{n}}\] All pass through ?P? These lines are also called CONCURRENT lines and the point P is called point of concurrence. ü     Two lines in a place are either intersecting or parallel   Collinearity of Points Three points A, B, C in a place are collinear if they lie on the same straight line. ü     One another way of testing collinearit6y of three points A, B and C is AB + BC = AC If this equality holds, then points are collinear. If this equality doesn?t hold, then points are non-collinear. ü     Ray: Part of line which extends indefinitely from a given point ?P? is called a ray. \[{{l}_{1,}}{{l}_{2,}}{{l}_{3..........}}{{l}_{n}}\]are all rays.   Line Segment  ü    Part of the line between two given points A and B on the line, is called a line segment. ü    Line segment AB is represented as\[\overline{AB}\]. It is measured in ?cm? or ?inch? ü    Two line segments AB and CD are equal, they are of same length. more...

  ARITHMETIC   FUNDAMENTALS ü     In this chapter, we shall study comparing quantities like ratio and proportion, profit and loss, discount simple interest, distance speed and time.   Ratio and Proportion ü     Ratio is a method of comparing two quantities of the same kind by division. ü     When two ratios are equal, they are said to be in proportion. ü     If two ratios are to be equal or are in proportion, their product of means should be equal to the product of extremes. Example: If a: b: c: d then the statement ad = be, holds good. If a: b and b: c are in proportion such that \[{{b}^{2}}\]= Ac than b is called the mean proportional of a: b and b: c ü     Multiplying or dividing terms of the ratio by the same number gives equivalent ratios.   Elementary Questions Q.        If\[5:6=a:18\], then\[a=?\]? Sol.      \[\frac{5}{6}-\frac{a}{18}=5\times 18=a\times 6\] \[\Rightarrow a=\frac{5\times 15}{6}=15\]   Elementary Question: Q.        \[\frac{37}{25}\]can also be written as, (a)\[\frac{147}{99}\]                              (b)\[\frac{149}{101}\]                             (c)\[\frac{148}{100}\]                                    (d)\[\frac{152}{97}\] Sol.      \[\frac{37}{25}=\frac{37\times 4}{25\times 4}=\frac{148}{100}\]   Percentage ü     Another way of comparing quantities is percentage. The word percent means per hundred. Thus 12% means 12 parts out of 100 parts ü     Fractions can be converted into percentages and vice= versa. Example:\[\frac{2}{5}=\frac{2}{5}\times 100%=40%\] (ii)\[25%=\frac{25}{100}=+\frac{1}{4}\]   ü     Decimals can be converted into percentages and vice-versa. Example: (i)\[0.36=0.36\times 100%\] (ii) \[43%=\frac{43}{100}=0.43\]   Simple Internet ü     When we deposit money in banks, bank give interest on money. Interest may be simple interest (called S.I.) A= Amount B= Principle R= Rate T= Time \[S.I.=\frac{P\times R\times T}{100}\] (Simple Interest)\[S.I.=A-P\]    

  FRACTION AND DECIMALS   FUNDAMENTALS ü     A fraction is a number representing a part of a whole ü     The fractions One-third, Three-fifths, Two-sevenths are written as: \[\frac{1}{3},\frac{3}{5},\frac{2}{7}\]respectively. ü     The lower part of a fraction, which indicates the number of equal parts into which the upper part is divided, is called denominator. The upper number, denotes the number of parts considered of the whole, is called numerator.   Types of Fraction ü     Proper Fraction: A fraction whose numerator is less than the denominator is called a proper fraction. Example: \[\frac{1}{3},\frac{2}{3},\frac{4}{5}\] ü     In the above fractions, the numerators 1, 2, 3, are less than denominators 3, 3, 5 respectively. ü     Improper fraction: A fraction whose numerator is more than or equal to denominator is called improper fraction. Example:\[\frac{5}{3},\frac{6}{5},\frac{7}{4},\frac{7}{7}\] etc. ü     Mixed Fraction: A combination of a whole number and a paper fraction is called a mixed fraction Example:\[1+\frac{2}{3}\] is written as\[1\frac{2}{3}\],\[2+\frac{1}{5}\] is written as\[2\frac{1}{5}\] ü     Like Fraction: Fraction with same denominators are called like fractions. Example: \[\frac{1}{8},\frac{2}{8},\frac{5}{8}\] etc. In all the above fraction denominators are equal, so they are like fraction. ü     Unlike Fractions: Fractions with different denominators are called unlike Fractions. Example: \[\frac{1}{3},\frac{1}{5},\frac{5}{8},\frac{3}{7}\] etc. ü     Equivalent Fractions: Fractions having the same value are called equivalent fractions. Example: \[\frac{1}{5},\frac{2}{10},\frac{3}{15}\] etc. In above fractions value of each fraction is equal so they are equipment fractions. ü     Decimal Fractions: A fraction whose denominator is powers of 10 is called a decimal fraction. Example:\[\frac{3}{10},\frac{1}{100},\frac{1}{1000}\] ü     Combined Fraction: A fraction of a fraction is called a combined fraction. Example: \[\frac{1}{2}\]of\[\frac{3}{8}\],\[\frac{1}{3}\] of \[\frac{4}{7}\] etc. ü     Continued Fractions:   FACTOR AND MULTIPLE   FUNDAMENTALS ü     One number is said to be a factor of another when it divides the other exactly.   Properties of Factors ü     1 is factor of every number Example:  \[85=1\times 85\] \[73=1\times ~73\] \[10=1\times 10\] etc. ü     Every non-zero number is a factor of itself. Example: \[18=18\times 1\] \[21=21\times ~1\] \[15=15\times ~1\] etc. ü     Factor of a non-zero number is less than or equal to the number. Example: \[18=1\times 2\times 3\times 3\]  (1, 2, 3, 6, 9, 18 are factor) \[17=1\times ~17\]           (1 and 17 are factors) \[33=1\times ~3\times ~11\]         (1, 3, 11 and 33 are factors) \[13=1\times ~13\] etc.     (1, 13) ü     1 is the only number having one factor only. ü     Every non-zero number other than 1 has at least two factors namely 1 and itself. Example: \[2=1\times ~2\]                        \[(1,\,\,2)\] \[6=1\times ~6\]                        \[(1,\,\,2,\,\,3,\,\,6)\] \[7=1\times ~7\] etc.                  \[(1,\,\,7)\] ü     Every non-zero number is a factor of 0. Example: \[0=1,\,\,2,\,\,3,\,\,4...............\] \[\left( \because \frac{0}{1}=0,\,\,\frac{0}{2}0,\,\,\frac{0}{1}=......... \right)\]   Prime Factorization ü     When a number is expressed as the product of prime numbers, it is called the Prime factorization of the given number. Examples:
3 45
3 15
  5
\[\therefore 45=3\times 5\times 5\]  
2   ROMAN NUMBER   FUNDAMENTALS ü     The system of Numeration, developed by Romans is called the Roman numerals system. In Roman numerals system there are seven distinct symbols. viz I, V, X, L, C, D and M.   Roman symbols and their corresponding Hindu-Arabic numbers
Roman Numerals I V X L C D M
Hindu-Arabic Numerals 1 5 10 50 100 500 1000
  Roman numerals formation rules ü     If a symbol in roman numeral system is repeated, its value is added as many times as it appears. Example: \[II=1+1=2\] \[XXX=10+10+10=30\] \[CC=100+100=200\] \[MMM=1000+1000+1000=3000\] It may be noted that no numerals can be repeated more than 3 times. Repetition is allowed only for symbols I, X and C. V, L and D are never repeated   ü     A symbols of small value is placed to the right of larger value and its value is added to the larger value. Example: \[XII=10+1+1=12\] \[XV=10+5=15\] \[LV=50+5=55\] \[CX=100+10=110\] ü     A symbol of smaller more...
NUMBER SYSTEM   FUNDAMENTALS ü     Numbers are expressed by means of figures- 0, 1,2, 3, 4, 5, 6, 7, 8 and 9 are called digits. Out of these digits, 0 is called insignificant digit and rest are called significant digits.   Numerals ü     A group of figures representing a number is called a numeral   Place value of a digit in Hindu-Arabic System
Periods Crores Lakhs Thousands Ones
Places Ten Crores 100000000 Crores 10000000 Ten Lakhs 1000000 Lakhs 100000 Ten Thousands 10000 Thousands 1000 Hundreds 100 Tens 10 Ones 1
       
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