Current Affairs 6th Class

  Fraction and Decimals   Fraction Fraction is a method for representing the parts of a whole number. An orange is divided into two equal parts and so the first part of orange is half of the whole orange and represented by \[\frac{1}{2}\] of the orange.   Types of Fractions   Proper Fractions A fraction whose numerator is less than denominator is called a proper fraction. \[\frac{3}{5}\]’ \[\frac{1}{2}\]’ \[\frac{7}{9}\] are Proper fractions.   Improper Fractions A fraction is called improper fraction even if:

• It has smaller denominator than numerator
• It has equal numerator and denominator

\[\frac{6}{5},\,\,\frac{5}{2},\,\,\frac{109}{34},\,\,\frac{6}{6}\]   Simplest form of a Fraction A fraction is said to be in the simplest or lowest form if its numerator and denominator have no common factor except 1.   Mixed Fractions Combination of a proper fraction and a whole number is called mixed fraction. Every mixed fraction has a whole and a fractional part.   Like and Unlike Fractions When two or more fractions have same denominator then they are called like fractions whereas unlike fractions do not have equal denominators.   Equivalent Fractions Two fractions are said to be equivalent if they are equal to each other. Two equivalent fractions may have a different numerator and a different denominator.   Example: Convert \[\frac{11}{2}\] into a mixed fraction.   (a) \[5\frac{1}{2}\]                                 (b) \[3\frac{1}{2}\] (c) \[\frac{1}{2}\]                                   (d) All the above (e) None of these Answer (a)   Example: \[\frac{5}{7},\,\frac{1}{2},\,\frac{2}{3}\]are: (a) like fractions              (b)  unlike fractions (c) equivalent fractions     (d) Mixed fractions (e) None of these Answer (b)   Operations on Fractions   Addition of Like Fractions Addition of like fractions is the addition of their numerators and common denominator is the denominator of the resulting fraction.   Addition of numerators Hence, the sum of like fractions =\[\frac{\text{Addition}\,\text{of}\,\text{numerators}}{\text{Common}\,\text{denominator}}\] Subtraction of Like Fractions Subtraction of like fractions is same as its addition except that addition is converted into subtraction. Let two like fractions are \[\frac{567}{456}\text{and}\,\frac{4546}{456}\] Their subtraction=\[\frac{\text{Subtraction}\,\text{of}\,\text{its}\,\text{numerators}}{\text{Common}\,\text{denominator}}\]   Multiplication of Fractions The following are the steps to perform the multiplication of like fractions: Step 1: Multiply the numerators and multiply the denominators. Step 2: Write the answer in lowest form.   or, Product of fractions= \[\frac{\text{Product}\,\text{of}\,\text{numerators}}{\text{Product}\,\text{of}\,\text{denominators}}\]   Division of Fractions Division of fractions is multiplication of the dividend by reciprocal of the divisor.   Example: Evaluate: \[\left\{ \left( \frac{3}{5}-\frac{7}{11}\times \frac{1}{2} \right) \right\}+\frac{9}{121}\] (a) \[\frac{3}{121}\]                               (b) \[\frac{43}{121}\] (c) \[\frac{431}{1210}\]                          (d) All the above (e) None of these Answer (c)   Explanation:   \[\left\{ \left( \frac{3}{5}-\frac{7}{11}\times \frac{1}{2} \right) \right\}+\frac{9}{121}=\frac{3}{5}-\frac{7}{22}+\frac{9}{121}\] \[=\frac{726-385+90}{1210}\] \[=\frac{431}{1210}\]   Example: What should be divided by \[\frac{\text{6}}{\text{11}\,}\,\text{to}\,\text{get}\,\frac{\text{3}}{\text{5}}\]?   (a) \[\frac{18}{55}\]                  (b) \[\frac{8}{55}\]  (c) \[\frac{55}{18}\]                  (d) \[\frac{30}{33}\]  (e) None of these             Answer (a) Explanation: Required number =\[\frac{6}{11}\times \frac{3}{5}=\frac{18}{55}\] Decimal Digits of decimal number are separated by a dot (.) called decimal point. Digits at the left from the dot (decimal) are called whole part and digits at the right side are called decimal part of the decimal number.   Place more...

  LCM and HCF   LCM (Least Common Multiple) LCM of two or more numbers is their least common multiple. LCM of 4 and 6 is 12, it means, 12 is the least common multiple of 4 and 6, therefore, 12 is exactly divisible by each of 4 and 6.   LCM by Prime Factorization Method The following steps are used to determine the LCM of two or more numbers by prime factorisation method: Step 1: Find the prime factors of each number. Step 2: Product of highest power of prime factors is their LCM.   LCM by Division Method The following steps are used to determine the LCM of two or more numbers by division method: Step 1: Numbers are arranged or separated in a row by commas. Step 2: Find the number which divides exactly atleast two of the given numbers. Step 3: Follow step 2 till there are no numbers (atleast two) divisible by any number. Step 4: LCM is the product of all divisors and indivisible numbers.   Example: Find the least number which is exactly divisible by each of 28 and 42. (a) 64                            (b) 84 (c) 52                            (d) All of these (e) None of these Answer (b)   Explanation: \[28=2\times 2\times 7,\,\,42=2\times 3\times 7\]            LCM =\[2\times 2\times 3\times 7=84\]   HCF (Highest Common Factor) Highest Common Factor is also called Greatest Common Measure (GCM) or Greatest Common Divisor (GCD). H.C.F of two or more numbers is the greatest number which exactly divides each of the numbers.   HCF by Prime Factorization Method The HCF of two or more numbers is obtained by the following steps: Step 1: Find the prime factors of each of the given number. Step 2: Find the common prime factors from prime factors of all the given numbers. Step 3: The product of the common prime factors is their HCF.   HCF by Continued Division Method The HCF of two or more numbers can also be obtained by continued division method. The greatest number is considered as dividend and smallest number as divisor.   Follow the following steps to perform the HCF of the given numbers: Step 1: Divide the greatest number by smallest. Step 2: If remainder is zero, then divisor is the HCF of the given number. Step 3: If remainder is not zero then, divide again by considering divisor as new dividend and remainder as new divisor till remainder becomes zero. Step 4: The HCF of the numbers is last divisor which gives zero remainder.   HCF of more than two Numbers The HCF of more than two numbers is the HCF of resulting HCF of two numbers with third number. Therefore, HCF of more than two numbers is obtained by finding the HCF of two numbers with third, fourth and so on.   HCF of Larger Numbers The HCF of smaller number (One or two digit numbers) is simply obtained by division but division of larger numbers take more more...

  Ratio and Proportion   Ratio Ratio of two quantities is the comparison of the given quantities. Ratio is widely used for comparison of two quantities in such a way that one quantity is how much increased or decreased by the other quantity.   For example, Peter has 20 litres of milk but John has 5 litres, the comparison of the quantities is said to be, Peter has 15 litres more milk than John, but by division of both the quantity, it is said that Peter has, \[\frac{20}{5}=4\] times of milk than John. It can be expressed in the ratio form as\[4:1\]   Note: In the ratio\[a:b\]\[(b\ne 0)\], the quantities a and b are called the terms of the ratio and the first term (ie. a) is called antecedent and the second term (ie. b) is called consequent.   Simplest form of a Ratio If the common factor of antecedent and consequent in a ratio is 1 then it is called in its simplest form.   Comparison of Ratio Comparison of the given ratios are compared by first converting them into like fractions, for example to compare \[5:6,\text{ }8:13\text{ }and\text{ }9:16\]first convert them into the fractional form i.e. \[\frac{5}{6},\frac{8}{13},\frac{9}{16}\]. The LCM of denominators of the fractions\[=2\times 3\times 13\times 8=624\] Now, make denominators of every fraction to 624 by multiplying with the same number to both numerator and denominator of each fraction. Hence,\[\frac{5}{6}\times \frac{104}{104}=\]\[\frac{520}{624},\frac{8}{13}\times \frac{48}{48}\]\[=\frac{384}{624}\]and\[\frac{9}{16}\times \frac{39}{39}\]\[=\frac{351}{624}\].Equivalent fractions of the given fractions are \[\frac{520}{624},\frac{384}{624},\frac{351}{624}\]. We know that the greater fraction has greater numerator, therefore the ascending order of the fractions are, \[\frac{351}{624}<\frac{384}{624}<\frac{520}{624}\] or \[\frac{9}{16}<\frac{8}{13}<\frac{5}{6}\] or \[9:16<8:13<5:6\], thus the smallest ratio among the given ratio is \[9:16\]and greatest ratio is\[5:6\].   Equivalent Ratio The equivalent ratio of a given ratio is obtained by multiplying or dividing the antecedent and consequent of the ratio by the same number. The equivalent ratio of \[\text{a}\,\,\text{:}\,\,\text{b}\] is \[\text{a}\,\times \,\text{q}\,\,\text{:}\,\,\text{b}\,\times \,\text{q}\]whereas, a, b, q are natural numbers and q is greater than 1.   Hence, the equivalent ratios of \[5:8\]are, \[\frac{5}{8}\times \frac{2}{2}=\frac{10}{16}\] or\[10:16\], \[\frac{5}{8}\times \frac{3}{3}=\frac{15}{24}\] or\[15:24\], \[\frac{5}{8}\times \frac{12}{12}=\frac{60}{96}\] or\[60:96\].   Example: Mapped distance between two points on a map is 9 cm. Find the ratio of actual as well as mapped distance if 1 cm = 100 m. (a) \[10000:1\]                (b) \[375:1\]         (c) \[23:56\]                    (d) \[200:1\] (e) None of these Answer (a)   Explanation: Required ratio =\[900\times 100:9=\] \[90000:9=10000:1\]   Example: Consumption of milk in a day is 6 litre. Find the ratio of Consumption of milk in month of April and quantity of milk in a day? (a) \[99:2\]                     (b) \[30:1\]         (c) \[123:3\]                    (d) \[47:3\] (e) None of these Answer (b) Explanation: Required ratio \[=30\times 6:6=30:1\]   Proportion The equality of two ratios is called proportion. If a cake is distributed among eight boys and each boy gets equal part of the cake then cake is said to be distributed in proportion. The simplest form of ratio \[12:96\]is \[1:8\]and\[19:152\]is \[1:8\]therefore, \[12:96\]and \[19:152\] are in proportion and written as \[12:96::19:152\]or more...

  Geometry and Symmetry   Basic Geometrical Shapes Lines and angles are the main geometrical concept and every geometrical figure is made up of lines and angles. Triangles are also constructed by using lines and angles.   Point A geometrical figure which indicates position but not the dimension is called a point. A point does not have length, breadth and height. A point is a fine dot. P is a point on a plane of paper as shown below.   Line A set of points which can be extended infinitely in both directions is called a line.     Line Segment A line of fix length is called a line segment.                                                    In the above figure RS is a line segment and the length of RS is fixed.   Ray A ray is defined as the line that can be extended infinitely in one direction.     In the above figure AB can be extended towards the direction of B. Hence, called a ray.   Note: A line segment has two end points, a ray has only one end point and a line has no end points.   Angle Angle is formed between two rays which have a common point.   Vertex or common end point is O. OA and OB are the arms of \[\angle AOB\] The name of the above angle can be given as \[\angle AOB\]or \[\angle BOA\] The unit of measurement of an angle is degree\[({}^\circ )\]   Types of Angles Acute Angle The angle between \[0{}^\circ \] and \[90{}^\circ \] is called an acute angle. For example, \[10{}^\circ ,\,\,30{}^\circ ,\,\,60{}^\circ ,\,\,80{}^\circ \]are acute angles.   Right Angle An angle of measure \[90{}^\circ \] is called a right angle.   Obtuse Angle An angle whose measure is between \[90{}^\circ \] and \[180{}^\circ \] is called an obtuse angle. Straight Angle An angle whose measure is \[180{}^\circ \,\,\text{is}\]called a straight angle.                                                  Reflex Angle An angle whose measure is more than \[180{}^\circ \] and less than \[360{}^\circ \]is called a reflex angle.   Complementary Angle Two angles whose sum is \[90{}^\circ \,\,\text{is}\] called the complimentary angle. Complementary angle of any angle \[\theta \] is\[90{}^\circ -\theta \].   Supplementary Angle Two angles whose sum is \[180{}^\circ \,\,\text{is}\] called supplementary angles. Supplementary angle of any angle \[\theta \] is\[180{}^\circ -\theta \].   Adjacent Angle Two angles are said to be adjacent if they have a common vertex and one common arm. In the following figure \[\angle AOC\] and \[\angle COB\]are adjacent angles.   Vertically more...

  Mensuration   Perimeter and Area of Plane Figures Perimeter of geometrical figure is the sum of its sides. There are different types of geometrical figures. Figures are classified by their shapes and sizes. Area of a geometrical figure is its total surface area.   Perimeter and Area of a Triangle

• Perimeter of a triangle = Sum of the length of all sides.
• Area of a right triangle \[\text{=}\frac{\text{1}}{\text{2}}\times \text{Base}\times \text{Height}\]
• Perimeter of an equilateral triangle \[\text{=3}\times \text{Side}\]
• Area of an equilateral triangle \[\text{=}\frac{\sqrt{\text{3}}}{\text{4}}\times {{\text{(Side)}}^{\text{2}}}\]

  Perimeter and Area of a Parallelogram Parallelogram is a quadrilateral whose opposite sides are equal and parallel to each other. In the given figure ABCD is a Parallelogram in which \[\text{AB}\parallel \text{CD,}\,\,\text{BC}\parallel \text{AD,}\,\,\text{AB}=\text{CD}\] and \[\text{AD=BC}\]   Perimeter of a Parallelogram = 2 (sum of two adjacent sides) Hence, perimeter of a parallelogram \[\text{ABCD=2(AB+BC)}\]Area of a parallelogram = Base \[\text{ }\!\!\times\!\!\text{ }\] Height Therefore, the area of a parallelogram \[\text{ABCD=AB }\!\!\times\!\!\text{ CE}\]   Perimeter and Area of a Rectangle A rectangle has four right angles and its opposite sides are equal. Longer side of a rectangle is called length and shorter side is called width.     Perimeter of rectangle  \[ABCD=AB+BC+CD+DA\] = length + width + length + width = 2(length + width) Hence, perimeter of a rectangle = 2(length + width) Area of a rectangle = length \[\times \]width   Perimeter and Area of a Rhombus A rhombus is a parallelogram with four equal sides. Therefore, perimeter of rhombus\[=4\times side\]. In the figure given below ABCD is a rhombus.   Perimeter of a rhombus, \[=4\times side\] Area of a rhombus = base \[\times \] height Also area of a rhombus \[\text{=}\frac{1}{2}\times \] product of length of diagonals. Perimeter and Area of a Square A square has four equal sides and each angle of\[90{}^\circ \]. In the picture given below, ABCD is a square because its all sides are equal and each angle is a right angle.     Perimeter of square = side + side + side + side\[=4\times side\] Area of a Square = side \[\times \]side = \[{{(side)}^{2}}\]   Perimeter and Area of a Trapezium A quadrilateral whose one pair of sides are parallel is called a trapezium. The given figure is a trapezium in which parallel sides are AB and CD and non-parallel sides are AD and BC     Perimeter of a trapezium = Sum of the length of all sides Area of a trapezium \[=\frac{1}{2}\times \] (Sum of lengths of parallel sides) \[\times \]distance between parallel sides.   Cirumference and Area of a circle A round plane figure whose all points are equidistant from a fixe point is called a circle and the fixed point is called centre of the circle more...

  Data Handling   In this chapter we will learn about pictograph and bar graph.   Data Data is a collection of facts, such as numbers, observations, words or even description things.   Observation Each numerical figure in a data is called observation.   Frequency The number of times a particular observation occurs is called its frequency.   Statistical Graph The information provided by a numerical frequency distribution is easy to understand when we represent it in terms of diagrams or graphs. To represent statistical data, we use different types of diagrams or graphs. Some of them are:   (i)  Pictograph (ii) Bar graph   Pictograph A pictograph represents the given data through pictures of objects. It helps to answer the questions on the data at a glance.   Example: The following pictograph, shows the number of cakes sold at a bakery over five days.              

Day	Number of cakes	= 10 cakes
Monday
Tuesday
Wednesday
Thursday
more... Catgeory: 6th Class Anology                                                                                             Analogy   Learning Objectives   What is Analogy Types of Problems   Analogy Simple meaning of analogy is similarity. But, in terms of reasoning, the meaning of analogy is logical similarity in two or more things. This similarity may be on the basis of properties, kinds, traits, shapes etc.   Example: (i) Student : School : : Patient : Hospital Explanation: A 'Student' goes to ‘School’ in the same way a 'Patient' goes to 'Hospital', In other words, school (place to take education) is a proper place for a student arid in the same way hospital (place to get treatment) is a proper place for a patient. 1st pair- Student: School (person and proper place relationship). 2nd pair - Patient: Hospital (person and proper place relationship). Clearly, both pairs show similar relationship in a logical way. Hence, both pairs are analogous or it is said that both pairs exhibit analogy.   (ii) Good : Bad : : Tall : Short Explanation: 1st pair - Good: Bad (opposite relationship). 2nd pair - Tall: Short (opposite relationship). Clearly, both pairs show similar relationship (opposite relationship). Hence, both pairs exhibit analogy.   Types of Problems Problems Based on Synonymous Relationship In such problems, the words given in one pair have same meaning and the same relationship that is found in another pair of words.   Example 1 Right: Correct:: Fat: Bulky Explanation: 1st pair - Right: Correct (synonymous relationship). 2nd pair - Fat: Bulky (synonymous relationship).   Example 2 Brave : Bold :: Wrong : Incorrect Explanation: 1st pair - Brave: Bold (synonymous relationship). 2nd pair - Wrong: Incorrect (synonymous relationship).   Commonly Asked Questions   Select the pair which is related in the same way as the pair of words given in the question. Tough : Hard \[::\text{ }\_\_\_\_\_\_\text{ }:\text{ }\_\_\_\_\_\_\_\_\] (a) Rich : Wealthy           (b) Rich : Poor (c) Tall : Short                (d) True : False (e) None of these   Answer (a) Explanation: Option (a) is correct because ‘Tough’ and 'Hard' are synonymous words. In the same manner 'Rich’ and ‘Wealthy' are synonymous words. Rest of the options is incorrect because words in option (b), (c) and (d) have opposite meanings and option (e) is useless because of the correctness of option (a).   'Start' is related to ‘Begin’ in the same way as ‘Joy’ is related to………….. (a) Right                        (b) False (c) True                                     (d) Delight (e) None of these Answer (d) Explanation: Option (d) is correct because ‘Start’ and ‘Begin’ have same meaning. Similarly, ‘Joy’ and ‘Delight' have same meaning. Rest of the options is incorrect because of the correctness of option (d).   Problems Based on Opposite Relationship In such more... Catgeory: 6th Class Current Affairs Categories National International Agreements Appointments Government Schemes Summits Awards & Honours Business Economy & Banking Defense Sports Ranks & Reports Important Days Persons Science & Technology State Environment Bills & Acts Schemes Miscellaneous Archive August 2020(12) February 2020(215) January 2020(211) July 2020(35) June 2020(143) March 2020(99) May 2020(49) April 2019(263) August 2019(324) December 2019(331) February 2019(280) January 2019(306) July 2019(359) June 2019(231) March 2019(259) May 2019(258) November 2019(228) October 2019(222) September 2019(322) April 2018(298) August 2018(290) December 2018(292) July 2018(306) June 2018(311) March 2018(5) May 2018(328) November 2018(277) October 2018(276) September 2018(281) Trending Current Affairs Smart Cities India 2018 Expo Underway In New Delhi CII Pegs India's GDP Growth At 7.3-7.7% For 2018-19 World Environment Day 2018 Celebrated In New Delhi President 3-Nation Visit: India & Cuba Sign MoUs SCM BrahMos Test Fired Under Extreme Conditions 4 Indian-Origin Names In List Of Fortune's 40 Young Influential People Colombia joins NATO as global partner Bangladesh Cabinet Clears Deal With India For Port Usage PM Inaugurates Key Development Projects In Varanasi Paisabazaar.com Launches India’s First ‘Chance of Approval’ Feature Please Wait you are being redirected.... You need to login to perform this action. You will be redirected in 3 sec × Reset Password. Email : Send Password Cancel Add Mobile Enter Mobile Number Submit Logout Enter OTP OTP has been sent to your mobile number and is valid for one hour Enter One Time Password Submit Change Mobile: Submit Logout Mobile Number Verified Your mobile number is verified. Close Free Videos × For free video lectures fill in the form below and we will get back to you. * Email Address: * Mobile Number: Submit Cancel