Current Affairs 6th Class

Fractions and Decimals

Fractions 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

of the orange. TYPES OF FRACTIONS Proper Fractions A fraction whose numerator is less than denominator is called a proper fraction.

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 are improper fractions.

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 Fraction 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

into a mixed fraction. (a)

(b)

(c)

(d) All the above (e) None of these Answer (a)

Example:

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. Hence, the sum of like fractions

Subtraction of Like Fractions Subtraction of like fractions is same as its addition except that addition is converted into subtraction. Let two like more...

Catgeory: 6th Class

LCM and HCF

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 LCIVI 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: \[28\text{ }=\text{ }2\text{ }\times \text{ }2\text{ }\times \text{ }7,\text{ }42\text{ }=\text{ }2\text{ }\times \text{ }3\text{ }\times \text{ }7\] LCM \[=2\times 2\times 3\times 7=\text{ }84\] 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 more...

Catgeory: 6th Class

Ratio and Proportion

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, \[\frac{20}{5}\text{ }=\text{ }4\]times of milk than John. It can be expressed in the ratio form as 4: 1. Note: In the ratio\[a:\text{ }b\text{ }\left( b~\ne 0 \right)\], 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 (i.e., 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, 8: 13 and 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 \[=2\times 3\times 13\times 8=\text{ }624\] 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 Tractions 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 : 6 < 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 \[a\,\,\times \,\,b\]is \[a\,\,\times \text{ q }:\text{ }b\text{ }\times \text{ }q\]whereas, a, b, q are natural numbers and q is greater than 1, Hence, the equivalent ratios of 5 : 8 are,

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 \[=\text{ }900\text{ }\times \text{ }100:\text{ }9\text{ }=\text{ }90000:\text{ }9\text{ }=-\text{ }10000:\text{ }1\]

Example:

Consumption of milk in more...

Catgeory: 6th Class

Geometry and Symmetry

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 0. OA and OB are the arms of

AOB The name of the above angle can be given as

AOB or

BOA The unit of measurement of an angle is degree (°) TYPES OF ANGLES Acute Angle The angle between

is called an acute angle. For example,

are acute angles. Right Angle An angle of measure

is called a right angle. Obtuse Angle An angle whose measure is between

is called an obtuse angle. Straight Angle An angle whose measure is

is called a straight angle.

Reflex Angle An angle whose measure is more than

and less than

is called a reflex angle. Complementary Angle Two angles whose sum is

is called the complimentary angle. Complementary angle of any angle

more...

Catgeory: 6th Class

Mensuration

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 \[=\frac{1}{2}\,\,\,\times \text{ }Base\text{ }\times \text{ }Height\]
Perimeter of an equilateral triangle \[=\text{ }3\text{ }\times \text{ }Side\]
Area of an equilateral triangle \[=\frac{\sqrt{3}}{4}\times {{\left( Side \right)}^{2}}\]

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 \[AB||\,\,CD,\,\,BC||\,\,\,AD,\text{ }AB\text{ }=\text{ }CD\text{ }and\text{ }AD\text{ }=\text{ }BC\]

Perimeter of a Parallelogram = 2(sum of two adjacent sides) Hence, perimeter of a parallelogram ABCD = 2(AB + BC) Area of a Parallelogram \[=\text{ }Base\text{ }\times \text{ }Height\] Therefore, the area of a parallelogram \[ABCD=AB\times CE\] 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 \[=\text{ }2\left( length\text{ }+\text{ }width \right)\] Hence, perimeter of a rectangle \[=\text{ }2\left( length\text{ }+\text{ }width \right)\] Area of a rectangle \[=\text{ }length\text{ }\times \text{ }width\] Perimeter and Area of a Rhombus A rhombus is a parallelogram with four equal sides. Therefore, perimeter of rhombus\[=\text{ }4\text{ }\times \text{ }side\]. In the figure given below ABCD is a rhombus.

Perimeter of a rhombus, \[=\text{ }4\text{ }\times \text{ }side\] Area of a rhombus \[=\text{ }base\text{ }\times \text{ }height\] Also area of a rhombus =\[\frac{1}{2}\] 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 \[=\text{ }side\text{ }+\text{ }side\text{ }+\text{ }side\text{ }+\text{ }side\text{ }=\text{ }4\text{ }\times \text{ }side\] more...

Catgeory: 6th Class

Data Handling

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 of 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 pictography shows the number of cakes sold at a bakery over five days. more...

Catgeory: 6th Class

Applied Mathematics

Applied Mathematics Set Set is a collection of well-defined objects which are distinct from each other. The objects in the set are called its elements. Sets are usually denoted by capital Letters A, B, C, ?.. and elements are usually denoted by small letters a, b, c, ........ For example/ the set of all even natural numbers less than 10 can be represented by N = {2, 4, 6, 8}. Methods for Describing a Set (i) Roster Method: In this method, a set is described by listing elements, separated by commas, within braces. e.g. A = {a, e, i, o, u} Note: This method is also called listing method or tabular form method. (ii) Set Builder Method: In this method, we write down a rule which gives us all the elements of the set by that rule. e.g. A = {x : x is a vowel of English alphabet} Finite Set A set containing finite number of elements or no element, is called a finite set, eg. The set of all persons in India is a finite set. Infinite Set A set containing infinite number of elements is called an infinite set. Cardinality of a Finite Set The number of elements in a given finite set is called cardinal number of finite set, denote by n (a), where A is the given set. e.g. \[P\text{ }=\text{ }\left\{ 5,\text{ }15,\text{ }25,\text{ }35,\,\,45 \right\}\Rightarrow ~n\left( P \right)=5\] Universal Set (U) A set consisting of all possible elements which occurs under consideration is called a universal set. e.g. Let the set U defines the set of all natural numbers then set of all odd natural numbers is another subset of U and the set of all even natural numbers is another subset of U. Equal Sets Two sets A and B are called equal, if every element of A is a member of B and every element of B is a member of A, Thus we write A = B. e.g. A = {2, 4, 6, 8, 10,} and {all the even natural numbers less than or equal to 10} i.e., A and B are equal sets.

Example:

Find cardinal number of a set A of the composite numbers between 10 and 25. (a) 4 (b) 6 (c) 8 (d) 9 (e) None of these Answer (d) Explanation: Here, A = {12, 14, 15, 16, 18, 20, 21, 22, 24} \[\Rightarrow \text{ }n\left( A \right)\text{ }=\text{ }9\text{ }\Rightarrow \]Cardinal number of set A = 9 Average Average is a calculated central value of a set of given number. The average is the sum of the numbers divided by the count. So, Average = \[\frac{sum\,of\,the\,number}{count}\] For example. Average of first ten natural numbers is \[\frac{1+2+3+4+5+6+7+8+9+10}{10}=\frac{55}{10}=5.5\] Percentage The word 'percent', more...

Catgeory: 6th Class

Reasoning Aptitude

Reasoning and Aptitude Reasoning and logic skills are an integral part of subjects like Mathematics. In this chapter, we will learn various problems related to reasoning and aptitude. Problems Based on Missing Numbers In these types of problems, we find out a missing number from a given set of numbers, which is appropriate and follow a certain pattern.

Example:

Complete the series given below: 4, 10, 26, 72, 208, 614? (a) 1815 (b) 1820 (c) 1830 (d) 1836 (e) None of these Answer (c) Explanation: Here the pattern is given below: \[4\times 3-2\times 1=\text{ }10;\text{ }10\times 3\text{ }-\text{ }2\times 2\text{ }=\text{ }26\] \[26\times 3\text{ }-\text{ }2\times 3\text{ }=\,\,\,72;\text{ }72\times 3\text{ }-\text{ }2\times 4\text{ }=\text{ }208\] \[208\times 3\text{ }-\text{ }2\times 5\text{ }=614;\text{ }614\times 3\text{ }-\text{ }2\times 6\text{ }=1830\] Problems Based on Coding-decoding In these types of problems, you will learn to code a word by using a certain pattern or rule.

Example:

If 'SAMPLE' is coded as 'FMNOBT' then how would you code 'CLIMAX'? (a) YBJLMD (b) YJBMLD (c) XJMNLD (d) DBJLMY (e) None of these Answer (a) Explanation: Here we have the following pattern.

Problems Based on Puzzle In these types of problems, the given information is summarized by a table.

Example:

Joseph and John are good in hockey and cricket. Ketan and Yash are good in cricket and football. Arjun and Tuffey are good in baseball and volleybalL Ketan and Tapan are good in hockey and baseball. Based on above information answer the given question. Who is good in Hockey, Cricket, Football and baseball? (a) Joseph (b) John (c) Ketan (d) Yash (e) None of these Answer (c) Explanation:

Days	Number of cake
Monday
Tuesday
Wednesday
Thursday
Friday

Joseph

John

Ketan

Yash

Arjun

more...

Catgeory: 6th Class

History and Briefing on Computer

History and Briefing on Computer Introduction A computer is a programmable machine. The two principle characteristics of a computer are: v It responds to a specific set of instructions in a well-defined manner. v It can execute a prerecorded list of instructions. The history of computer is also referred with its generations. Generation in computer terminology is a change in technology a computer is being used. The evaluation of computer started from 16th century and resulted in the form that we see today.

Types of Computers All the computers that are developed are not alike. They can have different designs and features. Computers can be as big as occupying a large building or as small as a laptop or may be a micro controller in mobile and embedded systems. Classification of Computers On the basic of principles of operations, there are three types of computer they are as listed below: Analog Computers Analog computers are used to process analog data. Such type of data includes temperature, pressure, speed weight, voltage, depth etc. These quantities are continuous having an infinite variety of values. Analog computers are the first computers being developed and they provided the basic for the development of the modern digital computers.

Digital Computers Digital computer works with digits to represent numerals, letters or other special symbols. Digital computers operate on inputs which are of ON-OFF type and its output is also in the form of ON-OFF signal. Normally, an ON is represented by 1 and OFF is represented by a 0. A digital computer can be used to process numeric as well as non-numeric data. It can perform arithmetic operations like addition, subtraction, multiplication and division and also logical operations. Most of the computers available today are digital computers: The results generated by digital computers are more accurate than the results generated by analog computers. Analog computers are faster then digital. Analog computer, lack memory whereas digital computers store information.

Hybrid Computers Hybrid computer are combination of digital and analog computers. It combines the best features of both types of computer, i.e. it has the speed of analog and the memory and accuracy of digital computers. Hybrid computers are mainly used in specialized applications where both kinds of data needs to be processed. Therefore, they both help the user to process both continuous and discrete data. For example a petrol pump contains a processor that converts fuel flow measurements into quality and price values.

Based on Configuration On the basic of configuration of operations, there are four types of computer. Configuration can more...

Catgeory: 6th Class

More About Networking and Internet

More About Networking and Internet A network is a set of inter connected devices, such as computers and printers. These novices are connected with transmission media or communication channel. Using network you can send and receive data from one computer to another computer. You can also-hare printer and scanner with other users. Internet is the technology that is used to connect different computer systems located in different geographic locations. The internet interconnects millions of computers, providing a global communication, storage, and computation infrastructure. Moreover, the Internet is currently being integrated with mobile and wireless technology.

The Purpose of Networking File and Data Sharing It allows files to be shared instantaneously across the network with hundreds of users. Resource Sharing It allows the sharing of network resources such as printers, dedicated services, input devices and internet connections without being relocated. Internal Communications It allows organizations to maintain internal communication system. It enables employees to co-ordinate meetings and work activities which intern increases productivity. Provides Reliability Computer network is a very reliable network. If one of the systems in a network collapse, data can be collected from another system in the same network. Different Types of Networks Computer networks are classified on the basis of various factors. They include geographical span, inter-connectivity, administration, architecture etc. The three main types of computer networks are:- v LAN v WAN v MAN Local Area Network (LAN) This type of network is usually a small network constrained to a small geographic area like a home, office, or group of buildings. It is normally used for a single business office or a residential apartment. The major purpose of such inter connectivity is to establish a communication system in order to make the work easier.

LAN provides a useful way of sharing the resources between end users. The resources such as printers, file servers, scanners and internet are easily sharable among other computers. Metropolitan Area Network (MAN) A Metropolitan Area Network is a network that connects two or more Local Area Network or Campus Area Network together but does not extend beyond the boundaries of the immediate town, city, or metropolitan area. Multiple routers and switches are connected to create a MAN. It provides high speed internet services throughout the area covered within the network.

Wide Area Network (WAN) WAN is a system of network that covers a large geographical area across the world. WAN is used to connect LANs and other types of networks together, so that users and computers in one location can communicate with users and computers in other locations. more...

Catgeory: 6th Class