6th Class

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
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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 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, \[\frac{20}{5}\text{ }=\text{ }4\]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 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 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 \[=\frac{1}{2}\,\,\,\times \text{ }Base\text{ }\times \text{ }Height\]
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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.  

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 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 more...

 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{ more...

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 more...

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 more...