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 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 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 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 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, 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.   more...

                                                                                            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 more...