5th Class

  Operation on Numbers   Operation on Numbers In the previous chapter we have studied about numbers, way of numeration and some properties of numbers. In this chapter we will study operation on numbers. Addition, subtraction, multiplication and division are four basic arithmetic operations. Let us know about them.   Addition Under the operation of addition two or more than two numbers are added with each other.  

• Example:

Add 544214474 and 904426456. Solution: \[544214474+904426456=1448640930~~~\]   Subtraction Under the operation of subtraction, difference between two numbers is to be calculate:  

• Example:

Subtract 234495 from 87445653. Solution:\[87445653-234495=87211158\]       Multiplication When a number is added to itself for a number of times, the process of addition becomes bigger and lengthy. Therefore a short cut method was developed to perform such additions, called multiplication. Thus, multiplication is a short cut method of repeated addition.    more...

  Factors and Multiples   Introduction We have studied about the operations on numbers. Now, we will study two important terms that is, 'factors' and 'multiples'. They are related to the operations of multiplication and division.   Factors Factors of a number is the number, which divides the given number completely. If a, b, c, d.... are factors of 'm' then 'm' will be exactly divisible by a, b, c, d....   How to Get Factors of a Number To find all possible factors of a number, we have to find all the numbers, which divide the given number exactly.   Rules of Divisibility

The numbers which have 0, 2, 4, 6, or 8 at the unit place is divisible by 2. Ex: 5666, 5654, 130 are divisible by 2.

If sum of digits of a number is divisible by 3 then the number is divisible more...

  Fractions   Fractions Faction is a number, which is used to represent the part of a whole. It is expressed, in the form of \[\frac{P}{Q}\] where P and Q are natural numbers. The upper part of the fraction is called numerator and the lower part is denominator. For example, \[\frac{5}{9}\] is a fraction, where 5 is numerator and 9 is denominator.  

• Example:

  Represent the shaded part of the figure as a fraction.   Solution: \[\frac{1}{4}\]   Like Fraction The fractions, which have the same denominators are called like fractions.   Example:     Unlike Fraction The fractions, which do not have the same denominators, in other words, the fractions with different denominators are called unlike fractions.  

• Example: \[\frac{8}{9},\frac{4}{13},\frac{9}{8},\frac{10}{12}\] are unlike fractions.

  Unit more...

  Operation on Fractions   Operation on the Fractions In the previous chapter, we have studied about the fractions. In this chapter we will study operations on the fractions, like addition, subtraction, multiplication and division on fractions.   Addition of Fractions Make the denominator of fractions same by multiplying a suitable number to the numerator and denominator of both fractions. The common denominator is the denominator of the resultant fraction and addition of numerators is the numerator of the resultant fraction.   Example:   Add \[\frac{12}{16}\] and \[\frac{13}{16}\].    Solution: \[\frac{12}{16}+\frac{13}{16}=\frac{12+13}{16}=\frac{25}{16}\]  

• Example:

  Add \[\frac{10}{9}\] and \[\frac{9}{10}\].   Solution: \[\frac{10}{9}=\frac{10}{9}\times \frac{10}{10}=\frac{100}{90}\]   \[\frac{9}{10}=\frac{9}{10}\times \frac{9}{9}=\frac{81}{90}\]   Therefore, their sum= \[\frac{100}{90}+\frac{81}{90}=\frac{100+81}{90}=\frac{181}{90}\]   Subtraction of Fractions                                                     _ Make the denominator of each fraction same by multiplying a suitable number to the numerator and denominator of both fractions. The common denominator is the denominator of resultant fraction more...

  Decimals and Its Operations   Decimals A fraction with the denominator as power of 10 (like 10,100, 1000 etc.) is called decimal. It is expressed as the numbers with a point in between, called decimal point. In other words, decimal consists of two parts which are separated by a decimal point.  

• Example:

2.564, 0.0023, 3.2565, 5431.23 are decimals.   Expanded Form of Decimals Expanded form of a decimal represents the addition of place values of the digits, respective to their positions in the decimal.  

• Example:

Write the expanded form of the decimal 69.4756.   Solution: \[60+9+\frac{4}{10}+\frac{7}{100}+\frac{5}{1000}+\frac{6}{10000}\]  

• Example:

Write the decimal 0.99 in expanded form.   Solution: \[\frac{9}{10}+\frac{9}{100}\]   Decimal Places The number of digits placed in right to the point of a decimal is called the decimal places of that decimal.  

• Example: The decimal more...

  Geometrical Figures   Introduction We observe different types of figures around us. They are in different shapes. In this chapter we will discuss about different types of geometrical figures such as line, angles etc. Point To show a particular location, a dot (.) is placed over it, that dot is known as point. Example:   In the above figure point A represents\[\frac{1}{3}\], point B represents\[\frac{2}{3}\], and point C represents 1. Line Segment Line segment is defined as the shortest distance between two fixed points. For example   It is denoted as \[\overline{AB}\].   Example: How many line segments are there in the figure?       (a) 2                              (b) 4 (c) 8                              (d) 16 (e) None of these Answer more...

  Area, Perimetre and Volume of Geometrical Figures   Perimeter Perimeter is referred as the length of the boundary line, which surrounds the area occupied by a geometrical shape.  

• Example:

Find the perimeter of the following figure.                                                                          Solution: Perimeter of the figure = \[4\text{ }cm+3\text{ }cm+4\text{ }cm+2.5\text{ }cm+5\text{ }cm+5\text{ }cm\]\[=23.50\text{ }cm.\]   Perimeter of the Triangles A triangles has three sides. Perimeter of a triangle is the sum of its all the three sides.   Perimeter of the triangle \[ABC=AB+BC+CA\]  

• Example

Find the perimeter of the following triangle.   Solution: Perimeter of the triangle PQR \[\begin{array}{*{35}{l}}    =4\text{ }cm+4.7\text{ }cm+6\text{ }cm  \\    =14.7\text{ }cm  \\ \end{array}\]   Perimeter of the Quadrilateral Perimeter of more...

  Graphical Representation of Data   Introduction You might have seen in the books, newspaper etc, graphs are used to give some valuable information, like people living under poverty line in different states, number of mal- nutritioned child in different Asian countries, number of unemployed people in India, number of uneducated people in a particular state etc. In this chapter we will study about the data and analysis of data with the help of graph.   Data The information, which is in the numeral form, is called data. The data is gathered in various ways. Then it is manipulated and represented on the graph.   Raw Data The initial data that the observer collects himself is called raw data.   Grouped Data When raw data is arranged in a table in order to extract the information contained by it easily, is called grouped data.   Presentation more...

                                                                                     Analogy   Learning Objective

• To get aware of analogy
• Increasing interest about this segment of reasoning.
• Improving the general awareness of Analogy.
• Increasing the word power.

  What is Analogy? Simple meaning of analogy is similarity. But, in terms of reasoning, the meaning of analogy is logical similarity between 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 and 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 more...

  Classification   Learning Objectives

• To get aware of classification.
• Increasing interest about this segment of reasoning.
• Improving the general awareness for solving problems.
• Increasing the word power for solving problems.

  What is Classification? You must have in your mind what classification means. In fact, in classification, we take an element out of some given elements and the element to be taken out is different from the rest of the elements in terms of common properties, shapes, sizes, types, nature, colours, traits etc. In this way the remaining elements form a group and the element that has been taken out is not the member of that group, as this single element does not possess the common quality to be possessed by rest of the elements. For example, if we compare the animals like lion, cow, tiger, panther, bear and wolf, then we find more...