Geometrical Figures
Introduction
In our day to day life we come across a number of objects. All the objects has a specific shape and size. We recognize a number of objects by their shape. Therefore, to know about the objects and of their shapes is very important. In this chapter we will study about the shapes of different geometrical figures.
Point
To show a particular location, a dot (.) is placed over it, that dot is known as a point.
\[\centerdot \,\xrightarrow{{}}A\]
A is a point
Line Segment
Line segment is defined as the shortest distance between two fixed points. It has fixed length.

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Area and Perimetre
Introduction
In the previous chapter we have studied about the shape and size of some geometrical figures. In this chapter we will study about area and perimetre of some close geometrical figures.
Area
Area is referred as the surface occupied by the geometrical shapes
Area of a Triangle
Area of a triangle \[=\frac{1}{2}\times Base\times Height\]
Where base is one side of a triangle and height is the length of altitude drawn from opposite vertex on the given base.
Area of the triangle ABC\[=\frac{1}{2}\times AD\times BC\]
Where BC is the base and AD is the height.

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Data and Handling
Introduction
In our day to day life, time to time we come across graphs while reading or watching news etc.
The graphs are prepared with the help of data. Data is collected through survey or other means. The data can be arranged in a specific order as per our need by using table. In this chapter we will study about some of the graphical representation of data, how to make the graphs and how to extract information’s contained by the graphs.
Data
The information which is collected in the form of numerals is called data.
Raw Data
The initial data that the observer collects himself is called raw data.
Grouped Data
To extract the information’s contained in the data easily, the data is arranged in ascending or descending order using tables.
Graphical Representation of Data
Data can be represented graphically by using Pictographs, Bar graphs, Pie charts etc. In this chapter we will learn about Pictographs and Bar graphs.
Pictograph
When the data is represented on the graph with the help of pictures the graph is known as Pictograph.

Onerepresents one six.
(a) Against which country Sehwag more...

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Australia | |

Pakistan | |

South Africa | |

Newzealand | |

England |

Number Sense and Numerations
Numbers
Numbers are mathematical objects by which we express date, time, position, quantity etc.
Writing and Reading Numbers
Numbers are written using symbols or digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) called numerals. For example, 3564 is a numeral in which four digits (3, 5, 6, and 4) are used. In this section, we will study two types of numeration.
(i)Indian system of numeration.
(ii) International system of numeration.
Indian System of Numeration
This method of numeration is based on the place value chart. This system is also known as Hindu - Arabic system.
Given below is the Indian place value chart

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Roman Numerals
Introduction
The numerals we use is commonly known as Indo-Arabic Numerals. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9__ __ __ __etc. are example of Indo - Arabic numerals. In ancient time Romans developed a system of numerations (numbering) which is known as Roman Numerals. I, II, III, IV, V, VI, VII, VIII, IX, ——— etc. are example of Roman Numerals.
Roman numerals are formed by using the following symbols:

Roman Numeral | Hindu-Arabic Numeral |

I | 1 |

V | 5 |

X | 10 |

L | 50 |

C | more...
Operation on Numbers Addition and Subtraction
Introduction
In our daily life, we come across many activities when we need to apply the method of addition and subtraction. We are aware of numbers and number system. Now we will discuss two simple algebraic operations, that is, addition and subtraction.
Addition
Addition is one of the very common arithmetic operation used in mathematics. Addition is the operation to know the total quantity, when two or more than two quantities are taken together.
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Operation on Numbers Multiplication and Division
Introduction
In this chapter we will study two important arithmetic operations "multiplication and division". Multiplication is repeated addition of a specific quantity, whereas division is a distribution of a quantity into some equal parts. Let us study them.
Multiplication
When a quantity is added to itself for a number of times, we use operation of multiplication to find the resulting quantity.
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Factors and Multiples
Factors of a Number
All the numbers, which divide a certain number exactly, without leaving a remainder are called factors of that number.
For example:
\[\Rightarrow \]1, 2, 3, 4, 6 and 12 are factors of 12.
Note: Factors of a number always include 1 and the number itself.
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Fractions and Decimals
Fraction
Fraction is used to indicate a part of a whole. Fraction is written as\[\frac{a}{b}\].
The top number in a fraction is called numerator and the bottom number is called denominator of the fraction. Hence in the given example 'a' is numerator and 'b' is denominator. Look at the shaded part in the following figures which has been represented by fractions:
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Unitary Method
Unitary Method
Unitary method is a method under which a calculation is carried out to find the value of the number of items, by first finding the value of one item.
From daily life experience, we know that when we increase the quantity of articles, their cost increases and when we decrease the quantity of articles, their cost decreases. In other words, more articles have more value and less articles have less value.
Note: In unitary method:
(i) To get more value we multiply.
(ii) To get less value we divide.
To solve the problems by unitary method we follow two steps:
Step 1: Get the value of a single unit.
Step 2: Then find the value of required units.
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