6th Class

 Whole Numbers      

• Counting numbers are called natural numbers. Natural numbers are represented by N

\[\therefore \]N\[=\]{1,2,3,4,.........} The least natural number is 1. The greatest natural number does not exist as there is no end for natural numbers.  

• Natural numbers along with 0 are called whole numbers.

Whole numbers are represented by W. \[\therefore \]W= {0, 1, 2, 3, 4,……} The least whole number is 0. The greatest whole number does not exist as there is no end for whole numbers.  

• Successor: A number which comes immediately after a given number is called its successor.

Successor = given number + 1  

• Predecessor: A number which comes immediately before a given number is called its
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 Playing with Numbers      

• A factor of a number is an exact divisor of that number.

 

• A number is said to be a multiple of any of its factors.

e.g.. We know that 35 = 1\[\times \]35 and 35 = 5 \[\times \] 7. This shows that each of the numbers 1, 5, 7 and 35 divides 35 exactly. Therefore 1, 5, 7 and 35 are all factors of 35 and 35 is a multiple of each one of the numbers 1, 5, 7 and 35.  

• All multiples of 2 are called even numbers.

e.g., 2, 4, 6,8,10, etc.  

• Numbers which are not multiples of 2 are called odd numbers.

e.g., more...

 Basic Geometrical Ideas      

• Point: A dot marked on a paper with the sharp tip of a pencil is called a point.

     

• A point is denoted by a single capital letter such as A, B, C etc. A point has only a position.

 

• Line: A countless number of points placed closely form a line. It extends indefinitely on both sides.

Two points on a line determine it. A line is denoted as\[\overleftrightarrow{~AB}\].  

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 Understanding Elementary Shapes      

• 1 Complete angle\[=\text{ }{{360}^{o}}\], 1 Straight angle =\[={{180}^{o}}\]; 1 Right angle =\[{{90}^{o}}\]; Zero angle = \[{{0}^{o}}\]

1 Revolution = 1 Complete angle 1 Straight angle \[=\frac{1}{2}\](Complete angle)\[=\frac{1}{2}\]\[\times \] \[{{360}^{o}}\]= \[{{180}^{o}}\]  

• (i) Acute Angle: An angle between \[{{0}^{o}}\]and \[{{90}^{o}}\] is called an acute angle.

(ii) Obtuse Angle: An angle between \[{{90}^{o}}\]and \[{{180}^{o}}\]is called an obtuse angle. (iii) Reflex Angle: An angle between \[{{180}^{o}}\]and \[{{360}^{o}}\]is called a reflex angle.   more...

Integers      

• The set of positive numbers, 0 and negative numbers is called the set of integers.

The set of integers is denoted by I or Z. Z ={.....,-3,-2,-1, 0,1,2,3,......}  

• Natural numbers are contained in the whole numbers. Therefore, N (= W.)

   

• Whole numbers are contained in the integers.

Therefore, We Z.  

• Negative numbers are placed at the bottom of 0 on the vertical number line. Zero is neither positive nor negative.

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Fractions      

• A fraction is a part of a whole.

 

• In the fraction \[\frac{6}{7}\] ,6 is called the numerator and 7 is called the denominator.

 

• The denominator is the number of equal parts into which a whole is divided.

 

• The numerator is the number of parts considered of the whole.

 

• Types of fractions

Like fractions: Fractions with the same denominators. e.g., \[\frac{4}{5},\frac{6}{5},\frac{3}{5}\]   Unlike fractions: Fractions with different denominators, e.g.,\[\frac{1}{2},\frac{9}{4},\frac{3}{7}\] Proper fractions: Fractions in which the denominator is greater than the numerator. e.g.,\[\frac{2}{9},\frac{5}{6},\frac{2}{3}\] Improper fractions: Fractions in which the numerator is greater than or equal to the denominator. e.g., \[\frac{9}{2},\frac{6}{5},\frac{3}{2},\frac{7}{7}\] Mixed fractions: Fractions with a whole number part more...

 Decimals      

• The number expressed in decimal form are called decimal numbers or simply decimals.

e.g., 5.8, 19.63, 7.269, 0.058, etc.,  

• A decimal number has two parts, namely

(i) Whole-number part and           (ii) Decimal part These parts are separated by a dot (.) called the decimal point.  

• Place value chart of a decimal number:

e.g., Write 236.784 in place value chart.