Category: Class 6

Students can go through AP Board 6th Class Maths Notes Chapter 11 Perimeter and Area to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 11 Perimeter and Area

→ Perimeter: The perimeter of a polygon is sum of all its sides.
The perimeter of an equilateral triangle is P = 3 × side
The perimeter of a rectangle P = 2 (length + breadth)
And its area A = length × breadth A = l × b
The perimeter of a square is P = 4 × side And its area A = side × side (or)
A = s × s The circumference of a circle C = 2πr where r is the radius of the circle.

→ Area: The region occupied by a plane figure is called its area.
To find the area of a complex figure, we divide the given shape into the combination of rectangles, squares and triangles where ever necessary.

Students can go through AP Board 6th Class Maths Notes Chapter 10 Practical Geometry to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 10 Practical Geometry

→ The above are the components we see in a geometry box. They are pair of set squares, protractor, graduated ruler, compasses and the divider.

→ Graduated ruler: A scale is used to draw straight edges of given length. It is also used to measure the lengths of the given line segments. A scale is also called a graduated ruler.

→ Compass: A compass is used to draw a circle of given radius. Sometimes we draw only a part of a circle which is called an arc. A compass is used in the construction of a line segment of given length, a perpendicular to a given line, given angle and in many more geometrical shapes.

→ Divider: A divider is used to measure the lengths of straight line segments and curved lines. It is also used to compare the lengths of two line segments.

→ Set squares: The pair of set squares is used to draw the pair of parallel lines.

→ Perpendicular bisector: The perpendicular bisector of a given line segment is the line which divides the given line segment into two equal parts at right angles.

→ Angle bisector: Angle bisector is a ray which divides the given angle into two equal parts.

Students can go through AP Board 6th Class Maths Notes Chapter 9 2D-3D Shapes to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 9 2D-3D Shapes

→ Space: A plane is a set of all points which extends in all directions endlessly in three dimensions.

→ Plane: A plane is a smooth surface which extends in all directions in two dimensions.
Eg: The surfaces of a table, the surface of a blackboard are examples for part of a plane.

→ Polygon: A simple closed figure formed by line segments is called a polygon.

→ Triangles:
A simple closed figure formed by three line segments is called a triangle.
The line segments \(\overline{\mathrm{AB}}\), \(\overline{\mathrm{BC}}\) & \(\overline{\mathrm{CA}}\) are called the sides of the triangle.

A triangle contains three sides.
A triangle contains three interior angles ∠A, ∠B & ∠C and three vertices A, B & C

→ A triangle divides the plane on which it lies into three sets of points.
1. Interior points on the triangle
2. Points on the triangle
3. Points in the exterior of the triangle

→ Quadrilateral:
A simple closed figure bounded by four line segments is called a quadrilateral.

→ Circle: If we draw a boundary along the edge of a round shaped object, then we get the following shape. The shape is called a circle. The length of the curved edge is called circumference. “A” is called the centre of the circle.

→ Chord: A line segment joining any points ‘A’ & ‘B’ on the circumference of the circle is called a chord. DE and FG are chords of the circle.

→ Diameter: The longest chord passing through the centre of the circle is called a diameter. AC & DG are diameters.

→ Arc: A part of the circle is called an arc.

CIRCLE TERMINOLOGY

→ Circumference: The distance around a circle.

→ Radius: The distance from the centre of a circle to the circumference. Half the diameter.

→ Diameter: A straight line passing through the centre of a circle to touch both sides of the circumference. Twice
as long as the radius.

→ Chord: A straight line joining two points on the circumference of a circle. The diameter is a special kind of chord.

→ Arc: A section of the circumference.

→ Sector: A section of a circle, bounded by two radii and an arc.

→ Segment: A section of a circle, bounded by a chord and an arc.

→ Tangent: A straight line touching the circumference once at a given point.

→ A circle divides the plane on which it lies into three parts.

1. Interior points
2. Exterior points
3. Points on the circle

→ BASIC PARTS OF A CIRCLE

• Interior of a Circle
  points A, B, C
• ON the circle
  point D
• Exterior of a Circle
  points E, F, G

→ The region in the interior of a circle enclosed by its boundary is called circular region.

→ Symmetry: Some figures appear beautiful because of their symmetry. Such shapes can be divided into two identical parts along a straight line which is called line of symmetry. A symmetrical figure may have more than one line of symmetry.

→ English alphabet – lines of symmetry:

3-D shapes:
→ NAMES OF 3D SHAPES

→ 3D SHAPES IN REAL – LIFE

→ Cube: A cube is a 3-dimensional figure. It has 6-identical faces. Each face of a cube is a square. All its sides are equal.

→ Cuboid: A cuboid is three a dimensional figure having three measures length, breadth and height.

→ Cylinder: A cylinder has circular faces at its both ends. It has two measures namely radius of the base and height of the cylinder.

→ Cone: A cone is a 3-d figure having curved surface with a circular base.

→ Prism and a Pyramid:

A Prism is a 3-d shape with parallelograms as its lateral surfaces. A Pyramid is a 3-d figure with triangles as its lateral surfaces.
A Prism / Pyramid may have a triangle/ square/rectangle…as its base.
A Prism/Pyramid is named as per its base.

→ Euler’s formula:
The number of faces (F), vertices (V) and edges (E) of a polyhedron are related by this formula: F + V = E + 2

Looking at the box to the right, calculate the number of edges:
Faces = 6
Vertices = 8
F + V = E + 2
6 + 8 = E + 2
14 = E + 2
E = 12

Students can go through AP Board 6th Class Maths Notes Chapter 8 Basic Geometric Concepts to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 8 Basic Geometric Concepts

 

→ Line: A line is a straight edge which extends endlessly on both sides. A line has no width.

Line is a set of infinite points extending in two opposite directions endlessly. A line is represented by any two points lying on it.
The above line is represented by \(\overline{\mathrm{AB}}\)
A line can also be represented by a lower case letter of English alphabet such as l.
A line has no end points.
A line may not be always straight. Sometimes it is curved as shown in the figure.

It is called a curved line.

→ Ray: A ray is a straight edge starting from a point and extends only in one direction endlessly.

A ray has no width.
A ray has only one end point. The end point is called the vertex of the ray. A ray is represented by the initial point and any arbitrary point in the direction in which it extends. Here the ray is \(\overline{\mathrm{AB}}\).

→ Line segment: A part of a line is called a line segment.
A line segment has two ends.

A line segment is represented by its two end points. Line segment \(\overline{\mathrm{AB}}\).
Recall that a small dot made by a shape edged pencil may be treated as a point.

→ History:
Geometry has a long and rich historical nature. The term ‘GEOMETRY’ is derived from the greek word ‘GEOMETRON’. ‘GEO’ means earth and ‘METRON’ means measurement. So, Geometry is the mathematics related to the earth’s measurement.
Early geometry was a collection Of empirically discovered principles concerning lengths, angles, areas and volumes which were developed to meet some practical need in surveying, construction, astronomy and various crafts.
In the ancient India Aryabhatta, Brahmagupta were some of the Indian Mathematicians who contributed their works in geometry.

→ Intersecting lines: Two lines meeting at a single point are called intersecting lines. The point is called the point of intersection. Two lines l & m intersecting at the point A.

→ Concurrent lines: Three or more lines passing through a single point are called concurrent lines and the point is called the point of concurrence.

Here the lines l, m & n are meeting at a single point O and hence are concurrent lines. The point of concurrence is O.

→ Parallel lines: Two lines are said to be parallel, if they never meet each other.

The distance between two parallel lines is constant throughout their length.
Here the lines l & m are parallel to one another.

→ Perpendicular lines: Two lines are said to be perpendicular, if they are straight to one another. Two adjacent sides of a paper are perpendicular to each other.

→ Measuring the length of a line segment: To measure the length of a given line segment we use a graduated scale or a divider in the instrument box.
Adjust the scale along the line segment and find the readings at the two end points. The difference of readings gives us the length of the line segment.
Adjust the two pointed legs of the divider on the two end points of the given line segment. Now measure the width between the legs on a graduated scale.
Measuring line segments in Centimeters

→ Angle: A figure formed by two rays with a common end point is called an angle.

The common end point is called the vertex of the angle. The two rays are called the two arms of the angle.

→ Sexagesimal system : A system related to number sixty is called sexagesimal system. We use this system in measuring angles.

Full angle is also called complete angle.
We use protractor to measure the angle.

Students can go through AP Board 6th Class Maths Notes Chapter 7 Introduction to Algebra to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 7 Introduction to Algebra

→ Expressions: 7 + 14 – 6 & 12 – 8 + 56 +…. such mathematical sentences are called numerical expressions.

When we try to make some general patterns we need to involve some constants and variables in the statements.
Eg: If three line segments are needed to construct a triangle, then the number of line segments needed to construct n-number of triangles is 3 × n.

Here the number of line segments required for a given number of triangles = 3x The value of the numeral is fixed and called a constant and x can take any value from 1, 2, 3, 4, 5, 6,…

So we say that x value is not fixed and varies and hence x is a variable.
If four line segments are needed to construct a square, then the number of line segments needed to construct n-number of squares is 4 × n.

Here the number of line segments required for a given number of triangles = 4x The value of the numeral 4 is fixed and called a constant and x can take any value from 1, 2, 3, 4, 5, 6, ….

So we say that x value is not fixed and varies and hence x is a variable.

→ A variable is an alphabet used to stand for a number.
A variable can like any value; it has no fixed value, but it is a number. We can perform binary operation such as addition, subtraction, multiplication and divisions on them.
Eg: If x is a variable,
then 5 more than x is x + 5
5 less than x is x – 5
5 times x is 5x
One fifth of x is \(\frac{1}{5}\).

→ A variable allows us to express relations in any special situation. Variables allow us to express many common rules of Geometry and Arithmetic in a more general way.
Eg: If the side of a square is s,
then its Area A = s × s
Perimeter = 4 × s
If the length and breadth of a rectangle are l & b, then its
Area A = l × b
Perimeter is P = 2 × (l + b).
The general form of an odd number = 2 × n + 1 = 2n + 1;
Even number = 2 × n = 2n
In the above we have number of line segments required for a given number of triangles is 3 × n.
Suppose the number of triangles is 4, then 4n = 12, this is an equation.
An expression involving the equality (=) symbol is called an equation.
The part l value of the expression on the left of the equality (=), is called LEFT HAND SIDE or L.H.S.
The part l value of the expression on the right of the equality (=), is called RIGHT HAND SIDE or R.H.S.
If the L.H.S. is not equal to R.H.S., then we do not get an equation.
Eg : 8 + 13 ≠ 15
2 + 3 < 9 – 2
56 + 3 > 25 + 5

→ Solution or root of an equation:
Solution of an equation is the value of the variable for which L.H.S and R.H.S are equal. The solution is also called the root of the equation.
Eg : Solution of x – 8 = 4 is x = 12
For the equation x + 3 = 8, x = 7 is not a solution.
We find the solution of an equation by Trial & Error method.
Trial -error method is a process in which the solution of an equation is found by taking some arbitrary values for the variable.

Students can go through AP Board 6th Class Maths Notes Chapter 6 Basic Arithmetic to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 6 Basic Arithmetic

→ If a comparison is made by finding the difference between two quantities, it is called comparison by difference.
Eg: Age of Harshita is 11 years and age of Srija is 8 years. Harshita is (11 – 8 = 3) 3 years older than Srija or Srija is 3 years younger than Harshita.

→ If a comparison is made by division it makes more sense than the comparison made by taking the difference.
Eg: If cost a key pad cell phone is Rs. 3000 and another smart phone is Rs. 15000, then the cost of the second phone is five times the cost of the first phone.

→ Ratio: Comparison of two quantities of the same type by virtue of division is called ratio. Eg: The weight of Ramu is 24 kg and the weight of the Gopi is 36 kg., then the ratio of weights is 24/36. It can also be written as 24:36 and read as 24 is to 36.
The ratio of two numbers ‘a’ and ‘b’ (b ≠ 0) is a ÷ b or a/b or \(\frac{a}{b}\) and is denoted as a : b and is read as a is to b.
In the ratio a : b the quantities a and b are called the terms of the ratio.
In the ratio a : b the quantity a is called the first term or antecedent and b is called the second term or the consequent of the ratio.
The value of a fraction remains the same if the numerator and the denominators are multiplied or divided by the same non-zero number so is the ratio.
That is if the first term and the second term of a ratio are multiplied or divided by . the same non-zero number.
3 : 4 = 3 × 5 : 4 × 5 = 15 : 20
Also 36 : 24 = 36 – 4 : 24 – 4 = 9 : 6.

→ Ratio in the simplest form or in the lowest terms:
A ratio a : b is said to be in its simplest form if its terms have no factors in common other than 1. A ratio in the simplest form is also called the ratio in its lowest terms. Generally ratios are expressed in their lowest terms.
To express a given ratio in its simplest term, we cancel H.C.F. from both its terms. To find the ratio of two terms, we express the both terms in the same units.
Eg: Ratio of 3 hours and 120 minutes is 3 : 2 (as 120 minutes = 2 hours) or 180 : 120 (as 3 hours = 180 minutes)
A ratio has no units or it is independent of units used in the quantities compared. The order of terms in a ratio a : b is important a : b ≠ b : a.

→ Equivalent ratio:
A ratio obtained by multiplying or dividing the antecedent and consequent of a given ratio by the same number is called its equivalent ratio.
Eg: 3 : 4 = 3 × 5 : 4 × 5 = 15 : 20. Here 3 : 4 & 15 : 20 are called equivalent ratios.
Also 36 : 24 = 36 ÷ 4 : 24 ÷ 4 = 9 : 6. Here 36 : 24 & 9 : 6 are called equivalent ratios.

→ Comparison of ratios: To compare two ratios
a) First express them as fractions
b) Now convert them to like fractions
c) Compare the like fractions

→ Proportion:
If two ratios are equal, then the four terms of these ratios are said to be in proportion. If a : b = c : d, then a, b, c and d are said to be in proportion.
This is represented as a : b :: c : d and read as a is b is as c is d.
The equality of ratios is called proportion.
Conversely in the proportion a : b :: c : d , the terms a and d are called extremes and b and c are called means.
If four quantities are in proportion, then
Product of extremes = Product of means .
If a : b :: c : d, then a × d = b × c
From this we have

→ Unitary method:
The method in which first we find the value of one unit and then the value of required number of units is known as unitary method.
Eg: If the cost of 8 books Rs.96, then find the cost of 15 books.
Cost of one book = 96/8 = 12 Cost of 15 books = 12 × 15 = 180
Distance travelled in a given time = speed × time From this we have

→ Percentage:
The word per cent means for every hundred or out of hundred. The word percentage is derived from the Latin language. The % symbol is uses to represent percent.
Eg: 5% is read as five percent
5% = \(\frac{5}{100}\) = 0.05
38% = \(\frac{38}{100}\) = 0.38

→ To convert a percentage into a fraction:
a) Drop the % symbol
b) Divide the number by 100
Eg: 25% = \(\frac{25}{100}\) = 0.25 = \(\frac{1}{4}\)

→ To convert a fraction into percentage:
a) Assign the percentage symbol %
b) Multiply the given fraction with 100
Eg: \(\frac{3}{4}\) = \(\frac{3}{4}\) × 100% = 75% = 0.75

Students can go through AP Board 6th Class Maths Notes Chapter 5 Fractions and Decimals to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 5 Fractions and Decimals

→ Fraction: A fraction is a numerical representation of apart of a whole. The whole may be a single object or a group of objects.
Eg: \(\frac{4}{7}\).
The fraction \(\frac{4}{7}\) represents four out of seven.
In the fraction \(\frac{4}{7}\), 4 is called the numerator and 7 is called the denominator.

→ Proper fraction: A fraction in which the numerator is less than its denominator is called a proper fraction.
Eg: \(\frac{1}{7}\), \(\frac{2}{5}\), \(\frac{3}{11}\), …..
All proper fractions are less than 1.

→ Improper fraction: A fraction in which the numerator is greater than its denominator is called an improper fraction.
Eg: \(\frac{5}{11}\), \(\frac{4}{7}\), \(\frac{2}{3}\),….
All improper fractions are greater than or equal to 1.

→ Mixed fraction: A mixed fraction is a combination of a whole number and a proper fraction.
Fraction in lowest terms: A fraction is said to be in its lowest terms if the numerator and the denominator have no factors in common other than 1.
Eg: \(\frac{2}{11}\), \(\frac{3}{7}\), \(\frac{18}{25}\),……
Equivalent fractions: Two fractions are said to be equivalent if they have same numerators and same denominators respectively when expressed in their lowest terms.
Eg : \(\frac{2}{5}\) & \(\frac{8}{20}\)
Equivalent fractions have the same value.

→ Like fractions:
Fractions with the same denominators are called like fractions
Eg: \(\frac{3}{13}\), \(\frac{4}{13}\), \(\frac{7}{13}\), \(\frac{21}{13}\), ….

→ Un-like fractions:
Fractions with different denominators are called like fractions.
Eg: \(\frac{7}{11}\), \(\frac{3}{5}\), \(\frac{9}{17}\), ….

→ Comparison of fractions:

• Out of two fractions with the same denominators (like fractions), the fraction with the smallest numerator is smaller than the other.
• Similarly out of two fractions with the same denominators (like fractions), the fraction with the greatest numerator is greater than the other.
  Eg: \(\frac{2}{11}\) < \(\frac{5}{11}\) \(\frac{9}{17}\) > \(\frac{4}{17}\)
• Out of two given fractions with the same numerator, the fraction with smaller denominator is greater than the other.
• Similarly out of two given fractions with the same numerator, the fraction with greater denominator is smaller than the other.
  Eg: \(\frac{11}{2}\) > \(\frac{11}{5}\) \(\frac{13}{8}\) < \(\frac{13}{11}\)
• To compare unlike fractions, convert them in to like fractions with L.C.M. as the same denominators, and then compare the like fractions.
  Eg: \(\frac{2}{3}\) and \(\frac{4}{5}\).
  LCM of 2, 5 is 15
  \(\frac{2}{3}\) = \(\frac{10}{15}\) \(\frac{4}{5}\) = \(\frac{12}{15}\)
  Now \(\frac{10}{15}\) < \(\frac{12}{15}\) there by \(\frac{2}{3}\) < \(\frac{4}{5}\)

→ Addition and subtraction of like fractions:

• To add like fractions we add their numerators while retaining the common denominator. Eg: \(\frac{5}{7}\) + \(\frac{2}{7}\) = 5 + \(\frac{2}{7}\) = \(\frac{7}{7}\)
• To subtract like fractions we subtract their numerators while retaining the common denominator.
  Eg: \(\frac{6}{13}\) – \(\frac{2}{13}\) = 6 – \(\frac{2}{13}\) = \(\frac{4}{13}\)

→ Addition and subtraction of un-like fractions:

• Convert the given unlike fractions in to like fractions, (denominator = LCM of given denominators)
• Now add or subtract as we do in case of like fractions.
• To multiply a fraction with a whole number, first multiply the numerator of the fraction by the whole number while keeping the denominator the same.
  Eg: \(\frac{3}{4}\) × 5 = 3 × \(\frac{5}{4}\) = \(\frac{15}{4}\)
  8 × \(\frac{2}{3}\) = 8 × \(\frac{2}{3}\) = \(\frac{16}{3}\)

→ Multiplication of two fractions = product of numerators/product of denominators
Eg: \(\frac{5}{6}\) × \(\frac{4}{9}\) = 5 × \(\frac{4}{6}\) × 9 = \(\frac{20}{54}\)

• The product of any two proper fractions is always less than each of its fraction.
  Eg: \(\frac{1}{5}\) × \(\frac{2}{7}\) = \(\frac{2}{35}\), \(\frac{2}{35}\) < \(\frac{1}{5}\) & \(\frac{2}{35}\) < \(\frac{2}{7}\)
• The product of any two improper fractions is always greater than each of its fraction.
  Eg: \(\frac{7}{3}\) × \(\frac{5}{2}\) = \(\frac{35}{6}\) \(\frac{7}{3}\) < \(\frac{35}{6}\) \(\frac{5}{2}\) < \(\frac{35}{6}\)
• The product of a proper fraction and an improper fraction is always greater than its proper fraction and less than its improper fraction.
  Eg: \(\frac{2}{5}\) × \(\frac{7}{4}\) = \(\frac{14}{20}\) \(\frac{2}{5}\) < \(\frac{14}{20}\) < \(\frac{7}{4}\)

→ Reciprocal of a fraction: A fraction obtained by interchanging the numerator and the denominator of a given fraction is called its reciprocal fraction.
Eg: Reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\)
\(\frac{1}{a}\) of b means \(\frac{1}{a}\) × b = \(\frac{b}{a}\)

→ Division of a whole number by a fraction: To divide a whole number by a fraction we multiply the given whole number by the reciprocal of the given fraction.
Eg: 5 ÷ \(\frac{3}{4}\) = 5 × \(\frac{20}{5}\) = \(\frac{4}{5}\)

• Any two non-zero numbers whose product is equal to 1 are called reciprocals to each other.
  Eg: \(\frac{3}{7}\) and \(\frac{7}{3}\) are reciprocals to each other.
• To divide a whole number by a mixed fraction, first convert the mixed fraction into improper fraction and then multiply the whole number with the reciprocal of the improper fraction.
  Eg: 7 ÷ 3\(\frac{2}{5}\) = 7 ÷ \(\frac{17}{5}\) = 7 × \(\frac{5}{17}\) = \(\frac{35}{17}\)

→ Division of a fraction by a whole number:

• To divide a fraction by a whole number we multiply the given fraction by the reciprocal of the given whole number.
  Eg: \(\frac{5}{4}\) ÷ 3 = \(\frac{5}{4}\) × \(\frac{1}{3}\) = \(\frac{5}{12}\)
• To divide a mixed fraction by a whole number, first convert the mixed fraction into an improper fraction and then multiply the improper fraction by the reciprocal of whole number.
  Eg : 4\(\frac{3}{4}\) ÷ 8 = \(\frac{19}{4}\) × \(\frac{1}{8}\) = \(\frac{19}{32}\)

→ Division of a fraction by another fraction: To divide a fraction by another fraction, we multiply the first fraction with the reciprocal of the second fraction.
E.g: \(\frac{3}{5}\) ÷ \(\frac{7}{11}\) = \(\frac{3}{5}\) × \(\frac{11}{7}\) = \(\frac{33}{35}\)

→ Decimal numbers or Decimal fractions: A decimal is a way of expressing a fraction.
The fraction \(\frac{1}{10}\) is written as 0.1 in decimal form.

Examples for decimal numbers: 0.7, 0.4, 0.23, ..etc The decimal number 0.7 is read as zero point seven.
The decimal number 5.8 is read as five point eight.
The dot or the point between the two digits is called the decimal point.
The number of digits after decimal point is called the number of decimal places. Decimal places of 5.247 is 3.
The decimal point separates a decimal number into two parts. The number on its left as integer part and the digits on its right as decimal part.
The decimal part of a decimal number is always less than 1. As we move from left to right each decimal place decreases by tenth of its previous value.
The decimal places after the decimal point are (\(\frac{1}{10}\)-tenths), (\(\frac{1}{100}\)-hundreths), (\(\frac{1}{1000}\)-thousandths) and so on.

These are also called the place values of the decimal part.
If we divide a whole number into ten equal parts each part of the whole represents tenths part. \(\frac{1}{10}\)
If we divide a whole number into hundred equal parts each part of the whole represents hundredths part. \(\frac{1}{100}\)
If we divide a whole number into thousand equal parts each part of the whole represents thousandths part. \(\frac{1}{1000}\)

→ Converting fractions into decimals and vice versa:
Fractions with denominators 10, 100, 1000 can be easily converted into decimals by placing decimal point in the numerator accordingly.

• If the denominator is 10, then we place the decimal point in the numerator after one digit from RHS. The number of decimal places is equal to 1.
  Eg: \(\frac{256}{10}\) = 25.6
• If the denominator is 100, then we place the decimal point in the numerator after two digits from RHS. The number of decimal places is equal to two.
  Eg: \(\frac{256}{100}\) = 2.56
• If the denominator is 1000, then we place the decimal point in the numerator after three digits from RHS, The number of decimal places is equal to three.
  Eg: \(\frac{256}{1000}\) = 0.256 and read as zero point two five six.

→ Decimals Can Also be converted into Conversion of simple fractions into decimal fractions:
To convert simple fractions into decimal numbers:
To convert simple fractions into decimal numbers first convert the denominators to 10/100/1000 accordingly and then place the decimal point in the numerator as required.
Eg: \(\frac{23}{2}\) = 23 × \(\frac{5}{10}\) = \(\frac{115}{10}\) = 11.5
\(\frac{7}{4}\) = 7 × \(\frac{25}{100}\) = \(\frac{175}{100}\) = 1.75
\(\frac{3}{5}\) = 3 × \(\frac{2}{10}\) = \(\frac{6}{10}\) = 0.6
Writing zeroes at the end of a decimal number does not change its value.
Eg: 5.2 = 5.20 = 5.200 = 5.2000 and so on
Like and unlike decimal fractions:
Decimals having the same number of decimal places are called like decimals.
Eg: 3.2,5.6,4.8.
Decimals having the different number of decimal places are called unlike decimals. Eg : 5.23, 8.3, 4.214
Unlike decimals can be converted into like decimals by converting them into equivalent decimals.
Eg: 2.7 & 6.54
2.7= 2.70 and now-2.70 and 6.54 are like decimals.

→ Comparing and ordering of decimals:
To compare the given decimals
a) First convert them to like decimals.
b) Now compare the integer / whole number part. The number with greater whole part is greater than the other.
c) If the whole / integer parts are equal, then compare the tenths digits. The number with greater tenths digit is greater than the other.
d) If the tenths digits are also equal, then compare the hundredths digits. The number with greater hundredths digit is greater than the other.
e) If the hundredths digits are also equal, then compare the thousandths digits. The number with greater thousandths digit is greater than the other.
Eg : 54.235 and 54.238
54.235 < 54.238

→ Addition and subtraction of decimal fractions:
To add or subtract the given decimal fractions first convert them into like decimals. Now add / subtract the digits in the corresponding place values.

→ Uses of decimals: Decimal fractions are used in expressing money, distance, weight and capacity.

Students can go through AP Board 6th Class Maths Notes Chapter 4 Integers to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 4 Integers

→ Positive numbers: All numbers which are greater than zero are called positive numbers {1, 2, 3, …..}

→ Negative numbers: In our real life we come across many situations where in we have to use numbers whose value is less than zero; such numbers are called negative numbers.
Example: Very low temperature, loss in a business, depth below a surface, etc. Negative numbers are represented by the minus symbol

→ Zero is neither a negative number nor a positive number.

→ Integers: The set of positive numbers, zero along with the set of negative numbers are called Integers. The set of integers is denoted by I or Z.
I = Z = {…. 4, -3, -2, -1, 0, 1, 2, 3,…..}

→ Historical Notes: Brahma Gupta (598 – 670 AD), Indian mathematician first used a special sign (-) for negative numbers and stated rules for operations on negative numbers.
The letter ”Z” was first used by the Germans because the word for Integers in the language is Zehlen which means NUMBER.

→ Representation of Integers on a number line:

On a number line all negative numbers lie on the left side of zero. All positive numbers lie on right side of zero.
A number line extends on either side endlessly.
All whole numbers are called non-negative integers.
The natural numbers are called positive integers.

On a number, of the given two numbers the number on LHS is always less than the number on the RHS.

On a number line as we move from left to right the value of numbers goes on increasing and vice versa.
A number line can be written in a vertical direction as given below.

Students can go through AP Board 6th Class Maths Notes Chapter 3 HCF and LCM to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 3 HCF and LCM

→ Divisibility Rules:
A divisibility rule is a process by which we can determine whether a given number is completely divisible by other given number or not without performing actual division.
Reasons behind the rules:
Our number system is based on base 10 system. Every place value increases by 10-times as move from right to left.

→ Divisibility rule for 2: In the above place value table except ones place all other places namely 100/1000/10 000…. are completely divisible by 2. So for divisibility by 2 we need to check the unit digit only.
A number is divisible by 2 if it has any of the digits 0, 2, 4 or 8 in its units place.
In other words all even numbers are divisible by 2.

→ Divisibility rule for 3:
10/3 → not divisible
100/3 → not divisible
1000/3 → not divisible and it goes on..
But in all the cases, the remainder is 1. As such if the number 56817 is divided by 3 we get remainder, 5, 6, 8, 1 and 7 respectively. The sum of these remainders 5 + 6 + 8 + 1 + 7 = 27 is divisible by 3 as is the number is divisible by 3.
In other words if the sum of the digits of a given number is divisible by 3, then the given number is also divisible by 3.
The digital root of natural number is the single digit value obtained by repeated process of summing digits.

Example: The digital root of 325698 is 3 + 2 + 5 + 6 + 9 + 8 = 33 = 3 + 3 = 6
Note: While adding the digits of a number we can ignore 9’s or combinations of digits summing up to 9.

Example: The digital root of 87459634572 is
By dropping (4+5), (9), (6+3), (4+5), (7+2), the remaining digits are 8 & 7. From these digits eliminate 9 that is 8 + 7 – 9 = 15 – 9 = 6
Therefore the digital root of 87459634572 is 6. Hence divisible by 3.

Now add these digits to get the total remainder. If this remainder is completely divisible by 3, then the given number is also divisible by 3.

Divisibility rule of 3 will add the digits and then check if its divisible by 3. This is applicable for numbers which leaves remainder 1 when 10 is divided by that number.

→ Divisibility rule for 4: In the place value table starting from 100, all other higher places namely 1000/10 000/100 000, …etc. are all completely divisible by 4. So we need to check the digits in ten’s and unit’s place for divisibility by 4.

A number is divisible by 4 if the number formed by the digits in its ten’s place and unit’s place taken in the same order is divisible by 4 and also zeros on both places.

Example: Is the number 87534 divisible by 4?
Number formed by last two digits 34 is not divisible by 4 and hence the given number is also not divisible by 4.

Example : Is the number 779956 divisible by 4?
Number formed by last two digits 56 is divisible by 4 and hence the given number is also divisible by 4.

→ Divisibility rule for 5: In the place value table starting from 10, all other higher places namely 10/100/1000/10000/1 00 000, ..’etc. are all completely divisible by 5. So we need to check the digits in unit’s place for divisibility by 5.
A number is divisible by 5 if the number ends in either zero of 5.

Example: Is the number 779956 divisible 5?
The digit in unit’s place is 6, so it is not divisible by 5.

Example: Is the number 77995 divisible by 5?
The digit in unit’s place is 5, so it is divisible by 5.

Example: Is the number 779950 divisible by 5?
The digit in unit’s place is 0, so it is divisible by 5.

→ Divisibility rule for 6 : If a number is divisible by both 2 and 3, then it is also divisible by 6.
Example: Is the number 612432 divisible by 6?
As the given number is an even number it is divisible by 2.
Also the digital root of the number is 3, it is divisible by 6.
Hence it is divisible by 6.
In other words if a number is divisible by two relatively prime numbers, then their product also divides the given number.

→ Divisibility rule for 8: In the place value table starting from 1000, all other higher places namely 10 000/1 00 000…etc., are all completely divisible by 8. So we need to check the digits in hundred’s, ten’s and unit’s place for divisibility by 8.
A number is divisible by 8 if the number formed by the digits in its hundred’s place, ten’s place and unit’s place taken in the same order is divisible by 8, are also zeros on three places.
Example: Is the number 875344 divisible by 8?
Number formed by last three digits 344 is divisible by 8 and hence the given number is also divisible by 8.

→ Divisibility rule for 9: The rule is same as rule for 3
10/9 → not divisible
100/9 → not. divisible
1000/9 → not divisible and it goes on ..
But in all the cases, the remainder is 1. As such if the number 56817 is divided by 9 we get remainder, 5, 6, 8, 1 and 7 respectively. The sum of these remainders 5 + 6 + 8 + 1 + 7 = 27 is divisible by 9 as is the number is divisible by 3.

In other words if the sum of the digits of a given number is divisible by 9, then the given number is also divisible by 9.
The digital root of natural number is the single digit value obtained by repeated process of summing digits.

Example: The digital root of 325698 is 3 + 2 + 5 + 6 + 9 + 8 = 33 = 3 + 3 = 6
Note: While adding the digits of a number we can ignore 9’s or combinations of digits summing up to 9.

Example: Is the number 7854963 divisible by 9?
The digital root of the given number is 7 + 8 + 5 + 4 + 9 + 6 + 3 = 42 = 4 + 2 = 6, not divisible by 9.

→ Divisibility rule for 10: In the place value table starting from 10, all other higher places namely 10/100/1000/10000/100000…etc., are all completely divisible by 10. So we need to check the digits in unit’s place for divisibility by 10.
A number is divisible by 10 if the number ends in zero.
Example: Is the number 779956 divisible 10?
The digit in unit’s place is 6, so it is not divisible by 10.

Example: Is the number 779950 divisible 10?
The digit in unit’s place is 0, so it is divisible by 10.

→ Divisibility rule for 11: A number is divisible by 11, if the difference between the sum of digits at even places and the sum of digits at odd place is either zero or a multiple of 11.
Example: Is the number 52487 divisible 11?
Sum of the digits at odd places = 7 + 4 + 5 = 16 Sum of the digits at even places = 8 + 2 = 10 Difference = 16 – 10 = 6, not divisible by 11.
Note: If two numbers are divisible by a given number, then their sum, difference and the product are also divisible by that number.

→ Factor: A factor of a number is an exact divisor of that number.
Example: 15 = 5 × 3, here 5 divides 15 completely and 3 divides 15 completely. As such 1, 3, 5, 15 are factors of 15.
Also 15 = 1 × 15. It means 1 is a factor of every number and every number is a factor of itself.
Every factor of a number is less than or equal to the number.
Perfect number: A number for which the sum of all its factors is equal to twice the number is called a perfect number.
Example: 6 = 1 × 6
= 2 × 3, here 1, 2,3 and 6 are factors whose sum is (1 + 2 + 3 + 6 = 12) 12, twice the given number 6. So 6 is a perfect number.
6, 28, 496, 8128…… are perfect numbers. Euclid has given a formula to derive perfect
numbers.
If q is a prime of the form 2p – 1 where p is a prime, then q(q+1)/2 is an even perfect number.

→ Multiple: Multiples of a given number can be obtained by multiplying the given number with natural numbers i.e. 1, 2, 3, 4, …. etc.
Example: Multiple of 6 are:
= 6 × 1, 6 × 2, 6 × 3, 6 × 4, …..
= 6, 12, 18, 24, …..

→ Prime number: Numbers having only two factors namely one and itself are called prime numbers.
A prime number is a whole number that has exactly two factors, 1 and itself.
Example: 2, 3, 5, 7, 11,
All the above numbers have only two factors namely 1 and itself.
We can write infinitely many prime numbers.
2 is the only even prime number. Also 2 is the smallest prime number.

→ Composite number: Numbers having more than two factors are called composite numbers.
Example: 4, 6, 8, 9, ….
1 is neither a prime number nor a composite number.
The Sieve of Eratosthenes is an ancient algorithm that can help us find all prime numbers up to any given limit.

→ How does the Sieve of Eratosthenes work?
The following example illustrates how the Sieve of Eratosthenes, can be used to find all the prime numbers that are less than 100.
Step 1: Write the numbers from 1. to 100 in ten rows as shown below.
Step 2: Cross out 1 as 1 is neither a prime nor a composite number.
Step 3: Circle 2 and cross out all the multiples of 2. (2, 4, 6, 8, 10, 12, ….)
Step 4: Circle 3 and cross out all the multiples of 3. (3, 6, 9, 12, 15, 18, ….)
Step 5: Circle 5 and cross out all the multiples of 5. (5, 10. 15, 20, 25, ….)
Step 6: Circle 7 and cross out all multiples of 7. (7, 14, 21. 28, 35, ….)
Circle all the numbers that are not crossed out and they are the required prime numbers less than 100.

Alternate method:
Finding prime numbers upto 100

First arrange the numbers from 1 to 100 in a table as shown above.
Enter 6 numbers in each row until the last number 100 is reached.
First we select a number and we strike off all the multiples of it.
Start with 2 which is greater than 1.
Round off number 2 and strike off entire column until the end.
Similarly strike off 4th column and 6th column as they are divisible by 2.
Now round off next number 3 and strike off entire column until end.
The number 4 is already gone.
Now round off next number 5 and strike off numbers in inclined fashion as shown in the figure (they are all divisible by 5). When striking off ends in some row, start again striking off with number in another end which is divisible by 5. New striking off line should be parallel to previous strike off line as. shown in the figure.
The number 6 is already gone.
Now round off number 7 and strike off numbers as we did in case of number 5.
8,9,10 are also gone.
Stop at this point.
Count all remaining numbers. Answer will be 25.

→ Prime numbers
There are 25 prime numbers less than 100.
These are:

What if we go above 100? Around 400 BC the Greek mathematician. Euclid, proved that there are infinitely many prime numbers.

→ Co-primes: Two numbers are said to be co-prime if they have no factors in common. Example: (2, 9), (25, 28)
Any two consecutive numbers always form a pair of co-prime numbers.
Example: (7 & 8), (21 & 22), …..
Co-prime numbers are also called relatively prime number to one another.
Example: 3, 5, 8, 47 are relatively prime to one another/co-prime to each other.

→ Twin primes: Two prime numbers are said to be twin primes, if they differ by 2. Example: (3, 5), (5, 7), (11, 13), …etc.

→ Prime factorization: The process of expressing the given number as the product of prime numbers is called prime factorization.
Example: Prime factorization of 24 is
24 = 2 × 12 = 2 × 2 × 6
= 2 × 2 × 2 × 3, this way is unique.
Every number can be expressed as product of primes in a unique manner. We can factorize a given number in to product of primes in two methods. They are
a) Division method
b) Factor tree method

→ Common factors: The set of all factors which divides all the given numbers are called their common factors.
Example: Common factors to 24, 36 & 48 are 1, 2, 3, 4, 6 & 12
Factors of 24 = 1, 2, 3, 4, 6, 8, 12 & 24
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18 & 36
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 & 48
Common factors to 24, 36 & 48 are 1, 2, 3, 4, 6 & 12
We can see that among their common factors 12 is the highest common factor. It is called H.C.F. of the given numbers. So H.C.F. of 24, 36 & 48 is 12.

→ H.C.F./G.C.D : The highest common factor or the greatest common divisor of given numbers is the greatest of their common factors.
H.C.F. of given two or more numbers can be found in two ways.
a) By prime factorization
b) By continued division
H.C.F. of any two consecutive numbers is always 1.
H.C.F. of relatively prime/co-prime numbers is always 1.
H.C.F. of any two consecutive even numbers is always 2.
H.C.F. of any two consecutive odd numbers is always 1.

→ Common multiples:
Multiples of 8: 8, 16, 24, 32, 40, 48, ….
Multiples of 12: 12, 24, 36, 48, ….
Multiples.common to 8 & 12: 24, 48; 72, 96, ….
Least among the common multiple is 24. This is called L.C.M. of 8 & 12. The number of common multiples of given two or more numbers is infinite, as such greatest common multiple cannot be determined.

→ L.C.M.: The least common multiple of two or more numbers is the smallest natural number among their common multiples.
L.C.M. of given numbers can be found by the
a) Method of prime factorization.
b) Division method.
L.C.M. of any two consecutive numbers is always equal to their product.
L.C.M. of 8 & 9 is 8 × 9 = 72
L.C.M. of co-prime numbers is always equal to their product.
L.C.M. of 8 & 15 is 8 × 15 = 120

→ Relation between the L.C.M. & H.C.F:
For a given two numbers N₁ & N₂, the product of the numbers is equal to the product of their L.C.M.(L) & H.C.F.(H)
N₁ × N₂ = L × H

Students can go through AP Board 6th Class Maths Notes Chapter 2 Whole Numbers to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 2 Whole Numbers

→ Natural numbers: The numbers which we use for counting are called Natural numbers N= {1, 2, 3, 4, 5, 6,…} .

→ Successor: Every natural number has a successor, which is one more than it. Example : Successor of 15 is 15 + 1 = 16

→ Predecessor: Every natural number has a predecessor except 0. Predecessor of a number is one less than it.
Example: Predecessor of 56 is 56 – 1 = 55

→ Whole numbers: The natural numbers along with zero forms the set of Whole numbers.
W = {0, 1, 2, 3, 4, 5, 6,…}

• Every whole number has a successor and every whole number has a predecessor except zero.
• Every natural number is a whole number and every whole number is a natural number except zero.
• The smallest natural number is 1.
• The smallest whole number is 0.
• Addition, subtraction and multiplication can be represented on a number line.

→ Closure property: Sum of any two whole numbers is always a whole number.
Example : 5 + 3 = 8, a whole number.
This is called closure property of whole numbers w.r.t. addition.

→ Closure property: Product of any two whole numbers is always a whole number. Example : 5 × 3 = 15, a whole number.
This is called closure property of whole numbers w.r.t. multiplication.
In other words whole numbers are closed under addition and multiplication.
But whole numbers are not closed under subtraction and division.
Example: 7 – 12, is not a whole number.
9 ÷ 14, is not a whole number.
Division by zero is not defined.
Example: 5 ÷ 0, is not defined

→ Commutative property: Sum of any two whole numbers taken in any order is always same.
Example: 5 + 3 = 3 + 5 = 8
This is called commutative property of whole numbers w.r.t. addition.

→ Commutative property: Product of any two whole numbers taken in any order is always same.
Example: 5 × 3 = 3 × 5 = 15
This is called commutative property of whole numbers w.r.t. addition.
In other words whole numbers are commutative w.r.t. addition and multiplication. But whole numbers are not commutative w.r.t. subtraction and division.
Example: 4 – 9 ≠ 9 – 4 and 8 ÷ 11 ≠ 11 ÷ 8

→ Associative property: The sum of any three whole numbers taken in any or der is always same.
Example : 5 + (8 + 3) = (5 + 8) + 3 =16
This is called associative property of whole numbers w.r.t. addition.

→ Associative property: The product of any three whole numbers taken in any order is always same.
Example : 5 × (8 × 3) = (5 × 8) × 3 = 120
This is called associative property of whole numbers w.r.t. multiplication.
In other words whole numbers are associative w.r.t. addition and multiplication.
But whole numbers are not associative w.r.t. subtraction and division.
Example : 5 – (8 – 3) ≠ (5 – 8) – 3
: 5 ÷ (8 ÷ 3) ≠ (5 ÷ 8) ÷ 3

→ Distributive property of multiplication over addition:
(Example: 5 × (8 + 3) = (5 × 8) + (5 × 3) = 55

→ Additive identity: If zero is added to any whole number, then the result is the number itself.- Here zero is called the additive identity.
Example: 5 + 0 = 5, 7 + 0 = 7, 0 + 9 = 9 and so on.

→ Multiplicative identity: If any whole number is multiplied by 1, then the result is the number itself. Here one is called the multiplicative identity.
Example: 5 × 1 = 5, 7 × 1 = 7, 1 × 9 = 9 and so on.
If we represent the number 1 as a (.) dot, then a whole number can be represented either as an array of a triangle or a square.
The triangular numbers are 3, 6, 10, 15, 21, 28, ……. etc.

The square numbers are 4, 9, 16, 25, 36, …… etc.

→ Multiplication by 9/99/999/9999….etc.
74 × 99 = (74 – 1)/(9 – 7)(10 – 4) = 73/26
256 × 999 = (256 – 1)/(9 – 2)(9 – 5)(10 – 6) = 255/744
4267 × 9999 = (4267 – 1)/(9 – 4)(9 – 2)(9 – 6)(10 – 7) = 4266/5733
Here the number of 9’s in the multiplier is equal to number of digits in the multiplicand.
Answer has two parts: LHS/RHS
LHS: (Multiplicand-1)
RHS: Subtract all digits from 9 but the last digit from 10

Students can go through AP Board 6th Class Maths Notes Chapter 1 Numbers All Around us to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 1 Numbers All Around us

HISTORICAL NOTES:
INDIA
→ Zero: Ancient Indians invented zero. The ancient Indian Bhakshali manuscript depicts zero, which is the recorded evidence of zero which we use today. We can also find the circular symbol ‘o’ to represent zero, the earliest epigraphical evidence at Chaturbhuj temple, Gwalior, Madhya Pradesh.

→ Number system:
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are called digits. Every number is written using these digits. We can write infinitely many numbers using these digits.

→ Reading numbers:
There are two commonly used methods of numeration.
i) Indian system of numeration also called Hindu-Arabic system of numeration.
ii) International system of numeration. ‘
We read numbers using place value of digits. The place values enable us to read numbers easily and clearly.

→ Indian system:


The digits in a number are separated by commas as per the above table i.e., starting from right we place a comma after three digits and thereafter we place a comma after every two digits.

In other words, to read numbers in the Hindu-Arabic system of numeration digits are divided into periods namely units/thousands/lakhs/crores and so on .from right to left.

The value of each digit in a number depends upon its place in the given number.
As we move from right to left the place value increases by 10 times to its previous place.

Example: 75698425
Placing commas at correct positions we have
7, 56, 98, 425: 7 crores 56 lakhs 98 thousand 4 hundred and twenty five : Seven crores fifty six lakhs ninety eight thousand four hundred and twenty five

Example: 600540283
Placing commas at correct positions we have
60, 05, 40, 283: 60 crores 05 lakhs 40 thousand 2 hundred and eighty three : Sixty crores five lakhs forty thousand two hundred and eighty three

→ International system of numeration:
The digits in a number are separated by commas as per the table below i.e., starting from right we place a comma after three digits.
In other words, to read numbers in the International system of numeration digits are divided into periods namely units/thousands/millions/billions and so on from right to left.

Example: 52463801221
Placing commas at correct positions we have
52, 463, 801, 221: 52 billions 463 millions 801 thousands 2 hundred and twenty one: Fifty two billions four hundred sixty three millions eight hundred one thousands two hundred and twenty one

Example: 956785020412
Placing commas at correct positions we have
956, 785, 020, 412: 956 billions 785 millions 020 thousands 4 hundred and twelve : Nine hundred fifty six billions seven hundred eighty five millions twenty thousands four hundred and twelve

→ Comparison between Hindu-Arabic & International systems of numeration:

Indian	international
1 lakh	100 thousands
10 lakhs	1 million
1 crore.	10 millions
10 crores	100 millions
100 crores	1 billion

Also we have higher place values mentioned in Vedic numbering system.
Eka/dasa/sata/sahasra/ayuta/laksa/niyuta/koti/sanku/mahasanku/vrnda/mahavrnda/padma/mahapadma/kharva/mahakharva/samudra/ogha/mahaugha…etc

→ Large numbers used in daily life situations:

• Areas of large countries when expressed in sq.km
• To measure water flow at dams
• To measure the weights of products like food grains
• To measure the population

Face value: The face value of a digit in a number is the digit itself.
Place value of digits:The place value of a digit in a number is the product of its face, value and the place value in which it is written in the number.
Example: Face value and the place value of 5 in the number 485796 is Face value = 5
Place value = 5 x 1000 = 5000

→ Comparison of numbers:
To compare two numbers
i) Align the digits by place value
ii) Compare the digits in each place, starting from the greatest place Ascending order : Ascending order means arrangement of numbers from the smallest to the greatest.
Descending order : Descending order means the arrangement of numbers from the greatest to the smallest.
Example : 52, 235; 75, 222 ; 86, 412 ; 1, 25, 896 ; 18, 259 ; 35, 986
Ascending order: 18, 259 ; 35,986 ; 52,235 ; 75, 222 ; 86,412 & 1,25,896 Descending order: 1, 25, 896 ; 86,412 ; 75,222 ; 52,235 ; 35,986 & 18,259

→ Rounding off and Estimation of numbers:
Rules to round off a number to a given place:

Example:
Round off 6879124 to its nearest tens, hundreds, thousands, ten thousands and lakhs.
68,79,124 when rounded off to tens: 68, 79, 120
68,79,124 when rounded off to hundreds: 68, 79, 100
68,79,124 when rounded off to thousands: 68, 79, 000
68,79,124 when rounded off to ten thousands: 68, 80, 000
68,79,124 when rounded off to lakhs: 69, 00, 000
68,79,124 when rounded off to ten lakhs: 70, 00, 000

Students can go through Andhra Pradesh SCERT AP State Board Syllabus 6th Class Maths Notes Pdf in English Medium and Telugu Medium to understand and remember the concepts easily. Besides, with our AP State 6th Class Maths Notes students can have a complete revision of the subject effectively while focusing on the important chapters and topics. Students can also read AP Board 6th Class Maths Solutions for exam preparation.

AP State Board Syllabus 6th Class Maths Notes

• Chapter 1 Numbers All Around us Notes
• Chapter 2 Whole Numbers Notes
• Chapter 3 HCF & LCM Notes
• Chapter 4 Integers Notes
• Chapter 5 Fractions and Decimals Notes
• Chapter 6 Basic Arithmetic Notes
• Chapter 7 Introduction to Algebra Notes
• Chapter 8 Basic Geometric Concepts Notes
• Chapter 9 2D-3D Shapes Notes
• Chapter 10 Practical Geometry Notes
• Chapter 11 Perimeter and Area Notes
• Chapter 12 Data Handling Notes

These AP State Board Syllabus 6th Class Maths Notes provide an extra edge and help students to boost their self-confidence before appearing for their final examinations.