Fraction

Let Us Learn About Fraction

A Fraction means a part of a group or a region or a whole.

Fraction is defined as an element of quotient field. Fraction can be represented as " x / y " here fraction variable 'x' denotes the value called as numerator and fraction variable 'y' denotes the value called as denominator and the denominator 'y' is not equal to zero.

Thus the fraction is classified as follows,

• Simple fraction / common fraction
  
• Proper fraction
• Improper fraction
• Complex fraction
• Mixed number

The word fraction has been derived from the Latin word fractus, means broken.

Fraction is a type of number which is used to represent the whole by the part .

Example :

1 is a whole nuber but it could be represented as follows

1 = 1/2 + 1/2 , where 1/2 is a fraction .

1 = 1/4 + 3/4 , where 1/4 and 3/4 is a fraction

The above two examples signifies what is the fraction .

Common Fraction and Proper Fraction

Common Fractions :

common Fraction is a fraction which consists of the numerator and the denominator , in which both are natural numbers. But the denominator should neither be equal to zero nor 1 .

Example :

3/4 ,

where 3 is the numerator , 4 is the denominator and both are natural numbers .

8/5

where 8 is the numerator , 5 is the denominator and both are natural numbers .

Proper fractions:

Proper fraction is a fraction whose value is less than 1. It is a type of fraction in which the denominator is greater than numerator .

Example

4/6

here 4 < 6 ie numerator is less than denominator and the value of it is 0.67

5/7

here 5 < 7 ie numerator is less than denominator and the value is 0.71

Improper Fraction and the Mixed Fraction

Improper Fraction :

Improper fraction is a fraction whose value is greater than or equal to 1 . It is a type of fraction in which numerator is greater than denominator .

Example

5/4

here the numerator is greater than denominator . And the value of the factor is 1.25

7/3

here the numerator is greater than numerator . And the value of the factor is 2.34

Mixed Fraction :

Mixed fraction is a type of fraction which consists of two tpes of numbers in it namely whole number and the proper fraction in it . Its value is greater than 1 .

Example

51/4 .

here 5 is a whole number and 1/4 is the fractional part . its value is 21/4 = 5.25

32/5

here 3 is a whole number and 2/5 is the fractional part . Its value is 17/5 = 3.4

Introduction of Fraction Minus Fraction:

Fractions are defined as the part of an object that means one and half, three by fourth like that at earliest days. Nowadays the fractions consist of numerator and denominator. For example the fraction 4/5 Here 4 is the numerator and 5 is the denominator. We can add, subtract, multiple and divide the fractions with certain procedure. Here we see how u minus the fraction from fraction.

Steps for Fraction Minus Fraction:

Step 1: Get the denominator of the fractions are the same.

Step 2: Minus the numerator of the fraction when the denominators of the fractions are same.

Step 3: after minus the numerator of the fraction, if possible the fraction can simplify. These are the procedure to minus fraction from fraction.

The fractions with regrouping are nothing but the fractions which has the formation of the understanding and easy recalling of the particular fractions can be done through the fractions. The regrouping fractions are made along the process that had done in the way which has the computation of the process. The computations of the fractions are done through the regrouping of the fractions.

In Rational:

Simple fraction:

Simple fraction is a fraction, which is composed of both numerator and denominator as whole number.

Examples:

1/5, 2/7, 8/9

Proper fraction:

It is a fraction, which is composed of a numerator less than its denominator, and the value of that fraction is less than one.

Examples:

3/5, 1/8, 24/25

Improper fraction:

Improper fraction is a fraction, where the top number of fraction that the numerator is greater than or equal to its own denominator (bottom number) and the value of that fraction is greater than or equal to one.

Examples:

7/2, 8 /8, 45/23, 123/120

Introduction to proper fraction:

What is a fraction is fraction are a way to represent parts of a whole number . The fraction contain two parts numerator and denominator . The fraction two types proper fraction and improper fraction and also mixed fraction. There are few steps we have to do to make sure we get the correct answer anyone can read and write fractions

· Adding fractions is easy if they have common denominators

· Subtracting fractions with common denominators is a snap.

· doing with improper fractions and mixed numbers doesn’t have to be scary.

·

Ex : 3/4

Proper Fraction Explanation:

If the numerator in a fraction is lesser than the denominator, assuming both are positive (we will deal with harmful signs later in this sheet, the fraction is said to be a Proper Fraction. Proper fraction represents number between 0 and 1.

The base number has always been larger than the top number. The top number, which tells you how many part you have, is called the numerator. The base number, which tells you how many equal part the strip is divided into, is called the denominator. If the top number is lesser than the bottom number we always have what is called a proper fraction. Proper fraction are always less than one value.

Mixed Numbers or Mixed fractions:

Mixed numbers is a fraction which is composed of one whole number part with a fraction part. It can be represented as x y/z.

Examples:

2 3/4, 1 5/7

Complex Fractions:

If a fraction is composed of numerator and denominator as a fraction, it is called complex fractions.

The complex fractions are also called as a rational expression because it has a numerator and denominator with fraction. Otherwise, the overall fraction includes at least one fraction.

Polygon

Let Us Learn About Polygons

Few names of polygons are as follows:

• Triangle or Trigon

This is a three-sided shape that having whole interior angle measurement as 180º.

• Quadrilateral or Tetragon

This is a four-sided shape that having whole inside angle measurement as 360º.

• Pentagon

This is a five-sided shape which contains the whole inside angle measurement as 540º.

The polygon is a closed path. The polygon has the different shapes. The shapes are depends on the number of sides. The Straight lines are form the polygon shapes. The polygons are having more number of straight lines to form the different polygons. Angles of the polygons are varied based on shape of the polygon.

The area of the regular polygon can be written as,

Area = S² N / 4 tan (pi / N).

Here, S = Length of any side, N = Number of side, Pi = 3.14.

Area of the Polygons

1) The given length of side:

Area Shape of polygon = S² N / 4 tan (Pi/N)

Here, S = Side length, N = Number of side, Pi = 3.14.

2) Given the radius(circum radius):

Area shape of polygon = (R² N sin (2Pi/N))/2.

Here, R = Radius of the polygon, N = Num

ber of side, Pi = 3.14.

3) Given the apothem (In radius):

Area Shape of polygon = A² N tan (Pi/N).

Here, A = Apothem length, N = Number of sides.

4) Given the apothem and Length of a side:

Area shape of polygon = A* P / 2.

Here, A = Apothem length, P = Perimeter.

More about Polygon:

Basic diagrammatic representation for polygon is as follows:

Polygon- A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

Regular Polygon- A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.

Quadrilateral- A four-sided polygon. The sum of the angles of a quadrilateral is 360^o.

Rectangle- A four-sided polygon having all right angles. The sum of the angles of a rectangle is 360^o.

Square- A four-sided polygon having equal-length sides meeting at right angles. The sum of the angles of a square is 360^o.

Parallelogram- A four-sided polygon with two pairs of parallel sides. The sum of the angles of a parallelogram is 360^o.

Rhombus- A four-sided polygon having all four sides of equal length. The sum of the angles of a rhombus is 360^o.

Trapezoid- A four-sided polygon having exactly one pair of parallel sides. The two sides that are parallel are called the bases of the trapezoid. The sum of the angles of a trapezoid is 360^o.

.Pentagon- A five-sided polygon. The sum of the angles of a pentagon is 540^o.

Hexagon- A six-sided polygon. The sum of the angles of a hexagon is 720^o.

Octagon- An eight-sided polygon. The sum of the angles of an octagon is 1080^o.

Nonagon- A nine-sided polygon. The sum of the angles of a nonagon is 1260^o.

Decagon- A ten-sided polygon. The sum of the angles of a decagon is 1440^o.

Convex- A figure is convex if every line segment drawn between any two points inside the figure lies entirely inside the figure. A figure that is not convex is called a concave figure.

Area of a square = side x side

= s x s

= s² sq units or units²

Area of a Rectangle = length x width

= l x w

= lw sq units or units²

Area of a Parallelogram= base x height

= b x h

= bh sq units or units²

Area of a Triangle = ½ x base x height

= ½ b h sq units or units²

Area of a Rhombus = base x height

= b x h

= bh sq units or unit²

Area of a Trapezoid = ½ (a+b)h sq units or units²

(Half of the sum of the lengths of the Parallel sides times height)

Polygon

Let Us Learn About Polygon

A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same number of angles as sides.

Polygons can be classified as either convex or concave.

A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon. In a convex polygon, each interior angle measures less than 180 degrees.

Concave polygons "cave-in" to their interiors, creating at least one interior angle greater than 180 degrees (a reflex angle).

Unless otherwise stated, we will be discussing convex polygons.

Listed below are some of the more commonly used polygons.

Types Of Polygon

A polygon is equilateral if all of its sides are of the same length.
A polygon is equiangular if all of its angles are of equal measure.

A regular polygon is a polygon that is both equilateral and equiangular.

Sum of Interior Angles of a Polygon = 180(n-2)

Each interior angle of a "regular" polygon = 180(n-2)/n

Sum exterior angles of any polygon = 360° (using one exterior angle at a vertex)

Each exterior angle (regular polygon) = 360/n

Standard Polygons:

The different standard polygons are:

1. Square

2. Rectangle

3. Parallelogram

4. Triangle

5. Rhombus

6. Trapezium / Trapezoid

Regular Polygon

Definition of Regular Polygon

• A polygon having all its sides equal and all the angles equal is called a Regular Polygon.

More about Regular Polygon

• The measure of each angle of a regular polygon with n sides is given as(n-2) x 180/n degrees.
• A circumscribed circle can be drawn through all the vertices of a regular polygon.