Learning on calculation pi

Introduction:-

In this lesson let me help on how to calculate pi ╥ (sometimes written pi) is a mathematical constant whose value is the ratio of any circle’s circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle’s area to the square of its radius

* pi is a dimensionless quantity.
* pi is an irrational number.
* pi is an transcendental number.
* Decimal notation of pi is 3.141593.
* Fraction notation of pi is [ 22/7.]

There are many formula's in the mathematics and science, which engage pi and pi calculation. This also helps us on examples of symbols

Help on Percentage Formula

Today let me try to help you on one among the important formula in math that is percentage formula with out which math is incomplete.

The formula for percentage is the following and it should be easy to use:




We will take examples to illustrate.Let us start with the formula on the left

An important thing to remember: Cross multiply

It means to multiply the numerator of one fraction by the denominator of the other fraction. This could also help us on working out percentages

Example :

25 % of 200 is____

In this problem, of = 200, is = ?, and % = 25

We get:

is/200 = 25/100

Since is in an unknown, you can replace it by y to make the problem more familiar

y/200 = 25/100

Cross multiply to get y × 100 = 200 × 25

y × 100 = 5000

Divide 5000 by 100 to get y

Since 5000/100 = 50, y = 50

So, 25 % of 200 is 50

Introduction to Isosceles trapezoid

Introduction to Isosceles trapezoid:

In this section let me help you on isosceles trapezoid. Isosceles trapezoid is one of the type of quadrilateral with a line of symmetry bisecting one pair of opposite sides, make it automatically a trapezoid .Isosceles trapezoid a two-dimensional figure produced by relating four segments endpoint to endpoint with each segment intersecting exactly two others. Isosceles trapezoid also has four sides and four angles.

Sum of interior angle of any polygon is (n-2) *180o. Here isosceles trapezoid has four sides so interior angle is (4-2)*180o = 360o.Exterior angle of any polygon is 360o so the exterior angle of a quadrilateral is 360 degree. In this article we shall discuss about isosceles trapezoid.This could also help us on online fraction calculator.


The diagonals of an isosceles trapezoid are same. Diagonals divide each other into segments of the same length. The isosceles trapezoid PQRS has diagonals PR and QS have the same length (PR = QS).Intersect the diagonals at point O and diagonals are divide each other in segments of the same length (PO = SO and QO = RO).

Help on Arithmetic Progression.

Introduction for Arithmetic progression:

There are two types of progressions .They are arithmetic and geometric progression. An Arithmetic progression which consists of the sequence of numbers and the terms except the first can be obtained by adding one number to its preceding number. Arithmetic progression is denoted as two consecutive numbers arrangement of progression which is constant.
Examples for Arithmetic Progression

Example 1:

The sequence terms of an A.P. 6, 1, –4...Find the 10 th term.

Solution:

Consider the A.P in the form a, a + d, a + 2d, ...

Here, a = 6, d = 1 – 6 = –5, n = 12

t_n = a + (n–1) d

t₁₀ = 6 + (10 – 1) (–5) = 6 + 9 x (–5) = 6 – 45 = – 39

:. The 12th term is –39. This could also help us on elements and compounds

There are three types of Progression in math,

• Arithmetic progression
• Geometric progression
• Harmonic progression

Introduction of coordinate plane graph paper

Introduction of coordinate plane graph paper:

In this section let me help you on coordinate plane graph paper. In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links.

A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. This could also help us on touch math worksheets

The mathematical images like square, pentagon, hexagon, and rectangle can be easily plotted in the coordinate planes.

Help on Conditional Probability

Conditional Probability

The conditional probability of an event B will be the probability that the event will occur given the knowledge that an event A has already occurred. This probability is written P(B|A), notation for the probability of B given A. In the case where events A and B are independent to the conditional probability of event B given event A is simply the probability of event B, that is P(B)..

Let us consider the events A and B are not independent, then the probability of the intersection of A and B (the probability that both events occur) is defined by

P(A and B) = P(A)P(B|A). This will also help us on how to calculate pi

From this definition, the conditional probability P(B|A) is easily obtained by dividing by P(A):

P(B|A)= P(A and B)/ P(A)

This expression is only valid when P(A) is greater than 0.

calculating probability

Calculating Probability concepts and probability theorems is an interesting topic to debate with. The word Probability is something which we use on day today conversation.

In everyday life, we come across statements such as
(1) It will probably rain today.
(2) I doubt that he will pass the test.
(3) Most probably, Kavita will stand first in the annual examination.
(4) Chances are high that the prices of diesel will go up.
(5) There is a 50-50 chance of India winning a toss in today’s match. This will also help us on how to calculate probability

The words ‘probably’, ‘doubt’, ‘most probably’, ‘chances’, etc., used in the statements above involve an element of uncertainty. For example, in (1), ‘probably rain’ will mean it may rain or may not rain today. We are predicting rain today based on our past experience when it rained under similar conditions.

Problems on Circumference

Introduction on Circumference:

Circles are simple closed curves which divide the plane into two regions, an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure (also known as the perimeter) or to the whole figure including its interior.

Circumference of a Circle:

The diagrammatic representation showing circumference of circle is shown:

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The Circumference of a circle can be calculated using the following formula:

Circumference = 2 ╥ r or ╥ d

where r ----> radius of circle

d ----> diameter of circle , r = d/2

Example Problems for Finding Circumference of Circle:

Following is the sample Problem on Circumference

1) Find the Circumference of a circle with radius 20 cm. Use 22/7 as pi value.

Solution:

Circumference of a circle = 2 ╥r

= 2 (22/7) 20

= 2 (3.14) 20

= 125.6 cm

Introduction for free 3rd grade math:

When we study about 3^rd grade math help we find may interesting topics to look in. In algebra basic arithmetic operation (addition, subtraction, multiplication, and division) generally used in day to day life. In these articles we are going to discuss about free 3rd grade math. Addition (+) defined as adding the two numbers. Subtraction (-) defined as the inverse of addition. Also helps in simplifying algebraic expressions.

3rd grade math – Addition example problems:

Following are the few examples on 3^rd grade math

Example 1:

Adding the given values

89775 – 16654

Solution:

89775

16654 (+)

-----------

106429

----------

So, the final answer is 106429

Example 2:

If there are 192 tickets in a box and Joshua puts 49 more tickets inside, how many tickets are in the box?

Solution:

If there are 192 tickets in a box and Joshua puts 49 more tickets inside,

= 192 + 49

= 241 tickets

241 tickets are in the box.

Fractions Problems on Addition and Subtraction

Before we read about Fractions Problems on Addition and Subtraction... Let me help you understand what is all about Fractions and how is it connected to Addition and Subtraction.

What is Fraction: -

A fraction is a number that is the portion or part of a whole. Key to understanding fractions is understanding how to represent part of the whole. Sometimes the whole will be a pizza, a measuring cup, a bar and it is important to understand what the part is each time the whole is different.

When starting with fractions, begin by focusing on 1/2 and the 1/4 before moving into equivalent fractions and using the 4 operations with fractions (adding, subtracting, multiplying and dividing)

Let me also show you one example on fractions problems on addition and subtraction.

Question -

Multiply the fractions and and reduce the final answer if possible

Solution:-

Given we need to multiply the fractions and 70/5 and 30/5

Fractions can be multiplied using this formula a.c/b.d

Here a = 70, b = 5, c= 30, d= 5.

= a.c/b.d

= 70.30/5.5 by solving it we get

= 2100/25

It can be reduced further as

= 84

Note on Subtracting Integers

Subtracting Integers

Before we start with subtraction Integers, let us review the terms of Subtraction.

Minuend: The first number from which the second number must be subtracted is called the minuend.

Subtrahend: The second number that is the number that has to be subtracted is called as the subtrahend.

Difference: The answer of subtraction.

To subtract Integers, all we have to do is to add the minuend and the opposite of the subtrahend. Remember that opposite of 5 is -5 and that -9 is 9!

Step 1: Change the sign of the subtrahend. If the subtrahend is positive, then make it negative and if it is negative change it to positive.

Step 2: Change the subtraction sign to addition

Step 3: Follow the rules of addition of Integers.

Addition of Integers

1. If both the numbers have same sign, then add the absolute values and give the common sign to the sum.

2. If the numbers are of opposite signs, then find the difference of the absolute values and give the sign of the number with greater absolute value.

There can be six possible cases.

Case 1: Both the minuend and subtrahend are positive. Like 9 – (+4)

Case 2: Both the minuend and subtrahend are negative. Like -9 – (-4)

Case 3: Minuend is positive and the subtrahend is negative. Like 9 – (-4)

Case 4: Minuend is negative and the subtrahend is positive. Like -9 – (+4)

Case 5: Minuend is zero. Like 0 – (4) or 0 – (-4)

Case 6: Subtrahend is zero. Like 4 – 0 or -4 – 0

Subtraction of Integers can be performed on a number line or using Models like counters or just by following the rules or steps.

Examples

Example 1: Follow rules of subtraction to solve 15 – (-7)

Solution: Step 1: Change the sign of the second number (subtrahend). The opposite of -7 is +7. So -7 is changed to +7

Step 2: Change the subtraction sign to addition. 15 – (-7) = 15 + 7

Step 3: Follow the rules of addition of Integers.

Since both the numbers are positive, we have to add them up and the answer is also positive.

15 + 7 = 22