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Introduction:In free triple 3 is an important relation used in trigonometry to solve right angles. This theorem was proposed by Pythagoras, a mathematician. The triangles which satisfy this theorem are said to be standard triangles and the ultimate reason for using this theorem is to find the missing side of the triangle i.e. problems involving triangles. It is one of the most important theorem used in trigonometry, it also holds a very good usage in real time applications. Pythagorean theorem and the commonly used Pythagorean triples are explained in the following sections.

Pythagorean Theorem:Learn solving problems graphical method

According to this theorem, The right angled triangle, the square of the larger side is equal to the sum of the squares of the other two sides need help with TOEFL. In other term it can be also said as the area of square formed by the bigger side is proportional to the sum of the areas of squares formed by the other two sides Gain free Math Knowledge.

Therefore, a² = b² + c²

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Introduction:

Multiplication (symbol "×") is the operation of scaling one number by another and multiplication calculator is very useful. It is one of the four basic elementary arithmetic (the others being addition, subtraction and division).

Because the result by whole numbers can be thought of as consisting of some number of copies of the original, multiplication by whole numbers is equivalent to repeated addition solving math word problems is now very easy;

Example: 3 X 4 (often said as "3 times 4") can be calculated by adding 4 copies of 3 together Need help with Math Linear Algebra Help

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Introduction to triangle geometry calculator:

In mathematics, the triangle geometry calculator is the calculator which is used to find the values of area of the triangle. In the triangle geometry calculator, we are going to find the value of area from the values base and height. In this topic we will discuss about the steps used in the triangle geometry calculator. The detailed explanation about the triangle geometry calculator is given below.

Triangle Geometry Calculator – Steps:

In the triangle geometry calculator, we have use only one formula to find the area of triangle.

The diagram for triangle is given below:

The Geometry definitions and formula used to find the area of triangle is given as ,

Area of triangle = ½ b*h

Steps involved in triangle geometry calculator:

Step 1: Enter the values of base and height in the specific boxes.

Step 2: Press the “calculate” button.

Step 3: Then the area of triangle is shown in the calculator within a minute.

This is were you find Only mathematics

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Introduction to algebra 2 problems :

These included in Algebra Complex numbers, real numbers, matrices, vectors . Arithmetic: 5 + 5 = 5 + 5 the same while representing in Algebra it would look like: x + y = y + x.

Do you face difficulties in solving math problems

While studying algebra 2 answers scale is represented by algebraic equations,same number done on both side of the scale.Find Algebra for all the Grades. The numbers used while study algebra 2 answers are the constant.

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Introduction to conditional probability distribution:

Conditional probability distribution is the kind of distribution & it deals with finding of an event in relation with the another event that occurred already.

In this distribution, they must deal with the two events, one of the two event will be calculated in respect with other. Here they will see some example issues to conditional probability.

In this topic we will illustrate about the solving conditional probability distribution.It also means Probability of an event or outcome based on the occurrence of a previous event or outcome.

For more help with conditional probability examples .Conditional probability is derived by multiplying the probability of the updated probability of the succeeding event by the preceding event .Do you really find Fun learning mathematics

Math Problem Solving

Introduction about kids fraction help:

Let us see some of the fraction issues for kids that can help the kids to understand the idea clearly. The dividing fraction contains quotient, remainder and divider. This is used to dividing the given fractions.

The Subtract fraction is variation of the five fractions .this is the subtracting fractions.The multiplying fractions are multiplying the five fractions.The Adding fraction is sum of the five fractions is called the adding fractions.

Adding the mixed kids fraction help Example:

Find the issue here to add [3 4/6] and [2 5/3]
Solution:

The five fractions are the same denominator that has the lowest number, so to solve a both denominators, for Free fraction help
Step 1:

The L.C.M of denominator 6, 3 is the 6.

Then the general denominator is

Therefore [2 5/3 ] = [2 10/6]
Step 2:

So now our addition issue becomes this

Finally the issue here is to add [3 4/6] and [2 10/6]

The denominators are equal. Therefore to add the fraction numbers

The whole numbers of 3+2 = 5; 10+4 = 14.... Get Math Homework here

Answer is [5 14/6]....

Precalculus help

Introduction grade 4 math:

Solving fractional equations as addition & subtract normal expressions is a royal pain, solving normal equations is simpler. solving fractional equations of addition & subtract is you depart from a normal expression to a normal equation get a whole unusual set of tools to work with. You can be able to multiply both sides of the equation to get rid of the denominators.

Fractional:

Find the answer following equations:

3 ⁄ 2 = x / 2

Solving this equations is x=3

the denominators are equal, so all solved the numerators.

Definition(Fractional):

The bottom part the denominator have several parts the whole is divided into, and the top part the numerator is effective add fractions.

Types of Fractions :

Proper fraction:

In the numerator is less than the denominator .

Example: 1/5 and 5/6 are the example of the proper fractions.

Improper fraction:

The numerator the is better than or equal to the denominator .

Example: 5/7 and 9/8 (nine eighths) are the example of the improper fractions

Mixed fraction:

The entire number & the fraction collective into the one "mixed" number. Start Growing up with Mathematics

Example: 1 1/2 (one and a half) is a mixed fraction

(and also Mixed Number)

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Definition of linear programming problems:
The problem of minimizing or maximizing linear constraints from linear function subject is defined as the linear programming problem. These linear constraints are mayor may not be equalities. That is it may either equality or non equality.
Structure of linear programming problem:
The linear programming problem generally consists of three components:

• Activities of variables and their relationships.
• Objective functions
• The constraints.

Solving a Linear programming Problem :
How to find the solution set is called the feasible region for a set of linear inequalities. These concepts will be used for solving Linear programming Problem and also linear algebra and its applications solutions.
A programming problem consists of Business problem where one faces several limitations causing restrictions. One has to remain within the frame work of these restrictions and optimize his goals. The strategies of doing so successfully, is called solving a programming math_problems.

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Introduction of learning algebra online:

Algebra is the division of arithmetic which treat of the relations and properties of measure by means of letters like x, y, z. and other signs like +, - ,*,/. A division of arithmetic in which signs, regularly letters of the alphabet represent numbers or members of a particular set and are used to represent quantities and to express general relationships that hold for every members of the set. There are many online solvers available to calculate the linear equation.

Learning Algebra Online Equations:

To establish an answer for an equation, use the basic rules of simplifying equations online.

• First estimate all parentheses, exponents, multiplications, divisions, additions, and subtractions in the usual order of operations. When estimate expressions, be careful to use the associative and distributive properties suitably learn algebra online free.
• Combine like terms. This method adding or subtracting variables of the same kind. The expression 3x + 5x simplifies to 8x. The expression 12 - 6 + 2 simplifies to 8.
• Plus some value to every side of the equation.
• Minus every value from each sides of the equation. This is finest complete by addition a negative worth to each side of the equation.
• Multiply equally side of the equation through any number except 0.
• Divide equally side of the equation through any number except 0.
• Growing up with Mathematics is very easy

Math is a Game

Introduction on Properties of Circle
By learning, Circle consists of set of points from middle point. The point from the all points on a circle are equidistant is called the center of the circle, and the distance from that point to the circle is called the radius of the circle. illustration of circles is in single letter, its center. Circle has center point C and a radius of length r.

Properties of Circle:

Let we see about the properties of learning circles:

• The arc of a circle has two points on the circle and all of the points on the circle that lie between those two points.

• Chord is a segment and consists of end points which is on a circle.

• Diameter of circle:

Length of diameter = 2 × length of the radius.

• Circumference of a Circle:

Circumference = 3 × diameter (approx.).
These are the properties of learning circles.
Formulas of learning circles:
The area of circle:
Area of circle = 'pi' * r²
where, r is the radius of the circle.
The diameter of circle:
Diameter of circle = 2 * r.
where, r is radius of the circle.
The circumference of circle:
Circumference of circle = 2* 'pi' *r (or) 'pi' *d.
where,r is the radius of the circle.
d is the diameter of the circle.
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Math is all about calculation

Learning Geometry Problems in Circle.

Parallelogram:
Area of parallelogram = length × base= l × b
Learning geometry problems online :
Find the area of parallelogram, which base is 5 and height is 6
Solution to solve geometry answers:
Given that length of base (b) = 5 cm, length (i) = 6 cm
Area of the parallelogram = b × l
= 5cm × 6 cm
= 30 cm²
Circle:
Area of the circle=π*R*R (R=radius)
Circumference of circle=2*π*R
Learning geometry problem:
Diameter of a circular garden is 9.8 m. find its area.
SOL:
Diameter, d = 9.8 m. Therefore, radius r = 9.8 /2 = 4.9 m
Area of the circle =π*R*R
= 3.14*4.9*4.9
= 75.40 m
I am sure you will find this helpful online geometry homework

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Introduction to Statistics

Here you have studied the classification of given data into ungrouped as well as statistics problem solver grouped frequency distributions. You have also learnt to represent the data pictorially in the form of various graphs such as bar graphs, histograms (including those of varying widths) and frequency polygons. In fact solved statistics answers , you went a step further by studying certain numerical representatives of the ungrouped data, also called measures of central tendency, namely, mean, median and mode. In this statistics homework online, we shall extend the study of these three measures, i.e., mean, median and mode from ungrouped data to that of grouped data. We shall also discuss the concept of cumulative frequency, the cumulative frequency distribution and how to draw cumulative frequency curves, called ogives.

Normal distribution table

Normal distribution table we can study bell curve normal distribution, which figure most significantly in statistical theory and in application. Normal distribution is also called as the Normal probability distribution. Let us see how to calculate normal distribution with the help of normal distribution table. The normal distribution probability looks like a bell shaped curve. Hence it is also known as bell curve normal distribution probability.

Definition of Normal Distribution Probability:

A continuous random variable X is said to follows a normal distribution with parameter μ and σ (or μ and σ2) if the probability functions is
f(x) = (1/ σ 2π) e ^{– ½} ((x – μ)/σ)² ; −∞ <> < ∞, − ∞ < μ < ∞, and σ > 0.
This is the formula which is used to show normal distribution probability table.
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Constants of Normal Distribution:

Mean = μ
Variance = σ2
Standard deviation = σ

The graph of the normal curve is shown above. The shape of the curve is bell. These are the constants which tell how to calculate normal distribution probability by using table.
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Explain Confidence Interval Calculator

Introduction:
     Estimation reliability is indicated by confidence intervals.Confidence level has parameter of interval. Population parameter has some kind of interval estimate. This is called as confidence interval in statistics.We can use a single value. This calculator is mainly used for test the proportions.
                   In Confidence Interval Calculator, If we want to check the sample means we should give the percentage of survey and number of interview updation. Confidence level should be considered under limitations. This calculator indicate the value of correct population percentage in a particular range. For example, we interview the people and get the 95 percentage confidence level and give the sample size as 50,60% of survey result. These values are given to the confidence level calculator. Then we get the confidencr interval and true proportion range as 13.58 and 46.42 to 73.58% respectively.
Following steps are followed in confidence interval calculator:
Step 1: Confidence level.
      First step is select the values  for calculation. After the survey it establish the confidence interval. We can choose the percentage of confidence interval. Siginificance level is relate the confidence level.
Step 2: Sample size.
      This give the response numbers for questions.
Step 3: Enter observed study result.
      Sample respondents are given as frequency formula or percentage. We can choose any one of these two.
Hope you liked the above explanation. Please leave your comments, if you have any doubts.

Learning Elementary Linear Algebra

Introduction:

Linear algebra is one of the subtopics in algebra. Algebra is classified into many subtopics like linear, non linear, quadratic, inequalities, system of equations. Linear algebra is one of the important topics in algebra. Linear algebra deals with variables and numbers. Simple linear equation consists of one variables and a constant. In elementary level, simple linear algebra is followed. Linear equation means, the x axis varies linearly with respect to the y – axis.

Elementary Linear Algebra Larson Pdf:

Ron Larson, mathematician in the Penn State Erie, The Behrend College, Pennsylvania. He wrote lot of books in math for intermediate level and also for the college level. He is well known for his article publishing and text books. His books mainly deal with algebra and pre algebra. Larson pdf in elementary linear algebra is an excellent pdf for intermediate students. This elementary linear algebra pdf file provides many simple problems and answers in linear algebra. Larson pdf for elementary linear algebra is useful for learning basic linear algebra problems.

Example 1:
Solve the linear equation
x + 10 = 25
Solution:
x + 10 = 25
Subtract 10 on both sides,
X + 10 – 10 = 25 – 10
X = 15
The answer is 15.
Hope you liked the above explanation. Please leave your comments, if you have any doubts.

Explain radius and diameter of a circle

Introduction:

                A circle is a 2D image. Diameter of a circle circumference article deals with the definition of the diameter and the circumference and the model problem related to it. Circumference is defined as the distance around the circle. Both the diameter and the circumference are measured in the units (like cm, m) etc. The dimensions of the circle are radius and diameter. Diameter of the circle is the distance between two points on a circle which should passes through the center of a circle. Radius is same as the half of the diameter and it is a distance between a center of a circle and any point on the circle using formula for circumference of a circle.

Example Diagram for Radius and Diameter of a Circle:

Radius = diameter/2

Diameter = 2* radius.

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Square Root Formula of 180

Introduction:

           The square root is the radical form of the method that are used in the calculation mathematical problems. The symbol for the square root is meant by root √. This could be in the form to describe their nature of working with the square root formula. There are numerous methods are available in the rooting, they are square (second) root `sqrt(x)` , cube (Third) root `root(3)(x)` up to nth root `root(n)(x)` . Here we are going to see about the formula method to solve the square root. There are number of methods available to solve square root. Here we are using newton's method to solve the square root formula of 180 and the problem solved.

                                                        

Procedure for Square Root by Newton's Method:

• Form the equation from the given function and differentiate with respect to x.
• Assume the value for the first initial value for x as x₀.
• And substitute the x₀ value in the formula to find the value for x₁.
• Repeat the above step up to the required result for the given function we get.

Formula for calculating the square root using the newton's method:
      Let the equation for the given function is f(x). Find the first derivative for the equation.
                          `sum_(n=0)^N x_(n+1) ` = `sum_(n=0)^N ( x_n - f(x_n)/(f'(x_n))) `
            Assume an value for the initial value for x₀

Hope you liked the above explanation. Please leave your comments, if you have any doubts.

Fundamental Theorem of Algebra

Introduction:

         The Fundamental Theorem of Algebra is a for equation solving. It means that every polynomial equation over the field of complex numbers of degree higher than 1 has a complex solution. Polynomial equations are in the form

                                               P(x) = a_nxⁿ + a_n-1 x ^n-1 + ... + a₁x + a₀ = 0,
where an is assumed non-zero in which case n is called the degree of the polynomial P and of the equation above.

Fundamental Theorem of Algebra:

       A number a is a solution to the equation P(x) = 0 if substituting a for x makes it identity: P(a) = 0. The coefficients are assumed to belong to a exact set of numbers where we also look for a solution. The polynomial form is very general but frequently studying P(x) = Q(x) is more suitable.
      To see how it works let's start with the counting numbers (N=numbers 1,2,3,...), and the simplest equation             x + a = b. For example, x + 5 = 12 has a solution x = 12 - 5 = 7. Introduction of negative numbers eases the problem:
Any equation x + a = b where a, b belongs to N has a solution x belongs to Z, where Z is the set of integers numbers like plus, minus whole numbers and zero.
Once we accepted the negatives, we have a stronger result:
Any equation x + a = b where a, b belongs to Z has a solution x belongs to Z.
Even if the coefficients are permitted to be negative, the equation still has a solution in Z. Now let's consider other equations over Z: 11x + 11= 0, x= -11 /11 = -1. 
   Any equation ax + b = 0 where a,b belongs to z has a solution x belongs to Q.
Moreover, we again get a stronger result,
Any equation ax + b = 0 where a,b belongs to Q has a solution x belongs to Q.
       Hope you liked the above explanation. Please leave your comments, if you have any doubts.

Trigonometric Complex Numbers with example

Introduction:
                   In mathematics, the trigonometric functions are also called as circular functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are the most important in the study of triangles and modeling periodic phenomena, among many other applications. Now let us discuss about the trigonometric complex numbers.

Problems on Trigonometric Complex Numbers:

Complex trigonometric functions
 Through Euler's formula we know that
 e^ix = Cos x + i Sin x   and hence, e^-ix = Cos x - i Sin x
 This gives us the two identities:
 Cos x = ½(e^ix + e^-ix)   and Sin x = ½(e^ix - e-^ix)
             Then complex trigonometric functions can be defined by analogy as: Cos z = ½(eiz + e-iz)  and Sin z = ½(eiz - e-iz);  while other complex trigonometric functions
1. Find Trigonometry complex   ( 3 + 5i) - (8 +3i)
Answer:          
               =(3 + 5i) - (8+ 3i)
               =(3 - 8) + (5i - 3i)
               =-5 + 2i

2. Solve the trigonometry complex triangle function of the sides a=8, b=5 and c=4 of the trigonometry area triangle
Solution:
             Trigonometry function of s= (`1/2` ) (a+b+c) =8.5
                Function area =√ [s(s-a) (s-b) (s-c)] = 9.045
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Trigonometric Functions of an Angle

Introduction of Trigonometric Functions of an Angle:
             The word trigonometry is derived from Greek meaning study of a triangle, a right triangle in particular.
Trigonometric function means a relation of the sides of a right triangle. The angle that is made by the hypotenuse with the base of a right triangle determines the ratio of different sides and hence it is important to study the trigonometric function of any angle.
With the rotation of the hypotenuse, the angle varies and hence the trigonometric function is also called as circular function.

Trigonometric Function of an Angle – Basic Concepts

            The basic trigonometric functions of any angle are Sine functions, Cosine functions and Tangent functions. The are abbreviated as sin, cos and tan respectively.

            The Sine function gives the ratio of the vertical component of the hypotenuse(rise) and the hypotenuse. The cosine function gives the ratio of the horizontal component of the hypotenuse(run) and the hypotenuse. The Tangent function gives the ratio of the vertical component of the hypotenuse (rise) and the horizontal component of the hypotenuse(run).
The reciprocal functions of Sine, Cosine and Tangent are called Cosecant, Secant and Cotangent functions respectively.

Function Notation Graph

Introduction:

Function in math describes a quantity of expression, when an n input is given to the expression we get an output called a function. It assigns a unique value to the specific expression. The function notation consists of even functions and odd functions. Here we will see the graph of the function notation in detail.

If f(x) = F (-x) then the function is even function.

Example: f(x) = cos x is an even function.

If f(x) ≠ f (-x) then the function is odd function.

Example: f(x) = sin x is odd function.

Below is the example for Function Notation Graph:

Function notation Graph - Example:

Graph the function y = x² – x

Solution:

Step 1: Find the values in the table.

x	-2	-1	0	1	2	3
y	6	2	0	0	2	6

Step 2: Design these points using function notation graph.

Step 3: Since y = 0 for both x = 0 and x = 1,

Step 4: The above function notation graph clear that the arc is continuous.

Hope you like the above explanation, Please leave your comments, if you have any doubts.

Methods of factoring trinomials calculator

Introduction:

The equation or a function is in the structure of ax²+bx+c =0 (where a≠0, b, c are constants ) called as trinomials.We can also refer it as a quadratic function. An algebraic expressions which has 3 terms known as trinomials.The trinomials having highest power 2.The trinomials have the two roots. There are two ways to factor the trinomial according to the co-efficient of x² . In the following section we are going to learn how to factor the trinomials by using trinomials calculator.

Factor Trinomials Calculator Method 1:

For factorind the trinomials we must know the below two methods.

Factor trinomial calculator Method 1:

If the coefficient of x² is one. That is a=1.

x²+bx+c=(x-r₁)(x-r₂), In this r₁ and r₂ are the roots of the trinomial equation

(x - r₁) and (x - r₂) are the factors of the trinomial.

Factor Trinomials Calculator Method 2:

In the trinomial equation ,the coefficient of x² has any value except 1. That is a≠1.

Hope you like the above explanation. Please leave your comments, if you have any doubts.

About General Circle Equation

Introduction to general circle equation:-

A circle is a simple shape of Euclidean geometry consists of that point in plane which is equidistant from a given point called the center. The common distance of the point of a circle from its center is called its radius. Circle simple close curve which divide the plane into two regions, an interior and an exterior. The circumference of a circle is the border of the circle (especially when referring to its length). In this article we shall discuss about general equation of circle.

General Form Circle Equation Example Problem:-

The circle equation of center radius of the circle in the form of (x – h) 2 + (y – k) 2 = r2. The center of the circle is starting at the point of (h, k) and the radius of the circle starting "r". This format of the circle equation is helpful, for easily find the center and the radius of the circle.

Example 1:-

Find the general equation of a circle, the center is at (2, - 6) and radius 6

Solution:-

Given (h, k) = (2, - 6) and r = 6

Substitute h, k vale and r value in the standard equation

(x - 2)² + (y - (- 6)) ² = 6²

(x - 2)² + (y + 6)² = 36

Different types of Variables

Introduction:

Quantities such as height, weight, age, amount can have several different values. Quantities which can assume different numerical values are called variables. A variable is any alphabet or combination of alphabets that contain the constant value. It can be vary. For example the speed of the vehicles is a variable. Variables with similar roles are mentioned with consecutive alphabets.

Variables are of two types:

(a) Continuous

(b) Discrete.

Continuous Variable

Consider an example. A person was asked to measure the thickness of a coin. He recorded the following readings:

(i) 0.2 cm with ruler

(ii) 0.23 cm with vernier

(iii) 0.231 cm with micrometer

The accuracy of thickness of the coin depended on the instrument used for measuring the thickness. Thus the thickness of the coin is a continuous variable. Variables like height, weight, time are also called continuous variables.

Discrete variable

Consider an example: The number of pupils in a class can be 30, 34, 40. But it cannot be 30.2, 35.1, because number of pupils can be expressed only as a whole number. Such numerical as number of children, trees, sheep are called discrete variables.

How to solve radicals equations

Introduction:

An equation with radical is an equation of the form X^m/n = a, for m, n integers.

Steps for solving equations with radicals:

When a variable is inside a square root, first take one of the radicals to one side of the equation. Squaring on both sides of the equation, we can eliminate the radicals (square root).

Now, depending on the equation, the variable involved in the new equation, either linear or quadratic methods used for solving the equation for unknown value. Now, we are going to see some radical equations problems.

How to solve radicals equations:

Example radical equation:

Find the value of x by solving the equation: `sqrt(x)` +8=9

Solution:

Subtract 8 on both sides

`sqrt(x)` +8-8=9-8

`sqrt(x)` =1

To eliminate square root, take square on both sides of the equation, we get

x=1²

x=1

So, the answer is x=1.

Example of solving Linear Equations in Two Variable

Introduction:

Solving linear equations in two variables is a process of finding the value of the unknown quantity for which the equation is true. The value so found is called the root or solution of the equation. The process of finding the value of the unknown quantity for which the equation is true, is called solving the equation. The value so found is called the root or solution of the equation.

An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear equation in one variable and with two variables is called as linear equation in two variable.

Example of solving Linear Equations in Two Variable

Example 1:

x = 1, y = 1 is a solution of 2x + 3y = 5

2(1) + 3(1) = 5

x = -2, y = 3 is also a solution of 2x + 3y = 5

2(-2) + 3(3) = 5

-4 + 9 = 5

Similarly, we can find many more solutions for 2x + 3y = 5

Example 2:

Find four solutions of the equation 2x + y = 5.

2x + y = 5

y = 5 - 2x

Put x = 0, y = 5

x = 1, y = 5 - 2 = 3

x = 2, y = 5 - 4 = 1

x = 3, y = 5 - 6 = -1

Hope you like the above explanation, Please leave your comments, if you have any doubts.

Ratios

Introduction:

This chapter takes us much further and adds to our already existing knowledge about Ratio and Proportion. We will have to use many of the algebraic manipulations learnt earlier, use them with expertise to solve problems in this chapter.

Proportions are built from ratios. A "ratio" is just a comparison between two different things. For instance, someone can look at a group of people, count noses, and refer to the "ratio of men to women" in the group. Suppose there are thirty-five people, fifteen of whom are men. Then the ratio of men to women is 15 to 20. Notice that, in the expression "the ratio of men to women", "men" came first. This order is very important, and must be respected: whichever word came first, its number must come first. If the expression had been "the ratio of women to men", then the numbers would have been "20 to 15". Expressing the ratio of men to women as "15 to 20" is expressing the ratio in words. There are two other notations for this "15 to 20" ratio: odds notation: 15 : 20 fractional notation: 15/20 You should be able to recognize all three notations; you will probably be expected to know them for your test. Given a pair of numbers, you should be able to write down the ratios. For example: There are 16 ducks and 9 geese in a certain park. Express the ratio of ducks to geese in all three formats. Consider the above park. Express the ratio of geese to ducks in all three formats.

Algebraic Equation

Basics of the Equation

The diagram on the right shows a basic equation. This equation is similar to problems which you may have done in ordinary mathematics such as:

__ + 16 = 30

You could easily guess that __ equals 14 or do 30 - 16 to find that __ equals 14.

In this problem __ stood for an unknown number; in an equation we use variables, or any letter in the alphabet.

When written algebraically the problem would be:
x + 16 = 30

and the answer should be written:
x = 14

Solving Equations

These equations can be solved relatively easy and without any formal method. But, as you use equations to solve more complex problems, you will want an easier way to solve them.

Pretend you have a scale like the one shown. On the right side there are 45 pennies and on the left side are 23 pennies and an unknown amount of pennies. The scale is balanced, therefore, we know that there must be an equal amount of weight on each side.

As long as the same operation (addition, subtraction, multiplication, etc.) is done to both sides of the scale, it will remain balanced. To find the unknown amount of pennies of the left side, remove 23 pennies from each side of the scale. This action keeps the scale balanced and isolates the unknown amount. Since the weight(amount of pennies) on both sides of the scale are still equal and the unknown amount is alone, we now know that the unknown amount of pennies on the left side is the same as the remaining amount (22 pennies) on the right side.

Hope you like the above explanation, Please leave your comments, if you have any doubts.

Rounding Numbers

Rounding Numbers:

When you have to round a number, you are usually told how to round it. It's simplest when you're told how many "places" to round to, but you should also know how to round to a named "place", such as "to the nearest thousand" or "to the ten-thousandths place". You may also need to know how to round to a certain number of significant digits; we'll get to that later.

In general, you round to a given place by looking at the digit one place to the right of the "target" place. If the digit is a five or greater, you round the target digit up by one. Otherwise, you leave the target as it is. Then you replace any digits to the right with zeroes (if they are to the left of the decimal point) or else you delete the digits (if they are past the decimal point).

I'll use the first few digits of the decimal expansion of pi: 3.14159265... in the example below.

• Round pi to five places.

"To five places" means "to five decimal places". First, I count out the five decimal places, and then I look at the sixth place:

3.14159 | 265...

I've drawn a little line separating the fifth place from the sixth place. This can be a handy way of "keeping your place", especially if you are dealing with lots of digits.

The fifth place has a 9 in it. Looking at the sixth place, I see that it has a 2 in it. Since 2 is less than five, I won't round the 9 up; that is, I'll leave the 9 as it is. In addition, I will delete the digits after the 9. Then pi, rounded to five places, is:

= 3.14159




Hope you like the above Explanation, Please leave your comments, if you have any doubts.

Solving Fractions

Definition:

We all have learnt fractions and decimals in earlier classes. The study of fractions included proper, improper and mixed fractions as well as their addition and subtraction. We also studied comparison of fractions, equivalent fractions, representation of fractions on the number line and ordering of fractions.

Our study of decimals included, their comparison, their representation on the number line and their addition and subtraction. We shall now learn multiplication and division of fractions as well as of decimals

How to Do Fractions:

1. In order to do fractions we first need to find the common factor of both the numerator and denominator (A common factor is any number that divides both the numerator and denominator). Like 3 divides 6 and 21.
2. Then continue dividing the fraction with the common factor till there are no more common factors in the numerator and denominator.
3. Now the fraction is called as simplified fraction as no common factors remaining which can divide both the numerator and denominator.

Example of simplifying fractions:

Lets take 12/14. Here both 12 and 14 are divisible by 2 so lets divide the fraction with 2.
So we get 12/14 = 6/7 Now 6/7 does not have any common factors so 6/7 is the simplified fraction
So both 18 and 42 are divisible with 2,3,6

Place Value

Definition:


The The idea of place value is at the heart of our number system. First, however, a symbol for nothing--our zero--had to be invented. Zero "holds the place" for a particular value, when no other digit goes in that position. For example, the number "100" in words means one hundred, no tens, and no ones. Without a symbol for nothing, our decimal number system wouldn't work.

Beginning with the ones place at the right, each place value is multiplied by increasing powers of 10. For example, the value of the first place on the right is "one", the value of the place to the left of it is "ten," which is 10 times 1. The place to the left of the tens place is hundreds, which is 10 times 10, and so forth.
For easier readability, commas are used to separate each group of three digits, which is called a period. When a number is written in this form, it is said to be in "standard form."

Examples
Numbers can be represented in many ways, but standard form is usually the easiest and shortest way. Here are some numbers expressed in different forms, with their standard form shown alongside. Which form do you think is the best?
Example 1
one billion, sixty million, five hundred twenty thousand
1,060,520,000
Example 2
four hundred sixteen thousand, seven hundred thirty-one
416,731
Example 3
6,000,000 + 70,000 + 20 + 1
6,070,021