How to calculate Area of Ellipse?

An ellipse is nothing but the planar curve which is resulted by the intersection by a plane of a cone in a way such that it will produce a closed curve. Circles can be said as a special case of ellipse which can be obtained by cutting in orthogonal plane of the cone’s axis. Ellipse can also be said as the locus of all the points in the plane in which the sum of the distances of two fixed points will be a constant. Before going into the formula for area of an ellipse, it is essential to know the elements of ellipse which forms the structure of it. An ellipse is said to be a smooth and closed curve symmetric about its vertical and horizontal axis. The longest diameter of an ellipse is called as major axis and the shortest diameter of an ellipse is called as the minor axis. These both axes are the lines that pass through the centre of an ellipse.

With the measurement of both these axis only, the area of a ellipse will vary. Each of the above said axes bisects perpendicularly with the other. Also, the sum of the distance from the two focus of the ellipse to any point P on the ellipse will be equal to the major axis. It can also be said that each axis cut the other equally into two parts and they cross at right angles to each other. Also, if these both axes are equal in length, then it is called as circle.

Area of an Ellipse Formula
The standard equation for representing the ellipse equation is given as,
X^2 / a^2 + Y^2 /b^2 = 1.

This equation is a standard equation in which when the ellipse is centred with origin.
But algebraically the ellipse area formula is given in other terms with the help of semi major axis (half of major axis) and semi minor axis (half of minor axis). Thus the formula for area of ellipse is given as Pi*a*b, where ‘a’ is the semi major axis and ‘b’ is the semi minor axis. This formula is actually arrived from the formula of circle Pi multiplied by radius square. Here the radius is split into semi major and semi minor axis.
Also at some special cases, when an ellipse is given by the implicit equation which is given as,
AX2 + Bxy + CY2 = 1, then the area of the ellipse would be 2*Pi whole divided by square root of 4AC subtracted with B square.

Understanding Fractions Better

Numbers have always fascinated humankind. Indians are credited with the invention of zero. Indians have always been good with numbers and the world looks at us with awe. We have great strides and come a long way. From natural numbers, whole numbers, integers, real numbers and complex numbers. We have also studied fractions. Let us what are fractions to understand the concepts of denominator numerator. A number can written in the form of A/B where A is an integer and B is an integer. A can be called the numerator and B can be called the denominator. So we see numerator v/s denominator to extend the concept further. The numerator is written on top of the horizontal line and the denominator is written below the horizontal line. So we understand what is a numerator and denominator if we didn’t know it earlier.

We must understand numerators and denominators to understand fractions better. Operations of addition, subtraction, multiplication and division between the fractions can be performed. Here both numerator and also the denominator come into picture. If the denominators are dissimilar they must be made similar to proceed further with the operations. For this we need to take the LCM of the denominators. Taking the LCM is a simple operation. Unless the denominators are equal we cannot proceed further. Once the denominators are equal, we can just add the numerators if the operation to be performed is addition. If subtraction is to be performed we just need to subtract the numerators after making the denominators equal. So we must know the definition of numerator and denominator to perform these operations. Only when we know it, we can do something.

After making the denominators equal if they are not, we proceed to perform addition, subtraction or any operation with fractions. Sometimes the fractions can be in the form of mixed fractions. We need to be careful in such cases. We must first convert them into improper fractions without proceeding. They cannot be directly used. For the process of finding LCM we need improper fractions in our hand. Once we get the improper fractions we first check whether their denominators are same or not. If they are same, our problem becomes very simple and easy. The numerators can be just added or subtracted as the case may be. If they are not equal only then the process of taking LCM is to be performed and addition or subtraction is to be done.

Distributive Property of Addition

The distributive property is expressed in the mathematics expressions as following equation: a (b + c) = ab + ac. You can understand this as the sum of a (b + c) is corresponding to the sum of a times b and a times c. Distributive property of addition would be inaccurate to multiply ab and just add c, or to multiply ac and add b.

Order of Operations:

The distributive property of addition that remind that all contained by the parenthesis needs to be multiplied by the outside number. Distributive property, when they are knowledge the order of operations.

Concept of that the problems anywhere present are different mathematical operations, such as multiple, addition, subtraction, parenthesis, you have to work in a certain order to get the right answer. This arrange is the parenthesis, exponent, multiplication,division , addition and subtraction, that may be abbreviate to the  PEMDAS.

Example Problems (distributive Property of Addition):

Example problems:

When you include a mathematics problem that use parenthesis you need to solve what’s in the parenthesis first, by you can move about on to solve further problems. If the mathematics problem largely has known numbers, it is somewhat easy to solve. 2(10+5) becomes 2(15) or is also equal under the distributive property of addition is 2(10) + 2(5). What obtain additional difficult is when you are functioning with variables (such as a, b, x, y, and so on) in algebra, and when these variables cannot be joint together.

Consider the equation 5(12a + 2), but we don’t know what the variable a stand for, we can’t add 12a + 2, but using the distributive property still allow us to just this expression because we identify this equation is equal to 5(12a) + 5(2). In order to simply the expression we can take each part separately and multiply it to 5, and we get 60a + 10.

Addition, Subtraction, Multiplication and Division

As the learning session for numbers is completed, the next session starts with addition, subtraction, multiplication and division. Understanding these calculations is the basics of learning mathematics. It is quite challenging to make kids’ understand the concepts of addition, subtraction, multiplication and division followed by order of operations, simplification and so on. In that case providing fun examples related to kids can be helpful. Let’s give it a try.

Addition: Addition denoted by the plus sign, “+”, is a mathematical operation that combines two or more collection forming larger collections.

For example: It is Tina’s birthday and she has received many beautiful dresses for girls – one from Annie aunty, another from grandpa and another one from her mother. Now adding all three we get, 1+1+1 = 3 dresses for girls. This mathematical operation is addition.

Subtraction: Subtraction denoted by the minus sign, “-”, is a mathematical operation that is inverse of addition. In this operation, a part is taken away from a collection and thus forming a smaller collection.

For example: Father brought 50 return gifts for kids on Tina’s birthday. Only 45 of her friends came for the birthday party. Now after subtracting the two, we can find, 50-45 = 5 return gifts for kids remaining. This mathematical operation is subtraction.

Multiplication: Multiplication denoted by the sign “x” is a mathematical operation that scales one number by another.

For example: Mother is planning to organize a fancy dress costumes competition on next Sunday. There are 5 groups of two members and therefore each group requires two costumes. Now by multiplying, we get 5 X 2 = 10 fancy dress costumes. This mathematical operation is multiplication.

Division: Division denoted by the sign “/” is a mathematical operation that includes a dividend, quotient, divisor and remainder.

For example: Tina has 5 best friends and she has 20 chocolates. She wanted to distribute the chocolates among them. Now diving the numbers we get, 20/5 = 4. Each of her friends will get 4 chocolates. This mathematical operation is division.

These are the basic operations of mathematics that form the first steps in learning mathematics for kids.