DIVISION ON FRACTIONS

Division on fractions is extremely easy. You just have to remember the rule to follow, and not get it confused with any other rule. You also have to remember to not do any "cross-canceling" until you have converted your division problem to multiplication as described below.

There is more than one method of dividing fractions. The easiest and most commonly taught way is to “invert and multiply.”To divide 2 fractions multiply the dividend by the reciprocal of the divisor.

Listed below is Dividing fractions examples:

(4/5) / (2/3) = (4/5) * (3/2)

(4/5) * (3/2) = (12/10)

12/10 = 1(1/5)

This is the quickest technique to divide fractions. The top and bottom are being multiplied by the same number and, since that number is the reciprocal of the bottom part, the bottom becomes one. Dividing anything by one leaves the value “anything” the same.

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GRAPH THEORY

Graph Theory is the study of graphs mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices.

Another important concept in graph theory is the path graph theory, which is any route along the edges of a graph. A path may follow a single edge directly between two vertices, or it may follow multiple edges through multiple vertices.

Below is one solved problem on Graph Theory:

Define a graph G such that V (G) = {3, 4, 5, 6, 12, 13, 14, 15} and two vertices ‘V’ and ‘A’ are adjacent if and only if GCD {V, A} = 1. Draw a figure of G and locate its size e(G).

Soultion:

The Graph theory answers for the above graph theory problem is e(G) = 21.

Note on Sphere

A Sphere can be described as the set of all points in space which are equidistant from a fixed point. The fixed point is called the centre of the sphere and the constant distance is called its radius. A line segment passing through the centre of the sphere with its end points on the sphere is called a diameter of the sphere. All diameters of a sphere are of the same length, being equal to twice the radius of the sphere. A sphere can also be considered as a solid generated by revolving a circle about a diameter.

A plane passing through the centre of a sphere divides the sphere into two equal parts. Each part is called a hemisphere.

For a sphere of radius r, we have

(i) Surface area = 4Πr²

(ii) Volume = 4/3Πr²

For a hemisphere of radius r, we have

(i) Curved surface area = 2Πr²

(ii) Volume = 2/3Πr²

(iii) Total surface area = 2Πr² + Πr² = 3Πr²

Note on Income Tax

As citizens am sure we all pay tax in one or the other way. What does this Tax actually mean?

Let us understand this today.

The Central and State government spends a lot of money on some basic amenities like health, education, defense of the country, maintenance of Law and order etc.. To meet all these expenses, government collects money from the people from different sources, the most important of it is Tax. There are different types of taxes like: income tax, sales tax, wealth tax, gift tax, excise and custom duty tax, etc.. all these taxes are proposed, enhanced, or decreased in the central Government's or State government's budget. In Maths there are different ways of calculating tax.

Hence, we can say that taxes are the contributions of the citizens towards the expenditure of the government in its multifarious economic and non-economic activities..

Coming next with further information on types of taxes........