What is a Natural number

In mathematics, from number theory tutorial there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition or the set of non-negative integers {0, 1, 2, ...} according to a definition first appearing in the nineteenth century.

Natural numbers have two main purposes: counting ("there are 3 apples on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively. (See English numerals.) A more recent notion is that of a nominal number, which is used only for naming.

Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partition enumeration, are studied in combinatorics.

When we add two natural numbers

we also get a natural number

Let's have a look at a simple problem from numeric and algebraic operations



2 is a natural number

5 is also natural number

2+5=7

7 is also a natural number.

We represent natural numbers with W

w={ 0,1,2,3.....}

If you know the basics of this you can get any math answers

How to convert Decimal into Fraction

Topic: Fraction

A fraction is a mathematical expression relating two quantities or numbers, one divided by the other. The numbers may be whole numbers integers- this is a rational number. For example, 1/2 is a fraction. They can also be polynomials - this is a rational function.

Let's have a look at the answer which have done by online algebra tutor
The process of decimal to fraction conversion involves the use of the fundamental rule of fractions; the fraction should be written in its lowest terms. The following examples demonstrate how to convert decimals to fractions.

Here is example of a 7th grade math equations




For similar problems of this type purple math will guide you.

Rules of Exponents

Topic: Exponents
Exponentiation is a mathematical operation, written aⁿ, involving two numbers, the base a and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication:

Here are some examples:

1.)Addition:An exponent can be added only when they have the same number.

For example: 2x1 + 2x1 = 4x1

   3x2 - 2x2 = 5x2


2.)Subtraction:The rule is same for subtraction.


3.)Multiplication:While multiplying, multiply the numbers and add the exponents.

For example: 3x1 * 2x1 = 6x2 (Add)

    4x2 * 3x3 = 12x5 (Add)


4.)Division:While dividing the exponents, the denominator takes the opposite sign and m

and mover to the numerator. The numbers should be divided as usual.

For example:

    36x8-4
 ___________ = 6x4
      64


     48x2+4
 ___________ = 8x6
     6x-4           

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problem on simple interest

Topic:- simple interest

Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money or, money earned by deposited funds. Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft, and even entire factories in finance lease arrangements.

Let's see a problem on this.

Question:

Greg invests $1200 at an annual rate of 6.5%. How long will it take until Greg earns $195 in interest?

Solution:

Formula to find the interest is

I = PTR/100

here p = profit=1200
   t = time
   r = rate=6.5

Substitute the values in formula,so that

        (1200 x T x 6.5)
195 = -----------------
             100

         T = 2.4

Greg will earn $195 in interest in 2.5 years.

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additoin of exponentials

Topic:- exponentials

Let's see what is exponent first, generally

BaseExponent

The exponent tells us how many times the base is used as a factor.

For example, to write 2 as a factor one million times, the base is 2, and the exponent is 1,000,000. We write this number in exponential form as follows:

2

1,000,000

read as two raised to the millionth power

This math help gives a example problem on addition of exponents.

Question:-

-3 z6(b3y2z2)

Answer:-

-3 z6(b3y2z2)
                   
Here we have 'z' for twice ,
So we can put them as 1 term by
additing the exponentials

we can add them by using exponent rule

formula of exponent

    am * a n = a m+n
So,
    -3 (z6+2*b3*y2)

    -3 (z8*b3*y2)

      -3z6+2*b3*y2 is the Answer

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Topic:Probability

Probability, is a way of expressing knowledge or belief that an event will occur or has occurred.

Here is some probability problems ,which help you to understand the concept much better.

Questions & Answers

1- Mr. Johnson taught a music class for 25 students under the age of ten. He randomlychose one of them. What was the probability that the student was under twelve?

Ans:-

The probability that the student was under twelve was 25/25, so P = 1.

2- The compact disk Jane bought had 12 songs. The first four were rock music. Tracks
number 5 through 12 were ballads. She selected the random function in her Compact
Disk Player. What is the probability of first listening to a balla?

Ans:-

The probability of listening to a ballad is 8/12, so P = 0.67.

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