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subject: Introduction To Rational Prime Number: [print this page]


The set of whole numbers is {0, 1, 2, 3, 4, 5, }. Such numbers as 5/5, 9/1 and 25/5 are also whole numbers because they can be written as a member of this set.

The set of rational numbers consists of all numbers that can be expressed as a/b,

where a and b are integers and b 0. The numbers 1/3 and -5 are rational numbers.

Some Decimals are Rational Prime Numbers.

Decimals either terminate or they go on forever. Every terminating decimal can be written as a fraction, so all terminating decimals are rational numbers. For example, 0.45 = 45/100 or 9/20.

Repeating decimals can always be written as fractions, so repeating decimals are always rational numbers. for example, 0.333

Decimals that do not terminate and do not repeat cannot be written as fractions and are not rational numbers.

Prime Number Definition:

In mathematics, a prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. The first twenty-five prime numbers are:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 , 59, 61, 67, 71, 73, 79, 83, 89, 97

Examples on Rational Prime:

The rational numbers, which are prime, is known as a rational prime number. The numbers that are terminating decimals are rational numbers. Moreover, those numbers must be a prime number. This is a rational prime.

Some examples of rational prime numbers

1) 25/5

Solution:

25/5 = 5 is a prime number, so 25/5 is a rational prime

2) 9/1

Solution:

9/1 = 9 is a prime number, So 9/1 is a rational prime number.

3)35/5

Solution:

35/5=7. Here 7 is a prime number, so 35/5 is a rational prime

4) 26/2

Solution:

26/2 = 13. Here 13 is a prime number, so 26/2 is a rational prime

5) 26/13

Solution:

26/13=2. Here 2 is a prime. So 26 / 13 is a rational prime.

Introduction to Rational equations:

In algebra solving rational equation is very simple,we have few rules to solve any type of equations. Whatever we do on one side of the equation, we must do to the other side also. If you have fractions, we can try to eliminate them by multiplying by the common denominator. If there are quadratics involved in our equations, we must get all the terms to one side with zero on the other.The basic rational expression is in the form of fraction.where there is at least one variable in the denominator.

free math solver with steps

Solved Example Based on Rational Equation :

Ex 1:Solve '3/x+6=2/(4x)'

Sol:

Step 1: The given equation is

'3/x+6=2/(4x)'

subtracting both sides by '2/(4x)'

'3/x+6-(2/(4x))=(2/(4x))-(2/(4x))'

Step 2: Rearrange the equation.

'3/x-2/(4x)+6=0'

subtracting both sides by 6.

'3/x-2/(4x)+6-6=0-6'

'3/x-2/(4x)=-6'

Step 3: Find the l.c.d(least common denominator) x and 4x

L.C.D=4x

'(12-2)/(4x)=-6'

'10/(4x)=-6'

Step 4:Multiply both sides by 4x.

'10/(4x)xx4x=-6xx4x'

10=-24x

Step 5:Divide both sides by -24

'10/(-24)=(-24x)/(-24)'

'x=-5/12'

The solution is [x=-5/12]

Example Based on Rational Equation:

Ex 2: Solve 'x/(x-2)+1/(x-4)=2/(x^2-6x+8)'

Sol:

Step 1:first factor the 'x^2-6x+8'

factors=(x-4)(x-2)

Step 2:convert common denominator to all

'(x/(x-2))((x-4)/(x-4))+(1/(x-4))((x-2)/(x-2))=2/((x-2)(x-4))'

'(x^2-4x)/((x-2)(x-4))+(x-2)/((x-2)(x-4))=2/((x-2)(x-4))'

'(x^(2)-4x)+(x-2)=2'

'x^(2)-4x+x-2=2'

'x^(2)-3x-4=0'

'(x-4)(x+1)=0'

'x=4 or x=-1'

If we submit the x=4 in the denominator,it is division by zero,so x=4 is not considerable.

x=-1 is the answer

by: johnharmer




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