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Simplify Rational Numbers

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					                   Simplify Rational Numbers
Simplify Rational Numbers

To solve Rational Numbers, we know that all arithmetical operations addition, subtraction,
multiplication and division can take place in rational numbers.

All operations used for simplification of rational numbers are similar to the methods of
simplification of fraction numbers.

Simplifying rational numbers is reducing the given rational number into its simplest form.
Rational numbers mean in math is number of the from ab where a and b are integers and b≠ 0
are known as rational number.

Q={ab | a ϵ z, b ϵ z and b ≠ 0} is the set of all rational numbers.

Rational number is the quotient of two integers.

Therefore, a rational number is a number that can be written down in the form ST, where S
and T are integers, and T is not equal to zero. A rational number note in this way is frequently
called a fraction .

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The first step is to factor the numerator and denominator and the second step is divide all
common factors that the numerator and denominator have.

Dividing a rational number is the most difficult part as it requires key skills. 18/5 divide by3/5
then we need to take a reciprocal of 3/5 . The reciprocal of 3/5 is 5/3.

In final step we need to Multiply 18/5 with the reciprocal. 18/5 x 5/3 = 6.

An inequality tells that two values are not equal. For example a ? b shows that a is not equal
to b. To solve inequalities, we need to learn the symbols of inequalities like the symbol <
means less than and the symbol > means greater than and the symbol ?

means less than or equal to etc. There are some principles onto which Inequalities solutions
depends.

Addition principle for solving problems of Inequalities is - If a > b then a + c > b + c

Multiplication principle for solving problems which deals in multiplicative Inequalities - If a >b
and c is positive, then ac > bc. If a > b and c is negative, then ac < bc (notice the sign is
reversed)

An expression is a combination of symbols or variables or operators with symbols that are
well-formed according to the rules applicable in the context at hand.

When we simplify the expression, an equivalent expression is found that is simpler than the
original one.

Sometimes the expression formed becomes very complicated, then it is very difficult to solve
such type of expressions. Various Homework helpers are available over the Internet for free to
solve such expressions.


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L.C.M. of 8 & 5 are 40, so to make the denominator 40, we proceed as follows: = (3*5)/(8*5) –
(6*8)/(5*8), = (15/40) – (48/40), = (15-48) /40, = (-33/40).

Let us take another example: Subtract (-4/5) from (-3/7), = (-3/7) – (- 4/5), L.C.M. of 7 & 5 is
35, On making denominators of both rational numbers same we get: = (-3*5)/(7*5) –(-4*7)/
(5*7) = (-15/35) + (28/35) = (-15+28) /35 = 13/ 35. · In another example we take both positive
rational numbers. Subtract (2/5) from (2/3), = 2/3 -2/5,

L.C.M. of 3 & 5 =15, =(2*5) / (3*5) – (2*3)/(5*3), =10/15 – 6/15, =(10-6) /15, =4/15. Procedure
for multiplication and division are different. Multiply 3/7 by (-5/4), We multiply numerator with
numerator & Denominator with a denominator, We get: = ( 3*-5)/ (7*4), =(-15) / 28.




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posted:5/15/2012
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