Standard form or lowest form of a rational number

STANDARD FORM OR LOWEST FORM OF A RATIONAL NUMBER

A rational number ^p/_q is said to be the standard form if q is positive, and the integer’s p and q have no common divisor other than 1 and in lowest form the rational number could be in negative form.

MULTIPLICATIVE INVERSE:

of a number is ^P/_Q form is ^Q/_P it is also known as reciprocal of .

EQUALITY OF RATIONAL NUMBERS

In order to test the equality of two rational numbers.

I^st Method: We express both the rational numbers in the standard form:

“If they have the same standard form they are equal, otherwise they are not equal”.

II^nd method: In this method to test the quality of two rational numbers ^a/_b and ^c/_d we use the following result.

Different terminology of Rational numbers or Fractions are

• Common fraction: Fractions whose denominator is not 10.
• (Decimal fraction: Fractions whose denominator is 10 or any power of 10.
• Proper fraction: Numerator < Denominator i.e.³/₅
• Improper fraction: Numerator > Denominator i.e.⁵/₃
• Mixed fraction: Consists of integral as well as fractional part i.e.3²/₇
• Compound fraction: Fraction whose numerator and denominator themselves are fractions. i.e. .
• Equivalent fractions: Equivalent fractions are that they are fractions that have the same overall value. i.e.

Things to remember

• All natural numbers, whole numbers and integers are rational.
• Rational numbers include all Integers (without any decimal part to it), terminating fractions (fractions in which the decimal parts terminating e.g. 0.75, – 0.02 etc.) and also non-terminating but recurring decimals e.g. 0.666…., -2.333….., etc.
• 0 is a rational number, since we can write, 0= ⁰/₁
• Every natural number is a rational number, since we can write,1=¹/₁, 2=²/₁, 3=³/₁ etc.
• Every integer is a rational number, since an integer a can be written as .¹/₁
• Every rational numbers can be expressed as fractions:
• Improper fraction can be written in the form of mixed fractions.