Mind Map

Rational Number

Any number that can be made by dividing one integer by another. The word comes from “ratio”.

Examples:

• 1 is a rational number (1/1)
• 2 is a rational number (2/1)
• 2.12 is a rational number (212/100)

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.

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.

a/b = c/d ⇔ a x d = b x c

Different terminology of Rational Numbers or Fraction

• 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.3 ^2/7
• 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 1/4 = 2/8 = 3/12 = 4/16

​ 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.

Also Check:

1. Number System
2. Multiplication of rational numbers
3. Division of rational numbers