Rational Numbers of Class 7
Any number that can be made by dividing one integer by another. The word comes from “ratio”.
- 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.
Ist 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”.
IInd 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.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 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.