Introduction: Rational Numbers
- A rational number is defined as a number that can be expressed in the form, where p and q are integers and q≠0.
- In our daily lives, we use some quantities which are not whole numbers but can be expressed in the form of. Hence we need rational numbers.
Equivalent Rational Numbers
- By multiplying or dividing the numerator and denominator of a rational number by a same non zero integer, we obtain another rational number equivalent to the given rational number.These are called equivalent fractions.
- ∴andare equivalent fractions.
∴andare equivalent fractions.
Rational Numbers in Standard Form
- A rational number is said to be in the standard form if its denominator is a positive integer and the numerator and denominator have no common factor other than 1.
- Example: Reduce.Here, the H.C.F. of 4 and 16 is 4.is the standard form of.
LCM
- The least common multiple (LCM) of two numbers is the smallest number (≠0) that is a multiple of both.
- Example: LCM of 3 and 4 can be calculated as shown below:
Multiples of 3: 0, 3, 6, 9, 12,15
Multiples of 4: 0, 4, 8, 12, 16
LCM of 3 and 4 is 12.
Rational Numbers Between 2 Rational Numbers
Rational Numbers between Two Rational Numbers
- There are unlimited number(infinite number) of rational numbers between any two rational numbers.
- Example: List some of the rational numbers between −35 and −13.
Solution: L.C.M. of 5 and 3 is 15.
⇒ The given equations can be written asand.
⇒ −615,−715,−815 are the rational numbers between −35 and −13.
Note: These are only few of the rational numbers between −35 and −13. There are infinte number of rational numbers between them. Following the same procedure, many more rational numbers can be inserted between them.
Properties of Rational Numbers
Properties of Rational Numbers
Addition of Rational Numbers
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Subtraction of Rational Numbers
Multiplication and Division of Rational Numbers
Multiplication of Rational Numbers
Negatives and Reciprocals
Negatives and Reciprocals
Additive Inverse of a Rational Number
Representing on a Number Line
Rational Numbers on a Number Line
Comparison of Rational Numbers
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