Chapter 9 Rational Numbers - Wisdom TechSavvy Academy

Online Class For 7th Standard Students (CBSE)

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Introduction: Rational Numbers

A rational number is defined as a number that can be expressed in the form p/q where p and q are integers and q≠0.

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.

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 : 2/3, 4/5 , 7/9 etc.

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 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 as -9/15 and -5/15 .
⇒ −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.