RATIONAL NUMBERS | NUMBER SYSTEM | UP BOARD | CBSE | ICSE | BASE2BRAIN

Video title- RATIONAL NUMBERS | NUMBER SYSTEM | UP BOARD | CBSE | ICSE | BASE2BRAIN



#mathematics #numbersystem #rationalnumbers #base2brain

About video -

The lesson transitions from a basic understanding of the number system (natural numbers, whole numbers, and integers) to a deep dive into Rational Numbers. The video is structured into four main sections:
​What are Rational Numbers? [00:39]
​Defines rational numbers as any number that can be expressed in the form p/q, where p and q are integers and q \neq 0 [00:46].
​Explains why the denominator cannot be zero (it becomes undefined) [01:06].
​Clarifies that all integers are rational numbers, but not all rational numbers are integers [01:46].
​Properties of Rational Numbers [02:15]
​Closure Property: Discusses how addition, subtraction, and multiplication of rational numbers result in another rational number, with division being an exception when dividing by zero [02:43].
​Commutative Property: Explains that the order of numbers doesn't change the result for addition and multiplication, but it does for subtraction and division [04:02].
​Associative Property: Shows that grouping numbers differently doesn't change the sum or product [05:20].
​Distributive Property: Demonstrates how multiplication distributes over addition and subtraction [07:06].
​Identity & Inverse: Covers the additive identity (0), multiplicative identity (1), additive inverse (negative of the number), and multiplicative inverse (reciprocal) [08:16].
​Equivalent Rational Numbers [09:46]
​Explains that different-looking fractions can represent the same value (e.g., 1/2 = 2/4 = 4/8) [10:45].
​Shows how to find equivalent fractions by multiplying the numerator and denominator by the same number [11:05].
​Finding Rational Numbers Between Two Given Numbers [12:16]
​Average Method: Finding a single number by calculating the mean of two rational numbers [12:22].
​LCM/Equivalent Method: A more efficient way to find multiple rational numbers (e.g., finding five numbers between 1/2 and 3/4) by equating denominators [13:31].

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