  Patterns of problems

## Real Numbers

- Analyze the patterns for better solving
1
Pattern:To find rational numbers between two rational numbers
Description: Use the common denominator method and LCM. Questions based on finding one, two or multiple rational numbers between two given ones.
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2
Pattern: To check if given number is irrational
Description: Use the knowledge of non terminating , non recurring decimal expansion. Questions can be subjective or objective, true false or solution based.
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3
Pattern: To check if given number is real
Description: Use the knowledge of rational and irrational numbers . Questions can be subjective or objective, true false or solution based.
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4
Pattern: To identify the type of decimal expansion
Description: A rational number has- terminating, non terminating and recurring decimal expansion based on its denominator ( where m and n are whole numbers). Questions can be subjective or objective, true false or solution based and require prime factorization of denominator.
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5
Pattern: Checking whether a positive integer can be written in form of another positive integer
Description: It is one of the first and foremost applications of Euclid Division Lemma.
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6
Pattern: Finding HCF of given numbers.
Description: Find the HCF using Euclid Division Lemma.
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7
Pattern: Express the given number as a product of prime factors
Description: Form a factor tree in order to get the required factors.
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8
Pattern: Proving a number to be irrational (subjective)
Description: Check for the operations involved between the participating numbers.
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