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Formula Sheet

Rational and Irrational Numbers — Formula Sheet

ICSE · Class 9 · Mathematics

13 formulas from Rational and Irrational Numbers (ICSE Class 9 Mathematics) on one page, grouped by topic. Part of the ICSE Class 9 Mathematics syllabus.

35 questions30 flashcards13 formulas & key relations5 concepts

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A nested Venn diagram illustrating the relationships between natural numbers (N), integers (Z), rational numbers (Q), and real numbers (R) as subsets of each other.
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13 Entries · 5 Sections

Formulas and Key Relations

1. Number System Basics

Q = {a/b : a, b ∈ Z, b ≠ 0}

R = Q ∪ Q̄

2. Rational Numbers

a/b = c/d ⇔ a × d = b × c

a/b > c/d ⇔ a × d > b × c

d = (y - x)/(n + 1)

n rational numbers between x and y: x + d, x + 2d, x + 3d, ..., x + nd

(a + c)/(b + d)

3. Irrational Numbers

Non-terminating and non-recurring decimal

√m is irrational if exact square root of m does not exist

√ab

(a + b)/2

4. Real Numbers and Relationships

Rational numbers = terminating or recurring decimals

Number System and Basic Classification

If x = 4, then √-4 is imaginary and √4 = 2 is real.

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Frequently Asked Questions

What are the important topics in Rational and Irrational Numbers for ICSE Class 9 Mathematics?
Key topics in Rational and Irrational Numbers include Number System and Basic Classification, Rational Numbers, Comparison, and Between Them, Decimal Representation of Rational Numbers, Irrational Numbers and Their Properties. Study these first, then practise questions on each for Class 9 exams.
How many formulas are in Rational and Irrational Numbers?
This sheet lists 13 formulas from Rational and Irrational Numbers, grouped by topic. Learn what each symbol stands for so you can apply the formula, not just recall it.
How should I revise Rational and Irrational Numbers for Class 9 exams?
Learn the core ideas first, then work through the 35 practice questions on Rational and Irrational Numbers. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Rational and Irrational Numbers

All ICSE Class 9 Mathematics Formula Sheet

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