the Mathematics textbook for Class VII, Semester 1, published by the State Council of Educational Research & Training (SCERT), Andhra Pradesh. It is a free distribution by Samagra Shiksha, Government of Andhra Pradesh.
Key Topics (Contents):
Chapter 1: Integers (Pages 02-39)
Chapter 2: Fractions and Decimals (Pages 40-87)
Chapter 3: Data Handling (Pages 88-117)
Chapter 4: Simple Equations (Pages 118-147)
Chapter 5: Lines and Angles (Pages 148-175)
Chapter 6: The Triangle and its Properties (Pages 176-215)
Chapter 7: Comparing Quantities (Pages 216-247)
Properties of Integers Discussed (Chapter 1):
Addition and Subtraction of Integers:
Closure under Addition: The sum of two integers is always an integer (a + b is an integer).
Closure under Subtraction: The difference of two integers is always an integer (a - b is an integer).
Commutative Property (Addition): Addition is commutative for integers (a + b = b + a). Subtraction is not commutative for integers.
Associative Property (Addition): Addition is associative for integers (a + (b + c) = (a + b) + c).
Additive Identity: Zero (0) is the additive identity for integers (a + 0 = a = 0 + a).
Multiplication of Integers:
The product of a positive and a negative integer is a negative integer.
The product of two negative integers is a positive integer.
Closure under Multiplication: Integers are closed under multiplication (a × b is an integer).
Commutativity of Multiplication: Multiplication is commutative for integers (a × b = b × a).
Multiplication by Zero: The product of any integer and zero is zero (a × 0 = 0 × a = 0).
Multiplicative Identity: One (1) is the multiplicative identity for integers (a × 1 = 1 × a = a).
Associativity for Multiplication: The product of three integers does not depend on the grouping ((a × b) × c = a × (b × c)).
Distributive Property: Multiplication distributes over addition and subtraction (a × (b + c) = a × b + a × c and a × (b - c) = a × b - a × c).
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