Ch 1 of Class 7 Maths builds on integer concepts from Class 6. Students explore the properties of addition, subtraction, multiplication, and division of integers, including closure, commutativity, associativity, and distributivity. These properties form the foundation for algebra.
Addition of integers is closed (sum of two integers is always an integer), commutative (a + b = b + a), and associative ((a + b) + c = a + (b + c)). Zero is the additive identity: a + 0 = a. Subtraction is closed but neither commutative nor associative.
Product of two positive or two negative integers is positive. Product of a positive and negative integer is negative. Multiplication is commutative, associative, and distributes over addition: a × (b + c) = a × b + a × c. The multiplicative identity is 1.
Division of integers is not closed (result may not be an integer). Division is neither commutative nor associative. When dividing integers: positive ÷ positive = positive, negative ÷ negative = positive, and mixed signs give a negative result.
Download: https://ncert.nic.in/textbook/pdf/gemh101.pdf | Complete book: https://ncert.nic.in/textbook/pdf/gemh1ps.zip
No. For example, 5 − 3 = 2 but 3 − 5 = −2. Since 2 ≠ −2, subtraction is not commutative for integers.
For any integers a, b, c: a × (b + c) = a × b + a × c. This means multiplication distributes over addition.
Book a Trial + Diagnostic session. Get a personalized Learning Path with clear milestones, tutor match, and a plan recommendation — all within 24 hours.
Book Trial + Diagnostic →