MathematicsClass 7Integers
Properties of Integers
Studying closure, commutative, associative, and distributive properties under various operations.
Class 7 · MathematicsCBSE & ICSE SOF IMO
Definition
Properties of integers describe how integers behave under arithmetic operations like addition and multiplication. Key properties include closure, commutativity, associativity, and distributivity. These rules help simplify complex numerical expressions and solve algebraic equations efficiently.
Key formula
a × (b + c) = (a × b) + (a × c)
Worked examples
1
Using the commutative property of addition: -5 + 3 is equal to 3 + (-5).
2
Using the distributive property: -2 × (3 + (-4)) = (-2 × 3) + (-2 × -4) = -6 + 8 = 2.
3
Demonstrating that integers are closed under addition because the sum of any two integers is always an integer.
Common mistakes
- • Assuming that subtraction and division are commutative, such as claiming that 5 - 3 equals 3 - 5.
- • Forgetting to distribute the outer multiplier to every term inside the parentheses.