Experts have designed these Class 7 Maths Notes and Part 2 Chapter 2 Operations with Integers Class 7 Notes for effective learning.
Class 7 Maths Chapter 2 Operations with Integers Notes
Class 7 Operations with Integers Notes
→ We know that numbers help us in counting, measuring, and comparing quantities in our daily lives. We use positive numbers to indicate gains, heights, or profits and negative numbers to indicate losses, depths, or temperatures below zero. These positive and negative numbers, together with zero, are called integers. In the first part of the book, we have learnt how to perform the operations of addition and subtraction on integers.
→ If an object moves a units to the right (positive direction) and then moves b units to the right, then the final position will be p=a+b, where p is the distance of the object from the starting point 0.
→ In case of integers, the magnitude of the product does not change when the signs of the multiplier and multiplicand change.
→ When both the multiplier and the multiplicand are positive, the product is positive,
i.e., (+a) × (+b) = +(a × b)
→ When both the multiplier and the multiplicand are negative, the product is positive,
i.e., (-a) × (-b)=+(a × b)
→ When one of the multiplier or multiplicand is positive and the other is negative, the product is negative, i.e., (-a)× (+b)=(+a) × (-b)=-(a × b)
→ For any two positive integers a and b, where b ≠ 0 the following holds:
- a ÷(-b) = -(a ÷ b)
- -a ÷ b = – (a ÷ b)
- -a ÷ (-b) = a ÷ b
→ Integer multiplication is commutative, i.e., for any two integers a and b, a×b=b×a.
→ Integer multiplication is associative, i.e., for any three integers a, b, and c
a ×(b×c)=(a×b) × c.
→ Integer multiplication is distributive over addition, i.e., for any three integers a, b, and c,
a×(b+c)=(a×b)+(a×c)