Chapter 10: Operations with Integers
We already add and subtract integers. In this chapter we recap them with puzzles, carrom coins and tokens, then learn to multiply and divide integers: why two negatives make a positive, the sign rules Brahmagupta wrote down, and how properties like swapping, grouping and distributing still hold.
In this chapter you will
- add and subtract integers using moves and tokens
- multiply integers and explain the sign rules
- divide integers
- use properties of integer operations in problems
Topics
- A Quick Recap of Integers NCERT P2 2.1
Integers carry size and direction; the final position after moves a and b is a + b.
- Multiplication of Integers NCERT P2 2.2
Same signs give a positive product; different signs give a negative product.
- Division of Integers NCERT P2 2.2
Division follows the same sign rules as multiplication.
Key words
- Integer
- a whole number, positive, negative or zero
- Additive inverse
- the number that adds to give 0: −a for a
- Zero pair
- a + token and a − token together
- Multiplier
- the number that tells how many times
- Commutative
- order can be swapped: a × b = b × a
- Distributive
- a × (b + c) = a × b + a × c
Summary
- Subtracting is adding the additive inverse: 4 − (−12) = 16.
- Same signs multiply to a positive, different signs to a negative.
- Division uses the same sign rules: (−100) ÷ (−4) = 25.
- Integer multiplication is commutative, associative and distributes over addition.