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Mathematics - Chapter 1 - Integers

(Key Points)

**⑴** Integers are a bigger collection of numbers which is formed by whole numbers and their negatives.

**⑵**You have studied in the earlier class, about the representation of integers on the number line and their addition and subtraction.

**⑶** We now study the properties satisfied by addition and subtraction.

(a) Integers are closed for addition and subtraction both. That is,

*a + b* and

*a – b* are again integers, where a and b are any integers.

(b) Addition is commutative for integers, i.e.,

*a + b = b + a* for all integers a and b.

(c) Addition is associative for integers, i.e.,

*(a + b) + c = a + (b + c)* for all integers a, b and c.

(d) Integer 0 is the identity under addition. That is,

*a + 0 = 0 + a = a* for every integer a.

**⑷**We studied, how integers could be multiplied and found that product of a positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer. For example,

*– 2 × 7 = – 14* and

* – 3 × – 8 = 24*.

**⑸** Product of even number of negative integers is positive, whereas the product of an odd number of negative integers is negative.