Mathematics - Chapter 1 - Integers
(Key Points)
⑴ Integers are a bigger collection of numbers which is formed by whole numbers and their negatives.
⑵You 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.
⑷We 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.
