Chap 2 Integers

Chap 2

Integers

Some Important facts:

1.    Every Positive integer is greater than every negative integer

2.    Zero is greater than every negative integer is less than every positive integer.

3.    If an integer ‘a’ is less than integer ‘b’ then the integer ‘- a’ will be greater than the integer ‘- b’.

4.    The absolute value of an integer is the numerical value of the integer regardless of its sign.

5.    If the integers a and b are both positive and both negative then to find their sum and their absolute values \a\ and \b\ and assign the signs of a and b to the sum i.e.

                            a + b = + (\a\ + \b\) if a and b are both positive.

                                   a + b = - (\a\ + \b\) if a and b are both negative.

6.    If integers a and b are of opposite signs, then to final a + b we find the difference of their absolute values and assign the sign of the value integer having greater absolute value of the difference.

7.    All the properties of whole numbers are valid for integers. Some of the properties are as follows:

(i)            If a and b are integers then their difference i.e. a – b is always an integer.

(ii)          For each integer a ; a x (-1) = (-1) x a = -a

(iii)         In integers there is no any number which is less than from the all number.

8.    For subtraction of any integer ‘b’ from ‘a’ we change the sign of ‘b’ and add it to ‘a’ as follows:

   a – b = a + (-b)

9.    To find the product of two integers with opposite signs, we find the product of their absolute values and assign negative (-) sign to the product.

10. To find the product of two positive integers or of two negative integers, we find the product of their absolute values and assign positive sign to the product.

11. If the dividend and the divisor are of same (like) sign (i.e. both positive or both negative) the quotient is always positive.

12. If the dividend and the divisor are of opposite signs, then the quotient is always negative.

13.                          (-1) positive odd integer = -1

         and          (-1) positive even integer = 1

14. In the expression aⁿ, the number a is called base and n is called exponent (power) and a x a x a x a………… n times = aⁿ i.e. n^th power of a.

15. Fundamental operations are performed according to the sequence – division, multiplication, addition, subtraction – from left to the right in order. The rule can be memorized.

16. Sequence of solving the brackets are as follow:

                     ( ), { }, [ ]

17. If there is minus sign just preceeding a pair of brackets then the signs of all the terms within the brackets are changed.

18. If there is plus sign just preceeding a pair of brackets then the brackets are removed without changing the signs of the terms inside.

19. In the expression the meaning of the operation ‘of’ is multiplication.

20. The difference of two integers may or may not be an integer.

21. The distance of an integer from 0 on the number line is called its absolute value.

22. The sum of two integers is always an integer.

23. Product of two positive or two negative integers are positive.

24. For any non zero integer a ; a ÷ a = 1

25. For any integer a, a ÷ 1 = a.

26. For any non zero integer a ; 0 ÷ a = 0.