Category : 6th Class
Integers
The set of integers is denoted by I or Z.
Z ={.....,-3,-2,-1, 0,1,2,3,......}
Therefore, We Z.
(a) Every positive integer is larger than every negative integer and zero.
(b) Zero is less than every positive integer.
(c) Zero is larger than every negative integer.
(d) Zero is neither negative nor positive.
(e) Farther a number from zero on the right, larger is its value.
(f) Farther a number from zero on the left, smaller is its value.
(g) When no sign is given before a number, it is considered as a positive number.
(h) It is compulsory to write a '-' (minus) sign before a negative number.
(h) Usually, negative numbers are placed within simple brackets to avoid confusion arising due to the operator before it.
(a) Comparing numbers of different signs: A positive number is always greater than a negative number and zero.
e.g., 6 > - 12; 6 > 0 etc.
(b) Comparing two positive integers: The positive number with larger value is larger and that with the smaller value is smaller.
e.g., 73 > 57; 45 > 36 etc.,
e.g.,-6 < - 2; - 12 > -18 etc.,
Note: If a a > b then – a < - b.
eg., 8 > 5 => -8 <-5
(a) Adding a positive number to a given number is represented by moving to the right on the number line.
e.g., - 4 + 5 = 1
e.g., 3+(- 4) = 3 – 4 = - 1
(a) Addition: We know that, negative numbers are placed within simple brackets to avoid confusion arising due to the operator before it.
(i) Two positive numbers are added and a positive sign is given to the sum.
e.g., (+5) + (+2) = +7
(ii) Two negative numbers are added and a negative sign is given to the sum. e.g., (-12) + (-3) =-15
(iii) One positive and one negative number are subtracted, and the sign of the larger number is given to the difference.
e.g., (+24) + (-3) = +21; (-32) + (+8) = -24
(b) Subtraction:
(i) Two positive numbers are subtracted and the sign of the larger number is given to the difference.
e.g., (+ 3) - (+ 4) = 3 – 4 =- 1
(ii) Two negative numbers are subtracted and the sign of the larger number is given to the difference.
e.g., ( - 5) - (- 7) = - 5 + 7 = 2
(iii) One positive and one negative number are subtracted by adding them and the sign of the larger number is given to the sum.
e.g., (+12) - (- 6) =+12 + 6 = 18
(-12) - (+6) = - 12 - 6 = - 18
Note: Subtracting a number means adding its additive inverse.
(c) Subtraction on the number line:
(i) Subtracting a positive number from a number is represented by moving to the left on the number line.
e.g., -2 - (+5) = -2 - 5 = -7
(ii) Subtracting a negative number from a number is represented by moving to the right on the number line.
e.g., - 4 - (- 6) =- 4 + 6 = 2
Using BODMAS rule we simplify the numerical expressions.
() Parenthesis
{} Flower or curly brackets and
[ ] Square brackets
First we remove () then {} and lastly [ ].
You need to login to perform this action.
You will be redirected in
3 sec