chapt 1.1 - numbers

Question 1

what are irrational numbers ?

Answer 1

cannot be expressed as a form of a/b (fractions) where b ≠ 0

e.g; root 2 , π

Question 2

what are rational numbers ?

Answer 2

includes integers (whole numbers) and fractions

e.g; 22/7

Question 3

what are prime factors ?

Answer 3

numbers that can only be divided by 1 and the number itself

e.g; 2 , 3 , 5 , 7 , 11 ….

Question 4

what is HCF and LCM ?

Answer 4

HCF: Highest Common Factor
- in the index notation , use the smaller numbers

LCM: Lowest Common Multiple
- in the index notation , use the bigger numbers

Question 5

what is anthr way of writing square root a ?

Answer 5

a^(1/2)

Question 6

what is the reciprocal of x ?

e.g ; reciprocal of 2y = 1/2y

Answer 6

reciprocal of x = 1/x

Question 7

arithmetic laws

Answer 7

1) commutative laws
; a + b = b + a
; a x b = b x a

2) associative laws
; (p + q) + r = p + (q + r)
; (p x q) x r = p x (q x r)

3) distributive laws
; p x (q + r) = (p x q) + (p x r)

4)
; + + = +
; + - = -
; - - = +

Question 8

indices laws

Answer 8

1) a^m x a^n = a^m+n
2) a^m ÷ a^n = a^m-n
3) (a^m)^n = a^mn
4) a^n x b^n = (a x b)^n
5) a^n ÷ b^n = (a/b)^n
6) a^0 = 1
7) a^-n = 1/a^n

8) fractional indices
; a^1/n = n root a
; a^m/n = n root a^m = (n root a)^m