Fractions

Fractions consist of two basic parts:

• denominator - or bottom number
• numerator - or the top number

Fraction:

a / b                      (1)

where

a = numerator

b = denominator

• proper fraction - the nominator smaller than the denominator 
• improper fraction - the nominator larger than the denominator
• reducible fraction - is a fraction that can be reduced to lower terms
• least common denominator - the smallest denominator value divisible
• mixed number - a combination of a whle number and a fraction

Laws of Fractions

(a / b) + (c / d) = (a d + b c) / (b d)                    (2)

(a / b) (c / d) = (a c) / (b d)                             (3)

(a / b) / (c / d) = (a / b) (d / c)                             (4)

(- a / b) = - (a / b) = a / (- b)                            (5)

((a / b) + (c / d)) / ((e / f) + ( g / h))

      = (((a / b) + (c / d)) / ((e / f) + (g / h))) ((b d f h) / (b d f h))

      = (((a d) + (b c)) f h) / (((e h) + (f g)) b d)                   (6)

Adding Fractions - Example

(1 / 4) + (3 / 16) + (7 / 8)

= (4 / 4) (1 / 4) + (3 / 16) + (2 / 2) (7 / 8)

= (4 / 16) + (3 / 16) + (14 / 16)

= (4 + 3 + 14) / 16

= 21 / 16

Multiplying Fractions - Example

(3 / 4) (9 / 16)

= ((3) (9)) / ((4) (16))

= 27 / 64

Dividing Fractions - Example

(3 / 4) / (9 / 16)

= ((3) (16)) / ((4) (9))

= 48 / 36