Fractions
Law of 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
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