# 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*