Algebra

To simplify a fraction, you can find the HCF of the numerator and denominator. 

Divide both the numerator and denominator by the HCF. 

If you get a large fraction, you can find the HCF to ensure a fully simplified fraction. 

A common factor is any number that divides both numbers evenly. 

$\frac{1 + 3 + 5 + ... + 1999 + 2001 + 2003}{2 + 4 + 6 + ... + 2000 + 2002 + 2004 + 2006 + 2008 + 2010}$

Number of odd  terms in numerator   =   [2003 +1] / 2  = 1002

Sum of  1st n odd terms =  n^2

Number of  even terms in  denominator =  [2010 - 2] / 2  + 1  = 1006

Sum of 1st n even terms  = (n)(n+1)

Evaluation

1002^2 / [ 1006 * 1007]  =   502002 /  506521