What is the value of $$\frac{7+21}{14+42}?$$
To solve this problem, I need to simplify the fraction by canceling out any common factors in the numerator and the denominator. I can do this by factoring both the numerator and the denominator and then dividing by any factors that appear in both. Factoring 7 and 21, I get $$\frac{7+21}{14+42}=\frac{7(1+3)}{7(2+6)}.$$ Now I can see that 7 is a common factor in both the numerator and the denominator, so I can divide both by 7 and get $$\frac{7(1+3)}{7(2+6)}=\frac{1+3}{2+6}.$$ Simplifying further, I get $$\frac{1+3}{2+6}=\frac{4}{8}.$$ Finally, I can reduce this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 4. This gives me $$\frac{4}{8}=\frac{1}{2}.$$ 