Let's say we're given the mixed number: 5 and 3/12.
I'm not sure if you wanted to leave the number in mixed fraction form or as an improper fraction. If you wanted to leave it in mixed fraction form, only pay attention to the fraction, and not the whole number, which is 3/12 in this case.
So simplify this fraction, you need to find the highest factor that both numbers have in common. First, make a list of the factors of each number.
Factors for 3: 1 and 3
Factors for 12: 1, 2, 3, 4, 6, 12.
The two numbers, 3 and 12, have a factor of 3 in common. So now we must divide both numbers by that factor. 3/3 = 1, and 12/3 = 4. So our fraction now is 1/4, giving us:
5 and 1/4 as the simplified mixed fraction.
If you wanted it in improper fraction form, you'd first have to set common denominators for both 1/4 and 5.
5's denominator is already 1 (because 5 = 5/1). So now think to yourself, what number should be multiplied to the denominator of 5/1 to give 4? And that would be 4. But as a rule of fractions, if you're multiplying the denominator by a certain number, you need to multiply the numerator by that same number in order to not change the value of the fraction. (5 * 4)/(1 * 4) = 20/4. So now we have:
20/4 + 1/4
Since they now have common denominators, we can now add the numerators straight across and place it over the denominator, which is 4.
(20 + 1)/4 = 21/4 <- This would be in improper fraction form.