Unit fractions and mixed numbers

A fraction can be broken into smaller fractions in many ways, as long as the parts keep the same denominator. For 5/6, the unit fractions give 1/6 + 1/6 + 1/6 + 1/6 + 1/6. We can also join some of them: 5/6 = 1/6 + 4/6 = 2/6 + 3/6. When fractions have the same denominator we add the numerators and keep the denominator: 2/6 + 3/6 = 5/6, because 2 sixths and 3 sixths make 5 sixths. The size of the pieces does not change, we only count them. Even a whole can be broken: 1 = 6/6 = 1/6 + 5/6. To check a break-up, add the numerators and see if they give the original numerator.