Final answer:
In adding or subtracting fractions, denominators cannot be added or subtracted; they must be common before combining the numerators. A fraction with equal numerator and denominator equals 1. The common denominator is found through multiplication, keeping equilibrium in an algebraic expression.
Step-by-step explanation:
When working with fractions, the addition or subtraction only involves the numerators, provided that the fractions have the same denominator. One cannot add or subtract denominators because they represent the parts that make up the whole. Therefore, the procedure for adding fractions like 1/2 and 1/3 involves finding a common denominator, which is often done by multiplying the denominators together, in this case resulting in 6. We then adjust the numerators correspondingly, turning 1/2 into 3/6 and 1/3 into 2/6, allowing for the addition of the numerators, resulting in 5/6. This process ensures that the resulting fraction represents the correct sum of the parts.
Any fraction with the same numerator and denominator equals 1, because the numerator and denominator cancel each other out. This principle is crucial in maintaining the equality in an algebraic expression when we perform the same operation on both sides of the equals sign. For example, multiplying both numerator and denominator by the same number does not change the value of the fraction.
In other contexts such as in chemistry, when calculating the equilibrium constant, products are placed in the numerator and reactants in the denominator, with their concentrations raised to the power of their coefficients from the balanced chemical equation. This does not relate directly to adding or subtracting denominators but demonstrates another concept where the numerator and denominator play specific roles.