Final answer:
To simplify a complex fraction, multiply the numerators and denominators if it's a multiplication of fractions, or find a common denominator for addition or subtraction. Reduce the result to its simplest form by canceling out common factors.
Step-by-step explanation:
To simplify a complex fraction, you can either find a common denominator or simplify each fraction individually and then perform the required operation. For example, if you have a fraction like 1/2 (one-half) of another fraction like 2/3 (two-thirds), you would multiply the numerators and the denominators. This particular example would result in 1×2 in the numerator and 2×3 in the denominator, simplifying to 2/6, which can be further reduced to 1/3. Similarly, if you are adding fractions like 1/2 and 1/3, you would find a common denominator, which in this case is 6, and re-express the fractions as 3/6 and 2/6 respectively, and then add them to get 5/6.
Understanding the process of combining fractions requires a good sense of how fractions work and relate to each other, such as knowing that three thirds is a whole or that 1/4 (one quarter) is half of 1/2 (one-half). Remember, always look to reduce fractions to their simplest form, as in the case where 30/120 reduces to 1/4 after common factors are canceled out.