Final answer:
To simplify the given complex fraction, we must convert the mixed numbers to improper fractions, find the reciprocal of the divisor, multiply, and then simplify by common factors, keeping in mind how units can cancel each other out systematically when performing operations.
Step-by-step explanation:
Simplifying a Complex Fraction
To simplify the complex fraction 3 + ⅒/5 divided by 3 + ⅔/5, we start by combining the whole numbers with the fractions in both the numerator and denominator. This gives us ⅛ divided by ⅞. Next, we convert these mixed numbers to improper fractions to get ⅟/5 divided by ⅟/5. When dividing fractions, we multiply by the reciprocal of the divisor, so we multiply ⅟/5 by 5/⅟. After multiplying the numerators together and dividing by the denominators, we simplify by any common factors. If the simplification yields a whole number or another fraction, that will be our answer. It's important to note that units like those in the example 5/1 - 2.75/1 cm can cancel out properly, leaving only the desired units in the answer.
In adding fractions, we need to find a common denominator to combine them correctly. For instance, in the case of adding ½ and 1/3, we find the common denominator to be 6, hence they become ⅔/6 and 2/6, and we can then add the numerators directly.